real-statistics.com | Top Sites

Document
llms.txt

Generated by All in One SEO v4.9.6.2, this is an llms.txt file, used by LLMs to index the site.

# Real Statistics Using Excel

Everything you need to perform real statistical analysis using Excel

## Sitemaps

- [XML Sitemap](https://real-statistics.com/sitemap.xml): Contains all public & indexable URLs for this website.

## Posts

- [Blogs](https://real-statistics.com/blogs/)
- [Real Statistics Release 9.8](https://real-statistics.com/real-statistics-release-9-8/) - Describes the features in the latest release of the Real Statistics Resource Pack, Rel 9.8, a free statistical analysis tool for Excel environments.
- [Real Statistics Release 7.0](https://real-statistics.com/real-statistics-release-7-0/) - Describes the new features of the latest release of the Real Statistics software, which expands the statistical analysis capabilities of Excel
- [Real Statistics Release 6.8](https://real-statistics.com/real-statistics-release-6-8/) - Describes the new features of the latest release of the Real Statistics software, which expands the statistical analysis capabilities of Excel
- [Real Statistics Release 6.7](https://real-statistics.com/real-statistics-release-6-7/) - Describes the new features in the Real Statistics Resource Pack, a free Excel add-in for statistical analysis. Includes Permutation MANOVA and trinomial test.
- [Real Statistics Release 6.6](https://real-statistics.com/real-statistics-release-6-6/) - Describes the new features in the latest release of the Real Statistics software, an Excel add-in to perform statistical analysis
- [Real Statistics Release 6.5](https://real-statistics.com/real-statistics-release-6-5/) - Describes the latest release of the Real Statistics Resource Pack, an Excel add-in that provides a great variety of statistical analysis capabilities
- [Real Statistics Release 6.4](https://real-statistics.com/real-statistics-release-6-4/)
- [Real Statistics Release 5.11](https://real-statistics.com/real-statistics-release-5-11/) - Describes the features in the latest release of the Real Statistics free statistical analysis add-in to Excel 2007 and 2011
- [Real Statistics Release 6.2](https://real-statistics.com/real-statistics-release-6-2/) - Describes the new capabilities in the Real Statistics Resource Pack, a free Excel add-in for statistical analysis
- [Real Statistics Release 6.3](https://real-statistics.com/real-statistics-release-6-3/) - Describes new features and bug fixes in Real Statistics Release 6.3.
- [Real Statistics Release 6.1](https://real-statistics.com/real-statistics-release-6-1/) - Describes the features in the latest release of the Real Statistics free statistical analysis add-in to Excel.
- [Real Statistics Release 5.4](https://real-statistics.com/real-statistics-release-5-4/)
- [Real Statistics Release 9.7.6](https://real-statistics.com/real-statistics-release-9-7-6/) - Announces Real Statistics Rel 9.7.6. This release corrects the errors that were inadvertantly included in Real Statistics Rel 9.7.5.
- [Real Statistics Release 9.7.5](https://real-statistics.com/real-statistics-release-9-7-5/) - Describes the features of the latest release of the Real Statistics Resource Pack, Rel 9.7.5. This release provides some new fetaures and bug fixes.
- [Real Statistics Release 9.7](https://real-statistics.com/real-statistics-release-9-7/) - Describes the new capabilities in Real Statistics Rel 9.7. Includes Partial Least Squares (PLS) Regression, Multivariate Regression, Bootstrapping in Regression
- [Real Statistics Release 8.0](https://real-statistics.com/real-statistics-release-8-0/) - Describes the new features in Rel 8.0 of the Real Statistics statistical analysis add-in to Excel. Incl. panel, repeated measures ANOVA, Lambda-like features.
- [Real Statistics Release 9.6.1](https://real-statistics.com/real-statistics-release-9-6-1/) - Describes the new capabilities provided in the latest release, Rel 9.6.1, of the popular, free Real Statistics statistical analysis add-in to Excel.
- [Real Statistics Release 9.6](https://real-statistics.com/real-statistics-release-9-6/) - Describes the new capabilities provided in the latest release, Rel 9.6, of the popular, free Real Statistics statistical analysis add-in to Excel.
- [Real Statistics Release 9.5.5](https://real-statistics.com/real-statistics-release-9-5-5/) - Describes the new features in Rel 9.5.5 of the Real Statistics statistical analysis add-in to Excel. Focus is on new Bayesian support and differential equations
- [Real Statistics Release 9.5](https://real-statistics.com/real-statistics-release-9-5/) - Describes new features of Real Statistics which provides additional statistical analysis capabilities in Excel. The focus of this release is Bayesian statistic.
- [Real Statistics Rel 9.4.5](https://real-statistics.com/real-statistics-rel-9-4-5/) - Describes the new features provided by the latest release of the Real Statistics free statistical analysis add-in to Excel.
- [Real Statistics Rel 9.4](https://real-statistics.com/real-statistics-rel-9-4/) - Describes the features of the latest release of the Real Statistics statistical add/in to Excel. Includes propensity score matching and coarsened exact matching
- [Real Statistics Resource Pack Release 9.3](https://real-statistics.com/real-statistics-resource-pack-release-9-3/) - Provides a description of the new features of Release 9.3 of the Real Statistics add-in to Excel for statistical analysis. Includes GMM.
- [Real Statistics Release 7.6](https://real-statistics.com/real-statistics-release-7-6/) - Describes Release 7.6 of the Real Statistics software, Includes minimum spanning tree, network graphs and improved bivariate normal distribution support.
- [Real Statistics Release 9.2.2](https://real-statistics.com/real-statistics-release-9-2-2/) - Describes the new bug-fix release for the Real Statistics Resource Pack, Release 9.2.2. Only change is for Gwet's AC2 and Krippendorff's alpha.
- [Real Statistics Release 9.2.1](https://real-statistics.com/real-statistics-release-9-2-1/) - Describes the new features in the latest release of the Real Statistics Resource Pack, Rel 9.2.1, as well as the various bug fixes.
- [Real Statistics Release 9.2](https://real-statistics.com/real-statistics-release-9-2/) - Describes the new features in the latest release, Rel 9.2, of the Real Statistics statistical analysis add-in to Excel. Includes Tobit regression.
- [Real Statistics Release 9.1.1](https://real-statistics.com/real-statistics-release-9-1-1/) - Describes the bugs that have been fixed in the latest release of the Real Statistics statistical add-in to Excel. Also includes a new lambda feature.
- [Real Statistics Release 9.1](https://real-statistics.com/real-statistics-release-9-1/) - Describes the features in the latest release of the Real Statistics statistical add-in to Excel, Release 9.1. Includes Brunner-Munzel test and Taguchi DOE.
- [Real Statistics Rel 9.0 for Mac](https://real-statistics.com/real-statistics-rel-9-0-for-mac/) - Announcing Release 9.0 of the Real Statistics Resource Pack for Mac users. See the previous blog for a complete description of the release.
- [Real Statistics Release 9.0](https://real-statistics.com/real-statistics-release-9-0/) - Describes the new features in the latest release of the Real Statistics Resource Pack, namely Rel 9.0. This release adds Neural Network support
- [Real Statistics Release 8.4](https://real-statistics.com/real-statistics-release-8-4/)
- [Real Statistics Release 8.3](https://real-statistics.com/real-statistics-release-8-3/)
- [Real Statistics Release 8.1.5](https://real-statistics.com/real-statistics-release-8-1-5/) - Describes the new features provided by the latest release of the Real Statistics Resource Pack, software that augments Excel's statistical analysis capabilities
- [Real Statistics Release 8.2](https://real-statistics.com/real-statistics-release-8-2/) - Describes the new features in Rel 8.2 of the Real Statistics Resource Pack. These calculate a winning strategy for Wordle and enhance the Anderson-Darling test.
- [How to win at Wordle](https://real-statistics.com/how-to-win-at-wordle/) - Describes a strategy for how to choose your guesses to maximize your chances of finding Wordle's target word in at most 3 guesses. Includes Excel support.
- [Real Statistics Release 8.3.1](https://real-statistics.com/real-statistics-release-8-3-1/) - Announces the latest bug-fix release of the Real Statistics Resource Pack, Rel 8.3.1,an Excel add-in for statistical analysis.
- [Update for Mac Users](https://real-statistics.com/update-for-mac-users/) - Describes upcoming new support for Mac users.
- [Real Statistics Release 5.7](https://real-statistics.com/release-5-7/) - Describes the new features in the latest release of the Real Statistics software, which provides a robust range of statistical analysis capabilities in Excel.
- [Real Statistics Release 5.6](https://real-statistics.com/real-statistics-release-5-6/) - Describes the new features in the Real Statistics Resource Pack Release 5.6, including support for analyses where there is missing data using the EM algorithm, Dot Plots and Cochrane-Orcutt regression.
- [Real Statistics Release 5.1](https://real-statistics.com/real-statistics-release-5-1/) - Describes the new features in Release 5.1 of the Real Statistics Resource Pack, a free statistical analysis addin for Excel.
- [Release 5.0](https://real-statistics.com/release-5-0/) - Describes the new features in Release 5.0 of the Real Statistics Resource Pack.
- [Real Statistics Release 7.3](https://real-statistics.com/real-statistics-release-7-3/) - Describes the features in the latest Real Statistics software release. Incl. simulated exact chi-square test, Rasch polytomous analysis, MSSD, Kronecker product
- [Real Statistics Release 7.1](https://real-statistics.com/real-statistics-release-7-1/) - Describes the new features & bug-fixes in the latest Real Statistics release. Real Statistics is a software package that performs statistical analysis in Excel
- [Real Statistics Release 7.2](https://real-statistics.com/real-statistics-release-7-2/) - Describes the new features in the latest release of the Real Statistics software package which provides statistical analysis capabilities in Excel.
- [Real Statistics Release 5.9](https://real-statistics.com/real-statistics-release-5-9/)
- [Real Statistics Rel 4.12](https://real-statistics.com/real-statistics-rel-4-12/) - Describes the new features in Release 4.12 of the Real Statistics Resource Pack, a popular Excel addin for doing statistical analysis.
- [Real Statistics Release 5.3](https://real-statistics.com/real-statistics-release-5-3/) - Describes the features in the latest release of the Real Statistics Resource Pack, including Ridge regression and LASSO regression
- [Real Statistics Release 5.8](https://real-statistics.com/real-statistics-release-5-8/) - Describes the new features of Release 5.8 of the Real Statistics Resource Pack, an Excel addin that provides a variety of statistical analysis capabilities
- [Real Statistics Release 6.0](https://real-statistics.com/real-statistics-release-6/) - Describes the features in the latest release, Rel 6.0, of the Real Statistics statistical analysis software. This is free software that works in Excel.
- [Release 5.0 for Mac](https://real-statistics.com/release-5-0-for-mac/) - Describes the latest release (5.0) of the Real Statistics Resource Pack for Mac computers
- [Changes to Website](https://real-statistics.com/changes-to-website/) - New theme for Real Statistics. Seeking comments and suggestions.|
- [Real Statistics Release 7.5](https://real-statistics.com/real-statistics-release-7-5/) - Describes the latest release of the Real Statistics statistical analysis software for Excel users. Focus is eigenvalues/vectors and Lp-based cluster analysis
- [Real Statistics Release 7.4](https://real-statistics.com/real-statistics-release-7-4/) - Describes the features of the latest Real Statistics release, including bounded linear regression and the Cochran-Armitage test.
- [Real Statistics Release 7.7](https://real-statistics.com/real-statistics-release-7-7/) - Describes Release 7.7 of the Real Statistics software, Includes ordinal regression, improved binary logistic and Probit regression and a new version of ANCOVA.
- [Real Statistics Release 7.8](https://real-statistics.com/real-statistics-release-7-8/) - Describes the new capabilities and bug fixes in the latest release of the Real Statistics Resource Pack that enhances statistical analysis support in Excel.
- [Real Statistics Release 7.9](https://real-statistics.com/real-statistics-release-7-9/) - Describes the new features in the latest release of the Real Statistics Resource Pack, Rel 7.9, an Excel-based platform for statistical analysis,
- [Real Statistics Release 7.10](https://real-statistics.com/real-statistics-release-7-10/) - Describes the new capabilities (rooting finding, GEV distribution, etc.) provided in the latest release, Rel 7.10, of the Real Statistics Resource Pack.
- [Real Statistics Release 8.1](https://real-statistics.com/real-statistics-release-8-1/) - Describes the new features in the latest release, Rel 8.1, of the free Real Statistics statistical software package, designed to work with Excel.
- [Real Statistics Release 8.8](https://real-statistics.com/real-statistics-release-8-8/) - Describes the new features in the latest release of the Real Statistics Resource Pack, an Excel add-in for statistical analysis
- [Real Statistics Release 8.7](https://real-statistics.com/real-statistics-release-8-7/) - Describes the new features in the latest release of the Real Statistics Resource Pack, an Excel add-in for statistical analysis
- [Real Statistics Release 8.9](https://real-statistics.com/real-statistics-release-8-9/) - Describes the new capabilities in the latest release, Rel 8.9, of the Real Statistics Resource Pack, an Excel add-in for statistical analysis
- [Real Statistics Release 8.8.1](https://real-statistics.com/real-statistics-release-8-8-1/) - Describes the new features in the latest release of the Real Statistics Resource Pack, Rel 8.8.1, as well as the latest bug fixes.
- [Real Statistics Release 8.8.2](https://real-statistics.com/real-statistics-release-8-8-2/) - Describes the new features of the latest release of the Real Statistics software, Release 8.8.2. This release contains bug fixes and O'Brien's test support.
- [Real Statistics Release 8.5](https://real-statistics.com/real-statistics-release-8-5/) - Describes the new features in Rel 8.5 of the Real Statistics Resource Pack, an Excel add-in that enhances the statistical analysis capabilities of Excel
- [Real Statistics Release 8.6.3](https://real-statistics.com/real-statistics-release-8-6-3/) - Describes the latest bug fix release of the Real Statistics Resource Pack, an add-in to Excel that performs enhanced statistical analyses.
- [Real Statistics Release 8.6](https://real-statistics.com/real-statistics-release-8-6/) - Describes the new features in Rel 8. of the Real Statistics Resource Pack, an Excel add-in that enhances the statistical analysis capabilities of Excel
- [Real Statistics Release 8.6.1](https://real-statistics.com/real-statistics-release-8-6-1/) - Describes the latest bug-fix release of the Real Statistics Resource Pack, Rel 8.6., a free statistical analysis add-in to Excel.
- [Real Statistics Release 8.9.1](https://real-statistics.com/real-statistics-release-8-9-1/) - Describes the bug fixes and new capabilities in the latest release, Rel 8.9.1, of the Real Statistics Resource Pack, an Excel add-in for statistical analysis.
- [Release 8.2.1](https://real-statistics.com/release-8-2-1/) - Describes the latest release, Rel 8.2.1, of the Real Statistics Resource Pack, an Excel add-in that supports a variety of statistical analysis capabilities.
- [Real Statistics Release 8.1.6](https://real-statistics.com/real-statistics-release-8-1-6/) - Describes the bug fixes in Release 8.1.6 of the Real Statistics Resource Pack, which is an Excel add-in providing advanced statistical analysis capabilities.
- [Note about Rel 8.0](https://real-statistics.com/note-about-rel-8-0/)
- [Note about Rel 7.10](https://real-statistics.com/note-about-rel-7-10/) - Update about the status of Real Statistics Rel 7.10. Also, includes a correction about support for the Harrell-Davis version of the MAD.
- [Real Statistics Release 7.7.2](https://real-statistics.com/real-statistics-release-7-7-2/) - Describes the features in the latest bu-release version of the Real Statistics Resource Pack. This release also includes a few new functions.
- [Release 7.6.1](https://real-statistics.com/release-7-6-1/) - Real Statistics Rel 7.6.1 is a bug-fix release. Includes fixes to Two-Factor MANOVA, HC4 errors for Robust Regression and distance values for Friedman-Rafsky.
- [Release 7.3.3](https://real-statistics.com/release-7-3-3/)
- [Real Statistics Release 7.0.5](https://real-statistics.com/real-statistics-release-7-0-5/)
- [Real Statistics Release 7.0.2](https://real-statistics.com/release-7-0-2/) - Describes the latest bug-fix release
- [Real Statistics Release 7.0.1](https://real-statistics.com/real-statistics-release-7-0-1/) - Bug-fix release. Fixes a bug in a sort routine used by a number of Real Statistics functions. Also, fixes a bug in the Regression data analysis tool for Mac.
- [Real Statistics Release 6.6.2](https://real-statistics.com/real-statistics-release-6-6-2/) - Describes the changes introduced in Rel 6.6.2 of the Real Statistics Resource Pack.
- [Problems introduced by latest Excel 365 release](https://real-statistics.com/problems-latest-version-excel-365/)
- [Bug Fix Release 6.2.1](https://real-statistics.com/bug-fix-release-rel-6-2-1/) - Announces a bug-fix release for Windows users. Not required for Mac users.
- [Bug Fix Release 6.2.2](https://real-statistics.com/bug-fix-release-6-2-2/) - Fixes a bug in the COV2Pooled function
- [Real Statistics Rel 6.2 for Mac](https://real-statistics.com/real-statistics-rel-6-2-for-mac/) - Announces that the latest release of the Real Statistics software is now available for Mac users
- [Compile Error in Hidden Module](https://real-statistics.com/compile-error-in-hidden-module/) - Describe how to deal with the error message "Compile error in hidden module …"
- [Real Statistics Release 5.10.1](https://real-statistics.com/real-statistics-release-5-10-1/) - Describes the latest Real Statistics release for Excel 2007 and Excel 2011 users.
- [Real Statistics Release 6.0.4](https://real-statistics.com/real-statistics-release-6-0-4/) - Describes the changes in Real Statistics Release 6.0.4
- [Real Statistics Release 5.10](https://real-statistics.com/release-5-10/) - Describes the new release of the Real Statistics Resource Pack for Excel 2007 and 2011 users. This release contains a subset of Rel 6.0.2 capabilities.
- [Bug Fix Release 6.0.2](https://real-statistics.com/bug-fix-release-6-0-2/) - Fixes a bug related to the chi square distribution
- [Bug Fix Release 6.0.1](https://real-statistics.com/bug-fix-release-6-0-1/) - Fixes a serious bug
- [Real Statistics Rel 5.9.2 for Mac](https://real-statistics.com/real-statistics-rel-5-9-2-mac/) - This release fixes an error in the T Test and Non-parametric Equivalents data analysis tool.
- [Real Statistics Rel 5.9.1 for Mac](https://real-statistics.com/real-statistics-rel-5-9-1-for-mac/) - Describes the latest release of the Real Statistics Resource Pack for the Mac.
- [Error in MWDIST Function](https://real-statistics.com/error-mwdist-function/) - Reports on a bug in the MWDIST function and how to correct it
- [Release 5.7 for Mac](https://real-statistics.com/release-5-7-for-mac/) - Announces new release, Release 5.7, is now available for the Mac (Excel 2011 and Excel 2016)
- [Real Statistics Release 5.5](https://real-statistics.com/real-statistics-release-5-5/) - Describes all the new features in the latest release of the Real Statistics Resource Pack. Especially useful are confidence intervals for effect size and power, Jonckheere–Terpstre Test, Breusch-Godfrey Test and Newey-West
- [Release 5.4.2](https://real-statistics.com/release-5-4-2/) - Describes a minor release consisting of two bug fixes.
- [Release 5.4.1](https://real-statistics.com/release-5-4-1/)
- [Release 5.3.2](https://real-statistics.com/release-5-3-2/)
- [Release 5.3.1](https://real-statistics.com/release-5-3-1/) - Describes the latest release to the Real Statistics Resource Pack
- [Release 5.3 for Mac Users](https://real-statistics.com/release-5-3-for-mac-users/) - Announces that Release 5.3 of the Real Statistics Resource pack is now available for Mac users of Excel 2011 and Excel 2016
- [Release 5.2](https://real-statistics.com/release-5-2/) - Provides a description of the new capabilities in Release 5.2 of the Real Statistics Resource Pack, esp. including enhanced Arima features
- [More about Release 5.1](https://real-statistics.com/more-about-release-5-1/) - Describes one new feature in Release 5.1, namely follow up testing after Three Factor ANOVA and provides a quick update on the release.
- [Release 4.14](https://real-statistics.com/release-4-14/) - Describes the new features of the Real Statistics Resource Pack, an Excel addin for statistics analysis.
- [Release 4.13](https://real-statistics.com/release-4-13/) - Describes the new features in the latest release (Rel 4.13) of the Real Statistics addin to Excel
- [Real Statistics with 64 bit Excel](https://real-statistics.com/real-statistics-with-64-bit-excel/)
- [Access via Quick Access Toolbar or Ribbon](https://real-statistics.com/quick-access-toolbar-ribbon/) - Update on how to access the Real Statistics data analysis tools using the Quick Access Toolbar or via an existing Ribbon
- [Release 3.7 of the Real Statistics Resource Pack](https://real-statistics.com/release-3-7-real-statistics-resource-pack/) - Describes the new features in the Real Statistics Resource Pack for performing statistical analysis in Excel
- [Real Statistics Rel 4.11](https://real-statistics.com/real-statistics-rel-4-11/) - Describes the new features in the latest release of the Real Statistics free addin for doing statistical analysis in Excel
- [Real Statistics Rel 4.10](https://real-statistics.com/23379-2/) - Describes the features in the latest release of the Real Statistics Resource Pack, a free Excel addin for statistical analysis.
- [Real Statistics disappears from Addin ribbon](https://real-statistics.com/real-statistics-disappears-from-addin-ribbon/) - Describes how to solve the case where the Real Statistics add-in disappears from the Add-in ribbon.
- [Real Statistics Release 4.9](https://real-statistics.com/real-statistics-release-4-9/) - Describes the new features of the Real Statistics Resource Pack, an Excel add-in for statistical analysis.
- [Quick Update 26 May 2016](https://real-statistics.com/quick-update-26-may-2016/)
- [Real Statistics Release 4.8](https://real-statistics.com/release-4-8/) - Describes the new features in Rel 4.8 of the Real Statistics Resource Pack, free Excel add-in for statistical analysis. Incl. Box-Cox, Mardia Test, Shapely-Owen
- [Release 4.7](https://real-statistics.com/release-4-7/) - Describes the features of Release 4.7 of the Real Statistics Resource Pack, which provides a variety of statistical analysis capabilities in Excel
- [Rel 4.6 Installation](https://real-statistics.com/rel-4-6-installation/) - Describes how to install Release 4.6 of the Real Statistics Resource Pack
- [Important Information about Rel 4.6](https://real-statistics.com/important-information-about-rel-4-6/) - Explains that you must make sure that Solver is loaded in order to use the latest release of the Real Statistics Resource Pack.
- [Release 4.6 Announcement](https://real-statistics.com/release-4-6-announcement/) - Describes the new features in the latest release of the Real Statistics add-in.
- [Release 4.5 Announcement](https://real-statistics.com/release-4-5-announcement/) - Describes the latest release of the Real Statistics add-in to perform statistical analysis in Excel. Includes d'Agostino-Pearson test and Bland-Altman.
- [Suggestion for Excel 2007 Users](https://real-statistics.com/suggestion-for-excel-2007-users/) - Suggestion for Excel 2007 Users regarding installation of Real Statistics
- [Bug Fix Release 4.4.3](https://real-statistics.com/bug-fix-release-4-4-3/)
- [Real Statistics Release 4.4.2](https://real-statistics.com/real-statistics-release-4-4-2/) - Describes the bug fixes in the Real Statistics Resource Pack Rel 4.4.2.
- [Real Statistics Release 4.4](https://real-statistics.com/real-statistics-release-4-4/) - Describes the latest release of the Real Statistics Resource Pack, an Excel add-in for statistical analysis. Includes robust standard errors and Gage R&R.
- [Website Changes](https://real-statistics.com/website-changes/) - Describes some minor changes to the menus on the Real Statistics website.
- [Release 4.3 of Real Statistics Resource Pack](https://real-statistics.com/release-4-3-real-statistics-resource-pack/) - Description of the latest release of the Real Statistics software, a free Excel add-in for statistical analysis. Focus is on survival analysis.
- [Interpolation Changes](https://real-statistics.com/interpolation-changes/) - Describes the addition of harmonic interpolation to various table lookup functions
- [Release 4.2 of Real Statistics Resource Pack](https://real-statistics.com/release-4-2-of-real-statistics-resource-pack/) - Description of the latest release of the Real Statistics Resource Pack, an Excel add-in for software analysis.
- [Bug Fix Release 4.1.1 Real Statistics Resource Pack](https://real-statistics.com/bug-fix-release-4-1-1-real-statistics-resource-pack/) - New release to fix a bug in the SRANK_TEST function
- [Release 4.1 of Real Statistics Resource Pack](https://real-statistics.com/release-4-1-real-statistics-resource-pack/) - Describes latest release of the Real Statistics Resource Pack, an Excel add-in for statistical analysis, incl. Fligner Killeen and Jarque-Barre tests.
- [Release 4.0 of Real Statistics Resource Pack](https://real-statistics.com/release-4-real-statistics-resource-pack/) - Describes the latest release of the Real Statistics Resource Pack, including cluster analysis, exponential regression, multivariate logistic regression.
- [Disappearing Add-Ins Ribbon](https://real-statistics.com/disappearing-add-ins-ribbon/) - Describes what causes the disappearance of the Real Statistics software option form the Add-Ins ribbon and what to do about it.
- [Release 3.8.1 of the Real Statistics Resource Pack](https://real-statistics.com/release-3-8-1-of-the-real-statistics-resource-pack/) - Announces the availability of Release 3.8.1 of the Real Statistics Resource Pack for Excel 2007 and 2010 environments.
- [Release 3.8 of the Real Statistics Resource Pack](https://real-statistics.com/release-3-8-real-statistics-resource-pack/) - Describes features in latest release of the free Real Statistics software, incl. nonlinear exponential regression and confidence intervals for weighted kappa.
- [Announcing Release 3.5.3 for Macintosh](https://real-statistics.com/announcing-release-3-5-3-for-macintosh/) - Describes the features in the latest release of Real Statistics software for Macintosh.
- [Bug Fix Release 3.6.2](https://real-statistics.com/bug-fix-release-3-6-2/) - Describes the latest release of the Real Statistics Resource Pack. Includes a fix to the hidden dialog box problem.
- [Bug Fix Release 3.6.1](https://real-statistics.com/bug-fix-release-3-6-1/) - Describes the bug fixes in Release 3.6.1 of the Real Statistics Resource Pack.
- [Release 3.6 of the Real Statistics Resource Pack](https://real-statistics.com/release-3-6-real-statistics-resource-pack/) - Describes the new features in Release 3.6 of the Real Statistics Resource Pack. Includes statistical power and sample size requirements for Cronbach's Alpha.
- [Quick Update 18 Jan 2015](https://real-statistics.com/quick-update-18-jan-2015/) - Describes two bug fixes to the Real Statistics Resource pack
- [Release 3.5 of the Real Statistics Resource Pack](https://real-statistics.com/release-3-5-real-statistics-resource-pack/) - Describes the new features in the latest release of the Real Statistics Resource Pack, an Excel addin used for statistical analysis.
- [Release 3.4 of the Real Statistics Resource Pack](https://real-statistics.com/release-3-4-real-statistics-resource-pack/) - Describes the new features available with Release 3.4 of the Real Statistics Resource Pack.
- [Quick Update 11 Dec 2014](https://real-statistics.com/quick-update-11-dec-2014/)
- [Release 3.3 of the Real Statistics Resource Pack](https://real-statistics.com/release-3-3-real-statistics-resource-pack/) - Describes the latest release (Rel 3.3) of the Real Statistics Resource Pack, a free statistical analysis package for use in Excel.
- [Quick Update 24 Nov 2014](https://real-statistics.com/quick-update-24-nov-2014/) - Describes changes to the website, examples workbooks and software, including new Real Statistics Resource Pack Release 3.2.2
- [Release 3.2 of the Real Statistics Resource Pack](https://real-statistics.com/release-3-2-real-statistics-software/) - Describes the new capabilities in the Real Statistics Resource Pack for doing statistical analysis in Excel. Features new ANOVA and MANOVA support.
- [Quick Update for Mac Users](https://real-statistics.com/quick-update-for-mac-users/) - Describes improvements to the Real Statistics Resource Pack for Mac users.
- [New Real Statistics Release for Mac Users](https://real-statistics.com/new-real-statistics-release-for-mac-users/) - Announces the latest release of the Real Statistics Resource Pack for Macintosh users. This resource pack provides a wealth of statistics capabilities from within Excel
- [Quick Update 1 October 2014](https://real-statistics.com/quick-update-1-october-2014/) - Describes the latest bu fixes for the Real Statistics Resource Pack.
- [Release 3.1 of the Real Statistics Resource Pack](https://real-statistics.com/release-3-1-real-statistics-resource-pack/) - Describes the latest enhancements to the Real Statistics Resource Pack, free statistics add-in for Excel.
- [Announcing Release 3.0 of the Real Statistics Resource Pack](https://real-statistics.com/release-3-0-real-statistics-resource-pack/) - Describes the new features of the Real Statistics Resource Pack
- [Release 2.17.1 Announcement](https://real-statistics.com/release-2-17-1-announcement/)
- [Quick Update 4 Sept 2014](https://real-statistics.com/quick-update-4-sept-2014/)
- [Release 2.17 of the Real Statistics Resource Pack](https://real-statistics.com/release-2-17-of-the-real-statistics-resource-pack/) - Describes new features in the Real Statistics add-in software, especially new inverse functions and statistical power functions.
- [Bug Fix Release 2.16.1](https://real-statistics.com/bug-fix-release-2-16-1/)
- [Release 2.16 of the Real Statistics Resource Pack](https://real-statistics.com/release-2-16-real-statistics-resource-pack/) - Describes the new functions in the latest release of the Real Statistics Resource Pack, an Excel statistics add-in.
- [Quick Update 26 June 2014](https://real-statistics.com/quick-update-26-june-2014/) - Description of the new webpages on the Real Statistics Using Excel website.
- [Release 2.15 of the Real Statistics Resource Pack](https://real-statistics.com/release-2-15-real-statistics-resource-pack/) - Describes new features in the the Real Statistics Resource Pack Release 2.15, incl. noncentral distributions, statistical power, two-sample Kolmogorov-Smirnov.
- [Release 2.14.1 of Real Statistics Resource Pack](https://real-statistics.com/release-2-14-1-of-real-statistics-resource-pack/) - Description of the mini-release, Rel 2.14.1, of the Real Statistics Resource Pack.
- [Release 2.14 of the Real Statistics Resource Pack](https://real-statistics.com/release-2-14-of-the-real-statistics-resource-pack/) - Description of the new capabilities in the Real Statistics Resource Pack and the changes to the Worksheet Examples and website.
- [Quick Update 11 May 2014](https://real-statistics.com/quick-update-11-may-2014/) - All the updates to the website to describe the new features in Release 2.13.1 have now been made.
- [Quick Update 9 May 2014](https://real-statistics.com/quick-update-9-may-2014/)
- [Quick Update 7 May 2014](https://real-statistics.com/quick-update-7-may-2014/)
- [Release 2.13 of the Real Statistics Resource Pack](https://real-statistics.com/release-2-13-real-statistics-resource-pack/) - Describes the latest release of the Real Statistics Resource Pack, featuring multiple imputation (MI via FCS) and full information maximum log-likelihood (FIML)
- [Release 2.12 of the Real Statistics Resource Pack](https://real-statistics.com/release-2-12-real-statistics-resource-pack/) - Describes the latest version of the Real Statistics add-in software. It adds new features and modifies existing capabilities to better deal with missing data.
- [Release 2.11 of the Real Statistics Resource Pack](https://real-statistics.com/release-2-11-real-statistics-resource-pack/) - Describes the features of the latest release of the Real Statistics Resource Pack for use with Windows and Mac versions of Excel
- [Quick Update 17 March 2014](https://real-statistics.com/quick-update-17-march-2014/) - Update on the latest capabilities on the Real Statistics website.
- [Quick Update 14 March 2014](https://real-statistics.com/quick-update-14-march-2014/) - Release 2.11 is now available on Excel 2007. The webpages in the Tools menu have now been updated to support Release 2.11.
- [Quick Update 6 March 2014](https://real-statistics.com/quick-update-6-march-2014/) - Describes some changes to the website, especially regarding the partial correlation coefficient and Studentized q distribution.
- [Quick Update 17 February 2014](https://real-statistics.com/quick-update-17-february-2014/) - Describes improved statistical support for Excel 2011 on the Macintosh.
- [Quick Update 6 February 2014](https://real-statistics.com/quick-update-6-february-2014/) - Description of new or updated webpages: Fleiss' Kappa, Runs, Binomial Distribution and Random Walks
- [Quick Update 31 Jan 2014](https://real-statistics.com/quick-update-jan-201/) - Update about the new beta version of the Real Statistics Resource Pack for Mac
- [Release 2.10 of the Real Statistics Resource Pack](https://real-statistics.com/release-2-10-real-statistics-resource-pack/) - Describe new features in the Real Statistics Resource Pack: an expanded ICC function and new functions for comparing slopes and testing correlation coefficient
- [Release 2.9 of the Real Statistics Resource Pack](https://real-statistics.com/release-2-9-real-statistics-resource-pack/) - Describes the new features in the Real Statistics Resource Pack.
- [Announcing Release 2.8 of the Real Statistics Resource Pack](https://real-statistics.com/announcing-release-2-8-real-statistics-resource-pack/) - Describes the new features of the Real Statistics Resource Pack, including multinomial logistic regression support.
- [Support for Excel 2003 and older versions of Excel](https://real-statistics.com/support-for-excel-2003-and-older-versions-of-excel/)
- [Quick Update](https://real-statistics.com/quick-update/)
- [Release 2.7 of the Real Statistics Resource Pack](https://real-statistics.com/release-2-7-real-statistics-resource-pack/) - Description of the new capabilities in the Real Statistics Resource Pack, esp. ROC curve and classification table for logistic regression and weighted kappa
- [Release 2.6 of the Real Statistics Resource Pack](https://real-statistics.com/release-2-6-of-the-real-statistics-resource-pack/) - Announcing Release 2.6 of the Real Statistics Resource Pack, describing new ANOVA features and software.
- [Release 2.5 of the Real Statistics Resource Pack](https://real-statistics.com/release-2-5-real-statistics-resource-pack/) - Description of the latest release of the Real Statistics Resource Pack and recent changes to the website.
- [Announcing Real Statistics Resource Pack Release 2.4](https://real-statistics.com/announcing-real-statistics-resource-pack-release-2-4/) - Describes the newest features in the Real Statistics software. This software is an Excel add-in available for free download.
- [New Website Capabilities](https://real-statistics.com/new-website-capabilities/) - New social media features have been added to the Real Statistics website, including a new twitter account and sharing via twitter, facebook, google+ & linkedin.
- [Other New Features in the Real Statistics Resource Pack](https://real-statistics.com/announcing-release-2-1-of-the-real-statistics-resource-pack/) - Description of the new features available in the Real Statistics Resource Pack, Excel add-in statistics software available for free download.
- [Announcing Release 2.3 of the Real Statistics Resource Pack](https://real-statistics.com/announcing-release-2-3-of-the-real-statistics-resource-pack/) - Description of the new features available in the Real Statistics Resource Pack, Excel add-in statistics software available for free download.
- [Announcing Release 2.2 of the Real Statistics Resource Pack](https://real-statistics.com/announcing-release-2-2-of-the-real-statistics-resource-pack/) - Description of the new features available in the Real Statistics Resource Pack, Excel add-in statistics software available for free download.
- [Announcing Release 2.0 of the Real Statistics Resource Pack](https://real-statistics.com/announcing-release-2-0-of-the-real-statistics-resource-pack/) - Announces new release of Excel add-in which adds multivariate statistics support to Real Statistics Resource Pack, including MANOVA, Hotelling's test, Box Test.
- [Announcing New Multivariate Statistics Capabilities](https://real-statistics.com/announcing-new-multivariate-statistics-capabilities/) - Announcing new multivariate support for Real Statistics Using Excel.
- [Announcing Release 1.8 of the Real Statistics Resource Pack](https://real-statistics.com/announcing-release-1-8-of-the-real-statistics-resource-pack/) - New release of the Real Statistics Resource Pack which improves the organization of the data analysis tools and add new Outliers and Missing Data features.
- [Release 1.8.2 of the Real Statistics Resource Pack](https://real-statistics.com/release-1-8-2-of-the-real-statistics-resource-pack/)
- [Announcing Release 1.7 of the Real Statistics Resource Pack](https://real-statistics.com/announcing-release-1-7-of-the-real-statistics-resource-pack/) - Release 1.7 of the Real Statistics Resource Pack includes support for sample sizes of up to 5,000 for the Shapiro Wik test plus upgrades to data analysis tools.
- [Announcing Release 1.6](https://real-statistics.com/announcing-release-1-6/) - Describes the new release of the Real Statistics Resource Pack.
- [New Releases](https://real-statistics.com/new-releases/) - Describes future releases of the Real Statistics Resource Pack
- [Announcing Release 1.5](https://real-statistics.com/announcing-release-1-5/)
- [Announcing Release 1.4](https://real-statistics.com/announcing-release-1-4/)
- [Welcome to the Real Statistics Website](https://real-statistics.com/hello-world/) - Request for feedback about the Real Statistics Using Excel website.

## Pages

- [Welcome](https://real-statistics.com/) - Free downloadable statistics software (Excel add-in) plus comprehensive statistics tutorial for carrying out a wide range of statistical analyses in Excel.
- [Kendall-Theil-Sen Regression](https://real-statistics.com/regression/kendall-theil-sen-regression/) - Describes the Kendall-Theil-Sen approach to robust, non-parametric regression, and shows how to do so in Excel. An example and software are also provided.
- [Gamma Measure of Association](https://real-statistics.com/correlation/gamma-association/) - Describes the gamma (symmetric) measure of association and explains how to calculate and test it in Excel. Examples and Excel worksheet functions are provided.
- [Tc correlation between several judges and a criterion](https://real-statistics.com/reliability/interrater-reliability/tc-correlation-between-several-judges-and-a-criterion/) - Describes the Tc correlation between several judges and a criterion, and explains how to calculate and test it in Excel. Incl. examples and Excel functions.
- [Kendall’s coefficient of agreement u for paired rankings](https://real-statistics.com/reliability/interrater-reliability/kendalls-coefficient-of-agreement-u-paired-ranks/) - Describes Kendall's coefficient of agreement u for paired ranks and explains how to calculate and test it in Excel. Incl. examples and Excel functions.
- [Kendall’s coefficient of agreement u for paired comparisons](https://real-statistics.com/reliability/interrater-reliability/kendalls-coefficient-of-agreement-u-paired-comparisons/) - Describes Kendall's coefficient of agreement u for paired comparisons and explains how to calculate and test it in Excel. Incl. examples and Excel functions.
- [Change Point Test](https://real-statistics.com/time-series-analysis/time-series-miscellaneous/change-point-test/) - Describes the Change Point Test (for numeric data) and explains how to implement it in Excel. Examples and Excel worksheet functions are provided.
- [Page's Test](https://real-statistics.com/anova-repeated-measures/pages-test/) - Describes Page's non-parametric repeated measures ANOVA test and explains how to calculate and perform it in Excel. Incl. examples and Excel functions.
- [Somers' d Measure of Asymmetric Association](https://real-statistics.com/correlation/somers-d-measure-of-asymmetric-association/) - Describes Somers' d (asymmetric) measure of association and explains how to calculate and test it in Excel. Examples and Excel worksheet functions are provided.
- [Change Point Test for Binary Data](https://real-statistics.com/time-series-analysis/time-series-miscellaneous/change-point-test/change-point-test-for-binary-data/) - Describes the Change Point Test for binary data and explains how to implement it in Excel. Examples and Excel worksheet functions are provided.
- [Anova with Random or Nested Factors](https://real-statistics.com/anova-random-nested-factors/) - Describes how to construct Anova models with random, nested, or mixed factors in Excel. Includes software and a number of examples
- [Data Analysis for Nested ANOVA](https://real-statistics.com/anova-random-nested-factors/nested-anova/data-analysis-nested-anova/) - Describes how to create a nested ANOVA model with one fixed factor and one random factor, esp. using a data analysis tool in the Excel environment
- [Random Factor Nested ANOVA](https://real-statistics.com/anova-random-nested-factors/nested-anova/random-factor-nested-anova/) - Describes the basic concepts of a nested ANOVA model with two random factors. We also provide an Excel-based data analysis tool for performing this analysis.
- [Fixed Factor Nested ANOVA](https://real-statistics.com/anova-random-nested-factors/nested-anova/fixed-factor-nested-anova/) - Describes the basic concepts of a nested ANOVA model with two fixed factors. We also provide an Excel-based data analysis tool for performing this analysis.
- [Real Statistics Math Functions](https://real-statistics.com/real-statistics-environment/real-statistics-math-functions/) - Provides a summary of various mathematical functions provided in the Real Statistics Resource Pack. These functions are not strictly statistical.
- [Real Statistics Non-Parametric Test Functions](https://real-statistics.com/real-statistics-environment/non_parametric-test-functions/) - Summary of worksheet functions contained in the Real Statistics Resource Pack that support non-parametric tests. Includes statistical table lookup functions.
- [Boschloo Exact Test](https://real-statistics.com/chi-square-and-f-distributions/boschloo-exact-test/) - Describes how to perform the Boschloo exact test. Also provides examples and worksheet functions associated with performing this test in Excel.
- [Real Statistics Multivariate Functions](https://real-statistics.com/real-statistics-environment/real-statistics-multivariate-functions/) - Summary of all the multivariate statistics functions contained in the Real Statistics Resource Pack, an Excel add/in that supports statistical analysis
- [Factor Scores](https://real-statistics.com/multivariate-statistics/factor-analysis/factor-scores/) - Tutorial on factor scores using three methods: regression, Bartlett's and Anderson-Rubin. Free downloadable Excel software add-in is available.
- [Real Statistics Descriptive Statistics and Reformatting Functions](https://real-statistics.com/real-statistics-environment/descriptive-statistics-and-reformatting-functions/) - Summary of worksheet functions contained in the Real Statistics Resource Pack that support descriptive statistics, reformatting and other capabilities.
- [Log-Rank Test](https://real-statistics.com/survival-analysis/kaplan-meier-procedure/log-rank-test/) - Describes how to calculate the log-rank test in Excel to compare the survival rates of two samples using the Kaplan-Meier procedure. Examples and Excel software
- [Cohen's h Effect Size](https://real-statistics.com/binomial-and-related-distributions/proportion-distribution/cohens-h-effect-size/) - Describes Cohen's h, an effect size for the proportion parameter; used in proportion testing. Also, shows how to calculate Cohen's h in Excel.
- [Real Statistics Data Analysis Tools](https://real-statistics.com/real-statistics-environment/supplemental-data-analysis-tools/) - Lists all the Real Statistics statistical data analysis tools and includes links to get more information about these tools.
- [2 x 2 Contingency Table Testing](https://real-statistics.com/chi-square-and-f-distributions/2-x-2-contingency-table-testing/) - Describes the testing of 2 × 2 contingency tables for independence, incl. the chi-square test and Fisher & Boschloo exact tests. Includes a data analysis tool.
- [Box-Cox Transformation Options](https://real-statistics.com/correlation/box-cox-transformation/box-cox-transformation-options/) - Describes more Box-Cox transformation features (incl. Hawkins-Weisberg) and a data analysis tool and Excel worksheet functions to support such transformations
- [Advanced Complex Number Operations](https://real-statistics.com/other-mathematical-topics/advanced-complex-number-operations/) - Provides some more of the theory about complex numbers used to create the various complex number operations. Emphasis on the power function.
- [Length of a Curve](https://real-statistics.com/other-mathematical-topics/integration/length-of-a-curve/) - Describes how to calculate the length of a curve in Excel using aworksheet function supplied by the Real Statistics Resource Pack.
- [Reformatting Capabilities](https://real-statistics.com/real-statistics-environment/data-conversion/reformatting-tools/) - Description of worksheet functions and data analysis tools in the Real Statistics Resource Pack for reformatting data (reverse, remove empty cells, etc.).
- [PCA Support in Excel](https://real-statistics.com/multivariate-statistics/factor-analysis/principal-component-analysis/pca-support-in-excel/) - How to perform Principal Component Analysis in Excel using the Real Statistics statistical analysis tool. Incl. data analysis tools and worksheet functions.
- [Mixed Factor Nested Design](https://real-statistics.com/anova-random-nested-factors/nested-anova/mixed-nested-design/) - Describes the basic concepts of a nested ANOVA model with one fixed factor and one random factor. Includes key formulas used to create the model.
- [Nested ANOVA](https://real-statistics.com/anova-random-nested-factors/nested-anova/) - Describes how to create nested ANOVA designs and perform Nested ANOVA in Excel. Includes examples and Excel add-in software.
- [Employing Factor Analysis](https://real-statistics.com/multivariate-statistics/factor-analysis/employing-factor-analysis/) - Provides an example where we use factor analysis in conjunction with regression analysis. We reduce the number of variables to eliminate multicollineariy.
- [Factor Analysis](https://real-statistics.com/multivariate-statistics/factor-analysis/) - Tutorial on how to perform factor analysis in Excel. Includes Excel add-in software. Also includes a description of Principal Component Analysis.
- [Factor Analysis Example](https://real-statistics.com/multivariate-statistics/factor-analysis/factor-analysis-example/) - Describes a Factor Analysis example that is used on all the web pages pertaining to factor analysis. In particular the data for this example are provided.
- [Real Statistics Resource Pack for Macintosh](https://real-statistics.com/free-download/real-statistics-resource-pack/real-statistics-resource-pack-macintosh/) - How to download and install the Real Statistics Resource Pack containing new statistics function for use with Excel 2011, 2016, 2019, 365 for the Macintosh.
- [Real Statistics Resource Pack](https://real-statistics.com/free-download/real-statistics-resource-pack/) - Provides access to a file containing the Real Statistics add-in for free download. Also, includes instructions on how to install the software.
- [Excel Sorting Formulas](https://real-statistics.com/excel-environment/sorting-and-filtering-functions/excel-sorting-formulas/) - Describes how to sort & remove duplicates in Excel using Excel tricks. Better approaches are available from Real Statistics and the latest Excel versions.
- [Ellipse: Area and Perimeter](https://real-statistics.com/other-mathematical-topics/integration/ellipse-area-and-perimeter/) - Describes how to calculate the area and perimeter of an ellipse. Provides formulas as well as examples and worksheet functions in Excel.
- [Numerical Integration](https://real-statistics.com/other-mathematical-topics/integration/) - Describes various ways of estimating a definite integral, including the midpoint rule, trapezoid rule and Simpson's rule.
- [Descriptive Statistics for a Frequency Table](https://real-statistics.com/descriptive-statistics/frequency-tables/descriptive-statistics-frequency-table/) - Describes how to calculate descriptive statistics (mean, median, variance, MAD, IQR, etc.) in Excel and by using Real Statistics functions.
- [Principal Axis Method of Factor Extraction](https://real-statistics.com/multivariate-statistics/factor-analysis/principal-axis-method/) - Tutorial on how to conduct the Principal Axis Factoring approach to Factor Analysis in Excel. Focus is on factor extraction.
- [Validity of Correlation Matrix and Sample Size](https://real-statistics.com/multivariate-statistics/factor-analysis/validity-of-correlation-matrix-and-sample-size/) - Tutorial on determining whether the sample is appropriate for factor analysis. Includes Kaiser-Mayer-Olkin, Bartlett's and Haitovsky tests.
- [Principal Component Analysis](https://real-statistics.com/multivariate-statistics/factor-analysis/principal-component-analysis/) - Brief tutorial on Principal Component Analysis and how to perform it in Excel. The various steps are explained via an example
- [Rotation](https://real-statistics.com/multivariate-statistics/factor-analysis/rotation/) - Describes how to use the Varimax orthogonal rotation algorithm in Excel. Also, describes how to access to Excel software to calculate Varimax.
- [Determining the Number of Factors](https://real-statistics.com/multivariate-statistics/factor-analysis/determining-number-of-factors/) - Tutorial on how to determine the number of factors to retain using Kaiser's criterion and scree plots. Access to free downloadable Excel add-in software.
- [Factor Extraction](https://real-statistics.com/multivariate-statistics/factor-analysis/factor-extraction/) - Tutorial on how to perform factor extraction in Excel using the principal component method. Describes loading factors and communalities.
- [Basic Concepts of Factor Analysis](https://real-statistics.com/multivariate-statistics/factor-analysis/basic-concepts-factor-analysis/) - Tutorial on the basic concepts of factor analysis plus access to a free downloadable software add-in that performs factor analysis in the Excel environment.
- [Linear Algebra Background for Factor Analysis](https://real-statistics.com/multivariate-statistics/factor-analysis/linear-algebra-background-factor-analysis/) - Summary of the key facts from linear algebra that are necessary to perform factor analysis, esp. the Spectral Decomposition Theorem.
- [Real Statistics Support for Factor Analysis](https://real-statistics.com/multivariate-statistics/factor-analysis/real-statistics-support-factor-analysis/) - Description of the Factor Analysis data analysis tool provided in the Real Statistics Excel free downloadable add-in software.
- [Negative Binomial Regression Predictions](https://real-statistics.com/negative-binomial-regression/negative-binomial-regression-predictions/) - Describes how to make predictions based on negative binomial regression models in Excel. Examples and worksheet functions are included.
- [Negative Binomial Regression Analysis Tool (Newton's Method)](https://real-statistics.com/negative-binomial-regression/negative-binomial-regression-analysis-tool-newtons-method/) - Describes Newton's method version of Real Statistics' Negative Binomial Regression data analysis tool and its use to perform count regression in Excel.
- [Negative Binomial Regression Analysis Tool (Solver option)](https://real-statistics.com/negative-binomial-regression/negative-binomial-regression-analysis-tool-solver-option/) - Describes Real Statistics' Negative Binomial Regression data analysis tool and how to use it to perform this type of count regression in Excel.
- [Creating a Negative Binomial Regression model using Solver](https://real-statistics.com/negative-binomial-regression/creating-a-negative-binomial-regression-model-using-solver/) - Describes how to construct a negative binomial regression model in Excel using Solver. Provides an example and worksheet functions.
- [Noncentral F Distribution](https://real-statistics.com/chi-square-and-f-distributions/noncentral-f-distribution/) - Describes how to calculate the noncentral F pdf, distribution and its inverse in Excel. Includes examples and Excel add-in.
- [Power of Two Sample Variance Testing](https://real-statistics.com/chi-square-and-f-distributions/power-of-two-sample-variance-testing/) - How to calculate the power of two sample variance testing and the sample size needed to achieve a specified power for such tests. Examples and Excel add-in.
- [Confidence Interval for Ratio of Variances](https://real-statistics.com/chi-square-and-f-distributions/confidence-interval-variance-ratio/) - Describe how to create a confidence interval for two-sample variance testing using an Ftest in Excel. Examples are provided.
- [Two Sample Hypothesis Testing to Compare Variances](https://real-statistics.com/chi-square-and-f-distributions/two-sample-hypothesis-testing-comparing-variances/) - Describes how to determine whether the variances for two samples are significantly different using Excel's F.TEST function and Excel's data analysis tool.
- [F Distribution](https://real-statistics.com/chi-square-and-f-distributions/f-distribution/) - Describes basic properties of the F distribution, esp. its relationship to the chi-square and t distributions. Shows how to use this distribution in Excel.
- [Confidence Intervals for Power and Effect Size for Chi-square Tests](https://real-statistics.com/chi-square-and-f-distributions/confidence-interval-power-effect-size-chi-square-test/) - Describes how to calculate confidence intervals for effect size, noncentrality parameter and power for chi-square tests in Excel. Software &examples included.
- [Power of Chi-square Tests](https://real-statistics.com/chi-square-and-f-distributions/power-chi-square-tests/) - Describes how to calculate the power of the chi-square goodness of fit and independence tests and the sample size requirements for these tests. Incl. examples.
- [Noncentral Chi-square Distribution](https://real-statistics.com/chi-square-and-f-distributions/noncentral-chi-square-distribution/) - Describes the noncentral chi-square distribution, including graphs, examples and Excel functions to calculate the distribution and its inverse.
- [Cochran-Mantel-Haenszel](https://real-statistics.com/chi-square-and-f-distributions/cochran-mantel-haenszel/) - Tutorial on how to conduct the Cochran-Mantel-Haenszel test of multiple 2×2 contingency tables in Excel. Examples and software are provided.
- [Independence Testing](https://real-statistics.com/chi-square-and-f-distributions/independence-testing/) - How to test in Excel whether two categorical random variables are independent. Data is organized in a contingency table and tested using a chi-square test.
- [Goodness of Fit](https://real-statistics.com/chi-square-and-f-distributions/goodness-of-fit/) - How to test for goodness of fit using Excel (chi-square). These tests can also be used to check whether observed data fit a certain pattern or distribution.
- [Power of One Sample Variance Testing](https://real-statistics.com/chi-square-and-f-distributions/power-one-sample-variance-testing/) - Describes how to calculate the power of a one sample variance test in Excel and the sample size required for this test. Includes examples and Excel add-in.
- [One Sample Hypothesis Testing of the Variance](https://real-statistics.com/chi-square-and-f-distributions/one-sample-hypothesis-testing-variance/) - We describe how to use the chi-square distribution to test whether the variance of a sample is equal to some value. We provide some examples in Excel.
- [Chi-square Distribution](https://real-statistics.com/chi-square-and-f-distributions/chi-square-distribution/) - Describe the basic properties of the chi-square distribution, especially its relationship to the normal distribution) and explain supporting Excel formulas.
- [Chi-square and F Distributions](https://real-statistics.com/chi-square-and-f-distributions/) - How to do hypothesis testing in Excel on the variances using the chi-square and F distributions. How to do goodness of fit and independence testing in Excel.
- [Tobit Regression Technical Information](https://real-statistics.com/multiple-regression/tobit-regression/tobit-regression-technical-information/) - Provides technical information about Tobit Regression. Explains how to estimate coefficients using MLE. This webpage uses calculus.
- [Cochran-Armitage Test](https://real-statistics.com/chi-square-and-f-distributions/cochran-armitage-test/) - Describes how to conduct the Cochran-Armitage test in Excel which determines whether there is a linear trend for proportional data An example is included.
- [Effect Size for Chi-square Test](https://real-statistics.com/chi-square-and-f-distributions/effect-size-chi-square/) - Describes three effect size measures for chi-square test of independence: phi, Cramer's V and odds ratio. Describes how to calculate them in Excel.
- [Simulation Chi-square Test](https://real-statistics.com/chi-square-and-f-distributions/simulation-chi-square-test/) - Describes how to calculate a quasi-exact version of the chi-square test for independence using simulation in Excel. Examples and software are provided
- [Fisher’s Exact Test](https://real-statistics.com/chi-square-and-f-distributions/fishers-exact-test/) - Show how to calculate the Fisher exact test for independence using Excel. Includes the Freeman-Halton extension. Examples and software are provided.
- [Two-sample Proportion Testing](https://real-statistics.com/binomial-and-related-distributions/proportion-distribution/two-sample-proportion-testing/) - Describes how to perform a two-sample proportion test in Excel using a normal approximation. Includes a step-by-step example to illustrate the concepts.
- [Tobit Model Description](https://real-statistics.com/multiple-regression/tobit-regression/tobit-model-description/) - Describes the Tobit regression model, including censored and uncensored characteristics. Includes pdf, cdf, and expectations.
- [Real Statistic Support for Tobit Regression](https://real-statistics.com/multiple-regression/tobit-regression/real-statistic-support-for-tobit-regression/) - Describes an Excel analysis tool that creates a Tobit model and Excel worksheet functions to estimate regression coefficients & censored/uncensored estimates.
- [Tobit Regression](https://real-statistics.com/multiple-regression/tobit-regression/) - Tutorial on Tobit regression (aka censored linear regression) and describes how to build a Tobit model in Excel. Includes examples and software.
- [Design of Experiments](https://real-statistics.com/design-of-experiments/) - Tutorial on Design of Experiments (RCBD, Split-Plot, Latin Squares, 2^k Factorial) and how to analyze these designs in Excel. Examples & software are included.
- [Poisson Distribution - Proof](https://real-statistics.com/binomial-and-related-distributions/poisson-distribution/poisson-distribution-advanced/) - Proof of Property 1 of Poisson Distribution, namely that a Poisson distribution can be approximated by a normal distribution.
- [Binomial Distribution Proofs](https://real-statistics.com/binomial-and-related-distributions/binomial-distribution/binomial-distribution-advanced/) - Presents a proof of Property 1 of the Binomial Distribution webpage (giving formulas for the mean and variance of the binomial distribution).
- [Box-Cox Linear Transformation](https://real-statistics.com/correlation/box-cox-transformation/box-cox-linear-transformation/) - Describes how to choose a value for lambda in Excel which optimizes the Box-Cox linear transformation. Shows how to do this using Goal Seek. Also examples given
- [Box-Cox Normal Transformation](https://real-statistics.com/correlation/box-cox-transformation/box-cox-normal-transformation/) - Describes how to calculate the value of lambda in Excel (using Goal Seek) which creates the best Box-Cox normal transformation. Includes software and examples.
- [Box-Cox Transformation](https://real-statistics.com/correlation/box-cox-transformation/) - Describes how to perform the Box-Cox transformations in Excel to create a transformation to normality. Finds optimal transformation. Software and examples.
- [RCBD Follow-up Testing](https://real-statistics.com/design-of-experiments/completely-randomized-design/rcbd-follow-up-testing/) - Describes follow-up tests when the randomized complete block design shows a significant difference between treatments. Examples given of contrasts and Tukey HSD
- [Randomized Complete Block Design](https://real-statistics.com/design-of-experiments/completely-randomized-design/randomized-complete-block-design/) - Describes Randomized Complete Block Design (RCBD) and how to analyze such designs in Excel using ANOVA. Includes examples and software.
- [Completely Randomized & Randomized Complete Block Design](https://real-statistics.com/design-of-experiments/completely-randomized-design/) - Describes completely randomized design (CRD) and its relationship to randomized complete block design (RCBD). provides links to related topics.
- [Sorting and Filtering Functions](https://real-statistics.com/excel-environment/sorting-and-filtering-functions/) - Describes the new dynamic array functions for sorting and filtering, SORT, SORTBY, UNIQUE and FILTER, available in Excel 365.
- [Sets](https://real-statistics.com/mathematical-notation/sets/) - Describes the notation used for sets and some of the basic properties of sets. Also includes the notation for open and closed intervals.
- [Negative Binomial Regression: Additional Insights](https://real-statistics.com/negative-binomial-regression/negative-binomial-regression-additional-insights/) - Describes a simple Negative binomial regression example which provides some additional insights about this way of modeling count data.
- [Comparing Poisson and Negative Binomial Regression Models](https://real-statistics.com/negative-binomial-regression/comparing-poisson-and-negative-binomial-regression-models/) - Describes how to test in Excel whether there is a significant difference between a Poisson regression and Negative Binomial regression model.
- [Anderson-Darling Distribution](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/anderson-darling-test/anderson-darling-distribution/) - Describes how to estimate the p-values and critical values for the Anderson-Darling test. Excel functions for calculating these values are also provided.
- [Mathematical Notation](https://real-statistics.com/mathematical-notation/) - Review of basic mathematical notation used elsewhere on the website. Includes set theory, combinatorics, functions, logs, and mathematical notation.
- [Nominal-Ordinal Chi-square Test](https://real-statistics.com/one-way-analysis-of-variance-anova/nominal-ordinal-chi-square-test/) - Describes how to use the Kruskal-Wallis test for testing of a contingency table with one nominal factor and one ordinal factor. An Excel example is also given.
- [Wilcoxon Rank Sum Test - Proofs](https://real-statistics.com/non-parametric-tests/wilcoxon-rank-sum-test/wilcoxon-rank-sum-test-advanced/) - Presents the proofs of Wilcoxon Rank Sum Test properties 1 and 2, which show how to calculate the mean and standard deviation.
- [Standard Error of Gini Index](https://real-statistics.com/non-parametric-tests/gini-coefficient/standard-error-of-gini-index/) - Describes how to calculate the standard error of the Gini coefficient using bootstrapping, and how to use this to create a confidence interval.
- [Lorenz Curve](https://real-statistics.com/non-parametric-tests/gini-coefficient/lorenz-curve/) - Provides step-by-step instructions on how to create a Lorenz curve in Excel. Describes the relationship between the Lorenz curve and the Gini index.
- [Mann-Whitney Median Confidence Interval](https://real-statistics.com/non-parametric-tests/mann-whitney-test/mann-whitney-median-confidence-interval/) - Describes how to calculate the confidence interval of the median based on the Mann-Whitney test. Examples given in Excel.
- [Mann-Whitney Power](https://real-statistics.com/non-parametric-tests/mann-whitney-test/mann-whitney-power/) - Describes how to calculate the power or sample size for a Mann-Whitney test using simulation or estimated from the power of a t test.
- [Mann-Whitney Simulation](https://real-statistics.com/non-parametric-tests/mann-whitney-test/mann-whitney-simulation/) - Describes how to use simulation to estimate the p-values of the Mann-Whitney test. This approach takes ties into account.
- [Mann-Whitney Exact Test](https://real-statistics.com/non-parametric-tests/mann-whitney-test/mann-whitney-exact-test/) - Describes how to calculate the Mann-Whitney test using the permutation distribution to get exact values. Software and examples included.
- [Mann-Whitney Test - Proofs](https://real-statistics.com/non-parametric-tests/mann-whitney-test/mann-whitney-test-advanced/) - This webpage provides proofs of Properties 1 and 2 for the Mann-Whitney Test. These are used to justify the normal approximation.
- [Wilcoxon Signed-Ranks Test](https://real-statistics.com/non-parametric-tests/wilcoxon-signed-ranks-test/) - How to perform the Wilcoxon signed ranks test in Excel for a single sample and for paired samples. Includes using a table of critical values or normal approx.
- [Signed-Ranks Test Power and Sample Size](https://real-statistics.com/non-parametric-tests/wilcoxon-signed-ranks-test/signed-ranks-power/) - Describes how to calculate the power or sample size for a Wilcoxon Signed-Ranks test using simulation or estimated from the power of a t test.
- [Signed-Ranks Median Confidence Interval](https://real-statistics.com/non-parametric-tests/wilcoxon-signed-ranks-test/signed-ranks-median-confidence-interval/) - Describes how to calculate the confidence interval of the median based on the Wilcoxon signed/ranks test. Examples given in Excel.
- [Signed-Ranks Simulation](https://real-statistics.com/non-parametric-tests/wilcoxon-signed-ranks-test/signed-ranks-simulation/) - Describes how to use simulation to estimate the p-values of the Wilcoxon Signed-ranks test. This approach takes ties into account.
- [Signed Ranks Exact Test](https://real-statistics.com/non-parametric-tests/wilcoxon-signed-ranks-test/wilcoxon-signed-ranks-exact-test/) - Describes how to construct the Wilcoxon Signed Ranks Exact Test usin the permutation distribution in Excel. Software and examples provided.
- [Resampling Data Analysis Tool](https://real-statistics.com/non-parametric-tests/resampling-data-analysis-tool/) - Describes how to use a data analysis tool provided in the Real Statistics Resource Pack to perform resampling tests in Excel. Software and examples given.
- [Goodness of Fit Tests based on the Characteristic Function](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/goodness-of-fit-tests-characteristic-function/) - Tutorial on goodness-of-fit tests in Excel based on the characteristic function. Examples provided for normal, uniform, Laplace, Weibull, etc. distributions.
- [Goodness of Fit Analysis Tools](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/goodness-of-fit-analysis-tools/) - Describes how to use the Real Statistics Goodness of Fit Analysis Tools. These tools work in Excel and can be used free of charge
- [Goodness-of-fit for Benford Distribution](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/goodness-of-fit-benford-distribution/) - Describes how to test whether data follows Benford's rule using the Chi-square test, KS test, and AD test. Excel functions and examples are included.
- [Chi-square Goodness of Fit Test](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/chi-square-goodness-of-fit-test/) - Describes how to conduct the Chi-square Goodness of Fit Test in Excel. A detailed example and an Excel worksheet function are provided.
- [Two-Sample Anderson-Darling Test](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/two-sample-anderson-darling-test/) - Describes how to perform a two-sample Anderson-Darling test to determine whether two data sets come from the same distribution. Examples & software provided.
- [One-Sample Anderson-Darling Test](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/anderson-darling-test/) - Describes how to perform a one-sample Anderson-Darling test for normal, exponential, gamma, Weibull, etc. distributions in Excel. Examples & software provided.
- [Two-Sample Kolmogorov-Smirnov Test](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/two-sample-kolmogorov-smirnov-test/) - Describes how to apply the Two Sample Kolmogorov-Smirnov Test to determine if two samples have the same distribution. Examples and Excel add-in software.
- [One-Sample Kolmogorov-Smirnov Test](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/one-sample-kolmogorov-smirnov-test/) - Describes how to use the One Sample Kolmogorov-Smirnov Test to determine whether sample data follows a specific distribution; examples, Excel add-in software.
- [Wilcoxon Rank Sum Exact Test](https://real-statistics.com/non-parametric-tests/wilcoxon-rank-sum-test/wilcoxon-rank-sum-exact-test/) - Describes how to perform an exact test version of Wilcoxon's Rank-Sum test for independence in Excel. Software and examples included.
- [Wilcoxon Rank Sum Test for Independent Samples](https://real-statistics.com/non-parametric-tests/wilcoxon-rank-sum-test/) - How to perform the Wilcoxon ranked sum non-parametric test for independent samples in Excel, a test used when the assumptions for the t test are violated.
- [ANOVA Follow-up Analyses](https://real-statistics.com/two-way-anova/anova-follow-up-analyses/) - Describes how to perform follow-up analyses to ANOVA in Excel. Approach is esp. applicable to Three Factor ANOVA. Incl. contrasts and Tukey HSD. Examples given.
- [Coefficient of Variation Testing](https://real-statistics.com/students-t-distribution/coefficient-of-variation-testing/) - Describes how to conduct one-sample and two-sample testing of the coefficient of variation in Excel. Software and examples are provided.
- [Markov Chains Limiting Probabilities](https://real-statistics.com/probability-functions/markov-chains/markov-chains-limiting-probabilities/) - Provides a description of more properties of Markov chains, especially their limiting probabilities, as well as stationary and periodic chains.
- [Markov Chain Examples](https://real-statistics.com/probability-functions/markov-chains/markov-chain-examples/) - Provides some examples of using discrete time Markov chains in the Excel environment. Example is based on all 6 results for a die appear
- [Markov Chains Basic Concepts](https://real-statistics.com/probability-functions/markov-chains/markov-chains-basic-concepts/) - Defines the concept of a discrete time Markov chain and provide some basic properties & concepts such as a probability transition matrix & an absorbing state.
- [Markov Chains](https://real-statistics.com/probability-functions/markov-chains/) - Tutorial on discrete time Markov chains. We provide examples of how to solve problems based on Markov chains using Excel.
- [Traditional Approaches for Handling Missing Data](https://real-statistics.com/handling-missing-data/traditional-approaches-handling-missing-data/) - Tutorial on traditional approaches for dealing with missing data, incl. listwise deletion and single imputation (regression, stochastic regression, etc.).
- [Permutation Brunner-Munzel Test](https://real-statistics.com/non-parametric-tests/brunner-munzel-test/permutation-brunner-munzel-test/) - Describes how to use the (random) permutation version of the Brunner-Munzel test to compare two independent samples. Provides an example and Excel function.
- [Brunner-Munzel Data Analysis Tool](https://real-statistics.com/non-parametric-tests/brunner-munzel-test/brunner-munzel-data-analysis-tool/) - Describes how to conduct the Brunner-Munzel Test or Permutation Brunner-Munzel Test in Excel using the Real Statistics data analysis tool.
- [Brunner-Munzel Test Example](https://real-statistics.com/non-parametric-tests/brunner-munzel-test/brunner-munzel-test-example/) - Provides an example of how to conduct the Brunner-Munzel test for stochastic equality in Excel. Also includes an Excel worksheet function to carry out the test
- [Non-parametric Tolerance Interval](https://real-statistics.com/non-parametric-tests/non-parametric-tolerance-interval/) - Tutorial on how to create a non-parametric tolerance interval in Excel for data that is not normally distributed. An example is also provided.
- [Gini Coefficient](https://real-statistics.com/non-parametric-tests/gini-coefficient/) - Describes the Gini coefficient (aka Gini index), and explains how it is used and how it is calculated, including the relevant formulas.
- [McNemar-Bowker Test](https://real-statistics.com/non-parametric-tests/mcnemar-bowker-test/) - Describes how to conduct the McNemar-Bowker Test in Excel. An example is provided, as well as software and the appropriate spreadsheet
- [Bootstrapping](https://real-statistics.com/non-parametric-tests/bootstrapping/) - How to create a bootstrap sample for any parameter. Also describes how to calculate a bootstrap confidence interval. Incl.Excel examples and worksheet functions
- [Jackknife](https://real-statistics.com/non-parametric-tests/jackknife/) - Describes how to create a jackknife sample for any parameter. Also describes how to calculate the standard error. Incl.Excel examples and worksheet functions.
- [Data Analysis Tools for Non-parametric Tests](https://real-statistics.com/non-parametric-tests/data-analysis-tools-non-parametric-tests/) - Describes how to use a data analysis tool provided in the Real Statistics Resource Pack to perform non-parametric tests in Excel. Software and examples given.
- [Resampling Procedures](https://real-statistics.com/non-parametric-tests/resampling-procedures/) - How to perform resampling tests, especially as non-parametric versions of the t-tests for independent samples and paired samples.
- [Goodness of Fit Tests](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/) - Tutorial on goodness-of-fit tests, incl. the chi-square test, Kolmogorov-Smirnov test, & the Anderson-Darling test. Incl. numerous Excel functions and examples.
- [Moses' Test for Equal Variability](https://real-statistics.com/non-parametric-tests/moses-test-for-equal-variability/) - Describes Moses' test for equal variability and explains how to calculate and test it in Excel. Examples and Excel worksheet functions are provided.
- [Siegel-Tukey Test for Equal Variability](https://real-statistics.com/non-parametric-tests/siegel-tukey-test-for-equal-variability/) - Describes the Siegel-Tukey test of equal variability and explains how to implement it in Excel. Examples and Excel worksheet functions are provided.
- [Two-Sample Runs Test](https://real-statistics.com/non-parametric-tests/two-sample-runs-test/) - Describes how to perform the Two-Sample (Wald-Wolfowitz) Runs Test. Includes an example showing how to perform the test in Excel and a worksheet function.
- [McNemar’s Test](https://real-statistics.com/non-parametric-tests/mcnemars-test/) - Describes how to perform McNemar's non-parametric test. Excel examples are provided as are worksheet functions to implement the test in Excel.
- [Permutation Test for Paired Samples](https://real-statistics.com/non-parametric-tests/permutation-test-for-paired-samples/) - Describes the permutation non-parametric test for paired samples and explains how to calculate and perform it in Excel. Incl. examples and Excel functions.
- [Fligner-Policello Test](https://real-statistics.com/non-parametric-tests/fligner-policello-test/) - Describes how to perform the nonparametric Fligner-Policello Test in Excel to determine whether two population medians are equal. An example is provided.
- [Permutation Test for Two Independent Samples](https://real-statistics.com/non-parametric-tests/permutation-test-for-two-independent-samples/) - Describes the two independent samples permutation non-parametric test and explains how to calculate and perform it in Excel. Incl. examples and Excel functions.
- [Mann-Whitney Test for Independent Samples](https://real-statistics.com/non-parametric-tests/mann-whitney-test/) - How to perform a Mann-Whitney non-parametric test for independent samples in Excel when the assumptions for the t-test are not met.
- [Mood's Median Test (for two samples)](https://real-statistics.com/non-parametric-tests/moods-median-test-two-samples/) - Describes how to apply the Mood's Median non-parametric test in Excel for two samples. Includes an example and Excel functions to calculate the results.
- [Trinomial Test](https://real-statistics.com/non-parametric-tests/trinomial-test/) - Describes how to conduct the trinomial test, a non-parametric test similar to the sign test but with more power, in Excel. Example and software are provided.
- [Sign Test](https://real-statistics.com/non-parametric-tests/sign-test/) - Describe how to perform the sign test in Excel. Also describes the supplemental Real Statistics function to perform the sign test.
- [Introduction to Non-parametric Tests](https://real-statistics.com/non-parametric-tests/introduction-non-parametric-tests/) - Provides an overview of when non-parametric tests are used, as well as the advantages and shortcomings of using non-parametric tests.
- [Brunner-Munzel Test](https://real-statistics.com/non-parametric-tests/brunner-munzel-test/) - Provides an overview of the Brunner-Munzel test for two independent samples, especially when the samples have unequal variances.
- [Noncentral t Distribution](https://real-statistics.com/students-t-distribution/noncentral-t-distribution/) - Describes the Noncentral t Distribution and how to calculate the cumulative distribution (cdf) and probability distribution (pdf) function values in Excel.
- [Exponential Smoothing Confidence Interval](https://real-statistics.com/time-series-analysis/basic-time-series-forecasting/simple-exponential-smoothing/exponential-smoothing-confidence-interval/) - Describes how to calculate the standard error and confidence interval of a forecast obtained via Simple Exponential Smoothing. Example and software are provided
- [Bibliography](https://real-statistics.com/appendix/bibliography/) - Provides a list of various references used throughout the Real Statistics website on a variety of statistical subjects. Where available a link is included.
- [Standard Errors of LAD Regression Coefficients via Bootstrapping](https://real-statistics.com/multiple-regression/lad-regression/standard-errors-lad-regression-coefficients-bootstrapping/) - Describes how to use bootstrapping to calculate the standard error of a parameter; shows how this is done for the LAD regression coefficients.
- [Autoregressive Process Proofs](https://real-statistics.com/time-series-analysis/autoregressive-processes/autoregressive-processes-basic-concepts/autoregressive-process-proofs/) - Provides the proofs of key properties about Autoregressive processes and time series. Proofs use the stationary property.
- [Homogeneity of Variances Tool](https://real-statistics.com/one-way-analysis-of-variance-anova/homogeneity-variances/homogeneity-of-variance-tool/) - Describes how to use Real Statistics' Homogeneity of Variances data analysis tool in Excel. Examples are provided to illustrate key issues.
- [Fligner Killeen Test](https://real-statistics.com/one-way-analysis-of-variance-anova/homogeneity-variances/fligner-killeen-test/) - Describes how to use the Fligner Killeen test to determine whether groups have homogeneity of variances. Examples and Excel software are provided.
- [Homogeneity of Variances](https://real-statistics.com/one-way-analysis-of-variance-anova/homogeneity-variances/) - How to test for homogeneity of variances (Levene's test, Bartlett's test, box plot), which is a requirement of ANOVA, and dealing with lack of homogeneity.
- [ARMA(p,q) Processes](https://real-statistics.com/time-series-analysis/arma-processes/arma-pq-processes/) - Describes some key properties of (stationary and invertible) autoregression moving average (ARMA) processes and time series.
- [ARMA Processes Basic Concepts](https://real-statistics.com/time-series-analysis/arma-processes/arma-processes-basic-concepts/) - Description of some of the basic concepts about autoregressive moving average (ARMA) processes and time series based on the backshift operator.
- [Other Unit Root Tests](https://real-statistics.com/time-series-analysis/autoregressive-processes/other-unit-root-tests/) - Describes the KPSS Test and PP Test, two unit root tests, used to determine whether a time series is stationary. Includes examples and Excel software.
- [Augmented Dickey-Fuller Test](https://real-statistics.com/time-series-analysis/autoregressive-processes/augmented-dickey-fuller-test/) - Describes how to perform the Augmented Dickey-Fuller Test (ADF), which tests whether a time series is stationary, in Excel. Examples and software are included.
- [Lag Function](https://real-statistics.com/time-series-analysis/autoregressive-processes/lag-function/) - Describes the lag function (aka backshift operator) and how to represent an autoregressive process using the lag function.
- [Finding AR(p) coefficients using Regression](https://real-statistics.com/time-series-analysis/autoregressive-processes/finding-ar-coefficients-using-regression/) - Describes how to calculate the coefficients of an AR(p) process that represents time series using linear regression in Excel. Examples and software are provided
- [Finding AR(p) coefficients](https://real-statistics.com/time-series-analysis/autoregressive-processes/finding-ar-coefficients/) - Describes how to calculate in Excel the coefficients of an autoregressive process which represents a time series using ACF (Yule-Walker) and PACF
- [Partial Autocorrelation for AR(p) Process](https://real-statistics.com/time-series-analysis/autoregressive-processes/partial-autocorrelation-for-arp-process/) - Provides graphs of the partial correlation function of autoregressive processes and describes the connection with the process coefficients
- [Autoregressive Processes Basic Concepts](https://real-statistics.com/time-series-analysis/autoregressive-processes/autoregressive-processes-basic-concepts/) - Describes key properties of autoregressive processes and time series, including the Yule-Walker equations, and shows how to simulate an AR(p) process in Excel.
- [Characteristic Equation for AR(p) Processes](https://real-statistics.com/time-series-analysis/autoregressive-processes/characteristic-equation-autoregressive-processes/) - Determine whether an autoregressive process is stationary based on properties of the characteristic equation, namely |z| > 1 for any root.
- [Mann-Kendall Test](https://real-statistics.com/time-series-analysis/time-series-miscellaneous/mann-kendall-test/) - Describes how to conduct the Mann-Kendall test to detect a trend in Excel. An example is worked out and software is provided.
- [Sen's Slope](https://real-statistics.com/time-series-analysis/time-series-miscellaneous/sens-slope/) - Describes how to calculate, step-by-step, Sen's Slope, a nonparametric estimate of the slope of a trend, in Excel. An example and software are also provided.
- [Pretest-Posttest Design](https://real-statistics.com/analysis-of-covariance-ancova/pretest-posttest-design/) - Describes three ways of creating a pretest-posttest design: analysis of gain, repeated measures ANOVA and ANCOVA. Excel example and software.
- [More Pretest-Posttest Design](https://real-statistics.com/analysis-of-covariance-ancova/pretest-posttest-design/more-pretest-posttest-design/) - Describes how to perform pretest-posttest analysis when there are more than two between-subjects groups. Excel examples are provided.
- [Pretest-Posttest Design using ANCOVA](https://real-statistics.com/analysis-of-covariance-ancova/pretest-posttest-design/pretest-posttest-design-using-ancova/) - Describes how to use ANCOVA for pretest-posttest analysis. Includes an Excel example and explains how to perform the analysis in Excel.
- [Cohen's d for Paired Samples](https://real-statistics.com/students-t-distribution/paired-sample-t-test/cohens-d-paired-samples/) - Describes three versions of Cohen's d for paired samples: d_diff (difference), d_av (average) and d_rm (repeated measures). Examples and software are provided.
- [EM Missing Multivariate Normal Data Tools](https://real-statistics.com/handling-missing-data/em-algorithm/em-missing-multivariate-normal-data-tools/) - Describes how to use Real Statistics functions and data analysis tool to implement the EM algorithm for Missing Multivariate Normal Data in Excel.
- [EM algorithm multiple patterns of missing data](https://real-statistics.com/handling-missing-data/em-algorithm/em-algorithm-multiple-missing-data-patterns/) - Describes how to impute missing data and estimate the parameters for multivariate normally distributed data with multiple missing data patterns in Excel.
- [EM multivariate normal with missing data](https://real-statistics.com/handling-missing-data/em-algorithm/em-multivariate-normal-with-missing-data/) - Describes how to use the EM algorithm in Excel to impute missing data elements for data that follows a multivariate normal distribution.
- [EM Algorithm Bivariate Normal Data](https://real-statistics.com/handling-missing-data/em-algorithm/em-algorithm-bivariate-normal-data/) - Describes the EM algorithm and shows how to use it in Excel with bivariate normally distributed data with missing data elements.
- [EM Algorithm](https://real-statistics.com/handling-missing-data/em-algorithm/) - Tutorial on using the EM algorithm for dealing with missing data in Excel. Includes multivariate normal data and independence testing with missing data.
- [Initializing clusters via k-means++ algorithm](https://real-statistics.com/multivariate-statistics/cluster-analysis/initializing-clusters-k-means/) - Describes an effective way to initialize the clusters in cluster analysis by using the k-means++ algorithm in Excel. Software and examples are provided.
- [Zero-Inflated Poisson (ZIP) Regression Predictions](https://real-statistics.com/poisson-regression/zero-inflated-poisson-regression/zero-inflated-poisson-zip-regression-predictions/) - Describes how to use a Zero-Inflated Poisson (ZIP) Regression model to make predictions about count data in Excel using Real Statistics resources.
- [ZIP Data Analysis Options](https://real-statistics.com/poisson-regression/zero-inflated-poisson-regression/zip-data-analysis-options/) - Describes how to use the (1) Use of the Init Coeff Range field and (2) LL0 options of Real Statistics' ZIP Regression data analysis tool.
- [Vuong's Test](https://real-statistics.com/poisson-regression/zero-inflated-poisson-regression/vuongs-test/) - How to use Vuong's test to determine whether the results from ZIP regression are significantly different from ordinary Poisson regression. Incl. Excel example.
- [Constructing a Zero-Inflated Poisson Regression Model](https://real-statistics.com/poisson-regression/zero-inflated-poisson-regression/constructing-a-zero-inflated-poisson-regression-model/) - We show how to construct a Zero-Inflated Poisson (ZIP) Regression model in Excel using a Real Statistics data analysis tool, which in turn uses Solver.
- [ZTP Regression Predictions](https://real-statistics.com/poisson-regression/zero-truncated-poisson-regression/ztp-predictions/) - How to use the Excel worksheet functions provided by the Real Statistics Resource Pack to make predictions based on Zero-Truncated Poisson (ZTP) regression.
- [Creating a ZTP Regression model using Solver](https://real-statistics.com/poisson-regression/zero-truncated-poisson-regression/creating-a-ztp-regression-model-using-solver/) - Describes how to use the Real Statistics Poisson Regression data analysis tool to perform Zero-Truncated Poisson (ZTP) regression in Excel.
- [Zero-Inflated Poisson Regression](https://real-statistics.com/poisson-regression/zero-inflated-poisson-regression/) - Describes how to perform zero-inflated Poisson (ZIP) regression in Excel. Includes examples and Excel-based data analysis support and worksheet functions.
- [Zero-Truncated Poisson Regression](https://real-statistics.com/poisson-regression/zero-truncated-poisson-regression/) - Describes how to perform zero-truncated Poisson (ZTP) regression in Excel. Includes examples and Excel-based data analysis support and worksheet functions.
- [Poisson Regression Proofs](https://real-statistics.com/poisson-regression/poisson-regression-proofs/) - Provides the proofs of properties related to Newton's method for estimating the Poisson regression coefficients and their standard errors. Requires calculus.
- [Poisson Regression Analysis Tool](https://real-statistics.com/poisson-regression/poisson-regression-analysis-tool/) - Describes how to use the Real Statistics Poisson Regression data analysis tool to create a Poisson Regression model from a data set.
- [Poisson Regression using Newton's Method](https://real-statistics.com/poisson-regression/poisson-regression-using-newtons-method/) - Describes how to estimate the Poisson regression coefficients and their standard errors using Newton's method. Also provides Excel worksheet functions for them.
- [Poisson Regression Predictions](https://real-statistics.com/poisson-regression/poisson-regression-predictions/) - Describes how to make predictions in Excel using a Poisson Regression model. Examples and Excel worksheet functions for doing this are provided.
- [Poisson Regression Over-dispersion Tests](https://real-statistics.com/poisson-regression/poisson-regression-over-dispersion-tests/) - Describes how to test for over-dispersion in Poisson regression. Shows how to perform the Score test and Lagrange Multiplier tests. Includes Excel example.
- [Poisson Regression Residuals and Goodness of Fit](https://real-statistics.com/poisson-regression/poisson-regression-residuals-and-goodness-of-fit/) - Describes how to calculate the residuals for a Poisson regression model and the goodness of fit statistics in Excel. Examples and software are furnished.
- [Poisson Regression using Solver](https://real-statistics.com/poisson-regression/poisson-regression-using-solver/) - Describes how to calculate the coefficients for a Poisson regression model using Excel's Solver. Provides an example to show how this is done.
- [Poisson Regression Basic Concepts](https://real-statistics.com/poisson-regression/poisson-regression-basic-concepts/) - Describes how to perform Poisson regression in Excel. Includes examples and free software for carrying out Poisson regression.
- [Poisson Regression](https://real-statistics.com/poisson-regression/) - Tutorial on how to perform Poisson regression in Excel. Examples and free software are provided. Poisson regression is used with count data.
- [Real Statistics Support for Bland-Altman](https://real-statistics.com/reliability/interrater-reliability/bland-altman-analysis/real-statistics-support-bland-altman/) - Describes, step-by-step, how to use the Real Statistics Bland-Altman data analysis tool to create a Bland-Altman Plot in Excel. An example is provided.
- [Confidence Interval for Bland-Altman](https://real-statistics.com/reliability/interrater-reliability/bland-altman-analysis/confidence-interval-bland-altman/) - Describes how to calculate confidence intervals for Bland-Altman in Excel. Includes formula for the standard error, as well asexamples and software.
- [Limits of Agreement](https://real-statistics.com/reliability/interrater-reliability/bland-altman-analysis/limits-of-agreement/) - Describes how to add the limits of agreement and mean (bias) to a Bland-Altman Plot in Excel. Also provides an example of advanced Excel charting techniques.
- [Bland-Altman Plot](https://real-statistics.com/reliability/interrater-reliability/bland-altman-analysis/bland-altman-plot/) - Describes how to construct a Bland-Altman plot in Excel in order to compare two measurements of the same variable and decide to replace one with the other.
- [ICC for Test/Retest Reliability](https://real-statistics.com/reliability/interrater-reliability/intraclass-correlation/icc-for-test-retest-reliability/) - Describes how to use the intraclass correlation coefficient (ICC) to perform test/retest reliability in Excel. Example and software provided.
- [ICC to compare against a gold standard](https://real-statistics.com/reliability/interrater-reliability/intraclass-correlation/icc-compare-against-gold-standard/) - Describes how to use the intraclass correlation coefficient (ICC) to measure agreement between a new process and a process that is the gold standard standard.
- [Other Intraclass Correlation Models](https://real-statistics.com/reliability/interrater-reliability/intraclass-correlation/intraclass-correlation-continued/) - Tutorial on six types of intraclass correlations: ICC(1,1), ICC(2,1), ICC(3,1), ICC(1,k), ICC(2,k), ICC(3,k), how to calculate them & confidence intervals.
- [Real Statistics Support for Krippendorff's Alpha](https://real-statistics.com/reliability/interrater-reliability/krippendorffs-alpha/real-statistics-support-krippendorffs-alpha/) - Describes Real Statistics support (Excel worksheet functions and data analysis tools) for Krippendorff's Alpha. Examples are given.
- [Gwet's AC2 Analysis Tools](https://real-statistics.com/reliability/interrater-reliability/gwets-ac2/gwets-ac2-analysis-tool/) - Describes Excel worksheet functions and data analysis tools to calculate Gwet's AC2 and its confidence intervals. An example is given.
- [Gwet's AC2 Confidence Interval](https://real-statistics.com/reliability/interrater-reliability/gwets-ac2/gwets-ac2-confidence-interval/) - Describes how to calculate the standard error and confidence intervals for Gwet's AC2 interrater reliability statistic in Excel. An example is given.
- [Gwet's AC2 Basic Concepts](https://real-statistics.com/reliability/interrater-reliability/gwets-ac2/gwets-ac2-basic-concepts/) - Describes how to calculate Gwet's AC2 (and AC1) interrater reliability statistic in Excel. Excel examples and software are provided
- [Gwet's AC1 and AC2](https://real-statistics.com/reliability/interrater-reliability/gwets-ac2/) - Tutorial on Gwet's AC2 (or AC1), including basic concepts, how to calculate alpha and its confidence interval in Excel. Examples and software are provided.
- [Non-Categorical Ratings for Krippendorff's Alpha](https://real-statistics.com/reliability/interrater-reliability/krippendorffs-alpha/non-categorical-ratings-krippendorffs-alpha/) - Describes how to calculate Krippendorff's alpha, a measure of interrater reliability, in Excel for interval, ordinal, or ratio ratings. Examples are provided.
- [Standard Error for Krippendorff's Alpha](https://real-statistics.com/reliability/interrater-reliability/krippendorffs-alpha/standard-error-for-krippendorffs-alpha/) - Describes how to calculate the standard error and confidence intervals for Krippendorff's alpha in Excel. Includes an example to demonstrate the steps.
- [Krippendorff's Alpha Basic Concepts](https://real-statistics.com/reliability/interrater-reliability/krippendorffs-alpha/krippendorffs-alpha-basic-concepts/) - Provides an overview of Krippendorff's Alpha, a measure of interrater reliability, and how to calculate it in Excel. Examples are provided.
- [Real Statistics Support for Forecast Accuracy](https://real-statistics.com/time-series-analysis/forecasting-accuracy/real-statistics-forecast-accuracy/) - Explains how to use the Real Statistics functions and data analysis tool to test the accuracy of time series forecasts. Software and examples are included.
- [Complex Linear Equations](https://real-statistics.com/other-mathematical-topics/complex-linear-equations/) - Describes how to solve a system of linear equations with complex coefficients. Examples using Excel are provided as well as Excel software.
- [Statistical Tests for Normality and Symmetry](https://real-statistics.com/tests-normality-and-symmetry/statistical-tests-normality-symmetry/) - Explains how to use statistical tests such as Shapiro-Wilk, Kolmogorov-Smirnov and Chi-square to determine whether data is normally distributed.
- [Bayesian Two-Sided Testing Examples](https://real-statistics.com/bayesian-statistics/bayesian-statistics-normal-data/bayesian-hypothesis-testing-normal/bayesian-two-sided-testing-examples/) - Gives examples of how to use the unit information and JZS Cauchy priors to perform two-sided hypothesis testing for normally distributed data in Excel.
- [Bayesian t Sample and Effect Size](https://real-statistics.com/bayesian-statistics/bayesian-statistics-normal-data/bayesian-hypothesis-testing-normal/bayesian-t-sample-and-effect-size/) - Provides tables of effect sizes needed to achieve a given level of support for a hypothesis for a given sample size, as well as the sample size needed in Excel.
- [Bayesian t Test Sample Size](https://real-statistics.com/bayesian-statistics/bayesian-statistics-normal-data/bayesian-hypothesis-testing-normal/bayesian-t-test-sample-size/) - Determine the effect size needed to achieve a given level of support for a hypothesis for a given sample size. Also find the sample size needed in Excel.
- [Bayesian t Test Tools](https://real-statistics.com/bayesian-statistics/bayesian-statistics-normal-data/bayesian-hypothesis-testing-normal/bayesian-t-test-tools/) - Describes various Excel worksheet functions provided by Real Statistics to perform Bayesian t-tests. A data analysis tool is also provided and various examples.
- [Data Analysis Tool for Item Analysis](https://real-statistics.com/reliability/item-analysis/data-analysis-tool-item-analysis/) - Describes how to use Real Statistics' Reliability data analysis tool to calculate difficulty and item discrimination index even with partial scores.
- [Partial Score in Item Analysis](https://real-statistics.com/reliability/item-analysis/partial-score-item-analysis/) - Describes how to calculate item difficulty and discrimination index in Excel when partial scores (partial credit) is possible. Examples and software is provided
- [Real Statistics Item Analysis Functions](https://real-statistics.com/reliability/item-analysis/calculations-item-analysis/) - Describes how to calculate difficulty and discrimination index using Real Statistics functions, including some difficult cases.
- [Item Analysis Interpretation](https://real-statistics.com/reliability/item-analysis/item-analysis-interpretation/) - Describes how to use the difficulty coefficient and discrimination index to improve the reliability of testing. Recommendations are made via an example.
- [Item Analysis Basic Concepts](https://real-statistics.com/reliability/item-analysis/item-analysis-basic-concepts/) - Description of the basic components of item analysis in testing, including item discrimination and item difficulty. Example of how to calculate these is given.
- [Lin's Concordance Correlation Coefficient](https://real-statistics.com/reliability/interrater-reliability/lins-concordance-correlation-coefficient/) - Describes Lin's concordance correlation coefficient and how to calculate it in Excel as well as a confidence interval. Also explains how to interpret Lin's CCC.
- [Bland-Altman Analysis](https://real-statistics.com/reliability/interrater-reliability/bland-altman-analysis/) - Tutorial on Bland-Altman analysis. Describes how to construct a Bland-Altman Plot in Excel and provides examples and software to facilitate this
- [Kendall’s Coefficient of Concordance (W)](https://real-statistics.com/reliability/interrater-reliability/kendalls-w/) - Tutorial on Kendall’s coefficient of concordance (W), including how to use and calculate it in Excel (even when there are ties).
- [Intraclass Correlation](https://real-statistics.com/reliability/interrater-reliability/intraclass-correlation/) - Describes how to calculate the interclass correlation (ICC) measure of consistency between a number of judges using Excel, including an example.
- [Krippendorff's Alpha](https://real-statistics.com/reliability/interrater-reliability/krippendorffs-alpha/) - Tutorial on Krippendorff's Alpha, including basic concepts, how to calculate alpha and its confidence interval in Excel. Examples and software are provided
- [Fleiss' Kappa](https://real-statistics.com/reliability/interrater-reliability/fleiss-kappa/) - Tutorial on how to calculate Fleiss' kappa, an extension of Cohen's kappa measure of degree of consistency for two or more raters, in Excel.
- [Weighted Cohen's Kappa](https://real-statistics.com/reliability/interrater-reliability/weighted-cohens-kappa/) - Provides a rief tutorial on when to use weighted Cohen's kappa and how to calculate its value in Excel. Examples and software are provided.
- [Inverse Gamma Function](https://real-statistics.com/other-key-distributions/gamma-function/inverse-gamma-function/) - Describes how to compute the inverse(s) of the gamma function. Includes examples and an Excel worksheet function that returns the inverse gamma function.
- [Newton's Method](https://real-statistics.com/matrices-and-iterative-procedures/newtons-method/) - Describes how to use Newton's method in Excel to find the roots of a non-linear equation and a system of non-linear equations.
- [Cohen's Kappa](https://real-statistics.com/reliability/interrater-reliability/cohens-kappa/) - Tutorial on how to calculate and use Cohen's kappa, a measure of the degree of consistency between two raters. Examples are provided using Excel.
- [Cronbach's Alpha Proof](https://real-statistics.com/reliability/internal-consistency-reliability/cronbachs-alpha/cronbachs-alpha-advanced/) - Provides a proof of a key property about Cronbach's Alpha internal consistency measure of reliability based on properties of variances and covariance
- [Cronbach's Alpha with Missing Data](https://real-statistics.com/reliability/internal-consistency-reliability/cronbachs-alpha/cronbachs-alpha-with-missing-data/) - Describes how to handle missing data when calculating Cronbach's alpha. Also describes how to deal with not applicable (N/A) data.
- [Cronbach's Alpha Power](https://real-statistics.com/reliability/internal-consistency-reliability/cronbachs-alpha/cronbachs-alpha-power/) - Describes how to determine the statistical power and minimum sample size when using Cronbach's alpha. Examples and software are provided.
- [Cronbach's Alpha Hypothesis Testing](https://real-statistics.com/reliability/internal-consistency-reliability/cronbachs-alpha/cronbachs-alpha-continued/) - Describes how to perform hypothesis testing for Cronbach's Alpha, including confidence intervals. Examples and software in Excel are provided.
- [Cronbach's Alpha Tools](https://real-statistics.com/reliability/internal-consistency-reliability/cronbachs-alpha/cronbachs-alpha-tools/) - Describes how to calculate Cronbach's alpha for dichotomous and Likert data in Excel using Real Statistics functions and data analysis tool.
- [ARIMAX Model and Forecast](https://real-statistics.com/time-series-analysis/time-series-miscellaneous/arimax-model-and-forecast/) - Describes how to perform ARIMAX analysis in Excel. An example is provided which shows how to use the Real Statistics ARIMAX data analysis tool.
- [Estimating Ridge Regression Lambda](https://real-statistics.com/multiple-regression/ridge-and-lasso-regression/estimating-ridge-regression-lambda/) - Describes approaches, in Excel, for estimating the lambda value for Ridge regression, including k-fold cross-validation and a Ridge trace.
- [Ridge and LASSO Regression](https://real-statistics.com/multiple-regression/ridge-and-lasso-regression/) - Tutorial on Ridge and LASSO regression. Explains the motivation behind these types of regression and how to carry them out in Excel. Incl. examples & software.
- [Ridge Regression Predictions](https://real-statistics.com/multiple-regression/ridge-and-lasso-regression/ridge-regression-predictions/) - Describes how to make forecasts based on a Ridge regression model. Also shows how to calculate residuals and mean squared error. Excel examples.
- [Ridge Regression Analysis Tool](https://real-statistics.com/multiple-regression/ridge-and-lasso-regression/ridge-regression-analysis-tool/) - Describes how to use the Real Statistics Ridge Regression data analysis tool. This tool implements Ridge regression in Excel.
- [Ridge Regression Example](https://real-statistics.com/multiple-regression/ridge-and-lasso-regression/ridge-regression-example/) - Describes how to perform Ridge Regression. Provides examples in Excel. Also provides Excel worksheet functions that streamline the task.
- [Ridge Regression Basic Concepts](https://real-statistics.com/multiple-regression/ridge-and-lasso-regression/ridge-regression-basic-concepts/) - Provides the motivation behind Ridge Regression and describes how to conduct Ridge Regression. Includes a description of key formulas and properties
- [Cliff's Delta](https://real-statistics.com/non-parametric-tests/mann-whitney-test/cliffs-delta/) - Describes how to calculate Cliff's Delta non-parametric effect size in Excel. Includes examples and an Excel worksheet function.
- [Fitting PERT Distribution via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-pert-distribution-via-mle/) - Describes how to estimate the a, b, and c parameters of the PERT distribution that fits a set of data using the MLE approach in Excel.
- [Engle-Granger Table](https://real-statistics.com/statistics-tables/engle-granger-table/) - Provides a table of the critical values for the Engle-Granger test of cointegration based on work by MacKinnon.
- [Engle-Granger Test](https://real-statistics.com/time-series-analysis/time-series-miscellaneous/engle-granger-test/) - Describes how to conduct the Engle-Granger Test in Excel to determine whether two time series are cointegerated. Example and software are provided.
- [YouTube Videos](https://real-statistics.com/youtube-videos/) - Provides links to YouTube videos that show how to perform a variety of statistical analyses using the Real Statistics Resource Pack.
- [Spearman-Brown Reliability Proof](https://real-statistics.com/reliability/internal-consistency-reliability/split-half-methodology/spearman-browns-predicted-reliability/spearman-brown-reliability-proof/) - Provides a proof for the formula we use to calculate the Spearman-Brown's predicted reliability and correction factor in the Excel environment.
- [Guttman Reliability](https://real-statistics.com/reliability/internal-consistency-reliability/split-half-methodology/guttman-reliability/) - Describes how to compute the Guttman lambda 4 reliability measurement in Excel as well as the Guttman correction for a split/half. Examples are given.
- [Spearman-Brown's Predicted Reliability](https://real-statistics.com/reliability/internal-consistency-reliability/split-half-methodology/spearman-browns-predicted-reliability/) - Describes how to calculate the Spearman-Brown's predicted reliability and correction in Excel and to estimate number items needed to achieve reliability goal.
- [Split-Half Basic Concepts](https://real-statistics.com/reliability/internal-consistency-reliability/split-half-methodology/split-half-basic-concepts/) - Describes how to use the split-half methodology in Excel to test the reliability of a test or questionnaire, incl. Spearman-Brown correction.
- [Basic Property of Reliability](https://real-statistics.com/reliability/internal-consistency-reliability/basic-property-of-reliability/) - Gives proof that reliability equals the ratio of standard deviation of the true value to the standard deviation of the error in measurements.
- [Cronbach's Alpha](https://real-statistics.com/reliability/internal-consistency-reliability/cronbachs-alpha/) - Describes how to calculate Cronbach's alpha coefficient for reliability in Excel by using a technique similar to that for KR20 as well as by using ANOVA.
- [Kuder and Richardson Formula 20](https://real-statistics.com/reliability/internal-consistency-reliability/kuder-richardson-formula-20/) - Describes how to calculate the Kuder and Richardson Formula 20 (KR20) and Kuder and Richardson Formula 21 (KR21) measures of reliability in Excel.
- [Split-Half Methodology](https://real-statistics.com/reliability/internal-consistency-reliability/split-half-methodology/) - Tutorial on how to use the split-half method to test reliability of a test instrument in Excel. Examples and software are included.
- [Item Response Theory](https://real-statistics.com/reliability/item-response-theory/) - Provides a tutorial on item response theory, with emphasis on testing using a Rasch model. Examples and software are provided.
- [Test Theory and Item Analysis](https://real-statistics.com/reliability/item-analysis/) - Tutorial on item analysis in testing, including item discrimination, using the discrimination index, and item difficulty. Examples and software are provided.
- [Bradley–Terry Model](https://real-statistics.com/reliability/bradley-terry-model/) - Describes how to create a Bradley-Terry model based on pairwise data using an iterative algorithm. Includes an Excel example and worksheet functions.
- [Interrater Reliability](https://real-statistics.com/reliability/interrater-reliability/) - Tutorial on interrater reliability, covering Cohen's kappa, Fleiss's kappa, Krippendorff's alpha, ICC, Bland-Altman, Lin's concordance, Gwet's AC2
- [Internal Consistency Reliability](https://real-statistics.com/reliability/internal-consistency-reliability/) - Explores internal consistency reliability, the extent to which measurements of a test remain consistent over repeated tests under identical conditions.
- [Econometric Data Types](https://real-statistics.com/panel-data-models/econometric-data-types/) - We characterize econometric data into four types: cross-sectional, time series, pooled and panel (aka longitudinal) data. Examples of each type are provided.
- [Demeaning Models over Two Time Periods](https://real-statistics.com/panel-data-models/demeaning-models-over-two-time-periods/) - Describes how to use demeaning to create a fixed-effects panel data model when there are two time periods. Equivalent to a differencing model.
- [Differencing Models over Two Time Periods](https://real-statistics.com/panel-data-models/differencing-models-two-time-periods/) - Describes how to use differencing to create a fixed-effects panel data model when there are two time periods. Equivalent to a demeaning model.
- [Panel Data over Two Time Periods](https://real-statistics.com/panel-data-models/panel-data-two-time-periods/) - Described fixed effects panel data models over two time periods: in particular, a description of the formatting of panel data and the regression models used.
- [Dummy Variable Panel Model](https://real-statistics.com/panel-data-models/dummy-variable-panel-model/) - Describes how to use a least-squares dummy-variable model to create a fixed-effects panel data model using Excel. Checks for differences between the units.
- [Demeaning for Panel Data](https://real-statistics.com/panel-data-models/demeaning-panel-data/) - Describes how to use demeaning to create a fixed-effects panel data model even when there are more than two time periods.
- [Differencing for Panel Data](https://real-statistics.com/panel-data-models/differencing-for-panel-data/) - Describes how to use differencing to create a fixed-effects panel data model even when there are more than two time periods.
- [Hausman Test](https://real-statistics.com/panel-data-models/hausman-test/) - Describes how to use Hausman's test to determine if a fixed-effects or random-effects model is a better fit for your panel data. Incl. Excel function & example.
- [REM Example and Functions](https://real-statistics.com/panel-data-models/rem-example-and-functions/) - Describes how to create a random-effects panel data model using a transformation. Excel examples and worksheet functions are described.
- [Random Effects Model (REM)](https://real-statistics.com/panel-data-models/random-effects-model-rem/) - Describes how to create a random-effects panel data model using a transformation. Explains how to estimate the transformation parameter.
- [Panel Data Analysis Tool](https://real-statistics.com/panel-data-models/panel-data-analysis-tool/) - Describes how to use the Real Statistics Panel Data analysis tool to create fixed-effects and random-effects models of panel data in the Excel environment.
- [Backward Propagation Details](https://real-statistics.com/neural-networks/training-a-neural-network/backward-propagation-details/) - Provides a proof of the backward propagation equalities using partial derivatives. These proofs use calculus, especially the chain rule.
- [Neural Network to Recognize Digits](https://real-statistics.com/neural-networks/neural-network-to-recognize-digits/) - Describes how to build, training, and test a neural network that recognizes hand-written digits from 0 to 9 in Excel using Real Statistics capabilities
- [Neural Network Excel Example](https://real-statistics.com/neural-networks/neural-network-excel-example/) - Describes how to use the Real Statistics training and testing data analysis tools to build a neural network that performs simple addition in Excel.
- [Neural Network Analysis Tools](https://real-statistics.com/neural-networks/neural-network-analysis-tools/) - Describes how to use the Real Statistics Training a Neural Network data analysis tool to train the XOR neural network in Excel.
- [Simple Neural Network Example](https://real-statistics.com/neural-networks/simple-neural-network-example/) - Provides an example of how to use an Excel spreadsheet to train a simple neural network to replicate an XOR gate. All formulas are explained.
- [Training and Testing Methodology](https://real-statistics.com/neural-networks/training-and-testing-methodology/) - We describe the approach used for testing a neural network, using backward propagation, as well as testing the accuracy of the neural network
- [Training a Neural Network](https://real-statistics.com/neural-networks/training-a-neural-network/) - We now describe how to train a neural network. Emphasis is placed on how backward propagation is performed using a set of training data.
- [Neural Networks Basic Concepts](https://real-statistics.com/neural-networks/neural-networks-basic-concepts/) - Describes the general concepts of a neural network. Describes how a neural network functions, including forward propagation and backward propagation.
- [FCS for Binary Categorical Data](https://real-statistics.com/handling-missing-data/multiple-imputation-mi/fcs-procedure-one-step/fcs-binary-categorical-data/) - Overview of how to use the FCS procedure for multiple imputation of missing data for binary categorical data. Provides an example using Excel.
- [Multiple Regression with Missing Data](https://real-statistics.com/handling-missing-data/multiple-imputation-mi/multiple-regression-missing-data/) - Describes how to carry out multiple regression in Excel when some of the data is missing. Gives an example and provides an add-in software to do this.
- [Number of Imputations](https://real-statistics.com/handling-missing-data/multiple-imputation-mi/number-of-imputations/) - A brief explanation of the recommended number of multiple imputations required to achieve a stated level of efficiency when performing multiple imputation.
- [Combining Multiple Imputations](https://real-statistics.com/handling-missing-data/multiple-imputation-mi/combining-multiple-imputations/) - Detailed description of how to combine multiple imputations in Excel using Little's rules. Includes examples and free add-in software.
- [One Complete Imputation using FCS](https://real-statistics.com/handling-missing-data/multiple-imputation-mi/one-complete-imputation-using-fcs/) - Detailed description of how to perform one imputation using FCS/MICE in Excel, including an example. Also explanation of free software support.
- [One Step of the FCS Procedure](https://real-statistics.com/handling-missing-data/multiple-imputation-mi/fcs-procedure-one-step/) - Provides a detailed description of one step in the FCS/MICE procedure for performing multiple imputation. Provides examples and a worksheet function in Excel.
- [Simple Imputation and Multiple Imputation Constraints](https://real-statistics.com/handling-missing-data/multiple-imputation-mi/multiple-imputation-constraints/) - Describes how to use constraints in performing multiple imputation. Excel functions for dealing with this issue are provided as are examples in Excel.
- [Frequency and Patterns of Missing Data](https://real-statistics.com/handling-missing-data/multiple-imputation-mi/missing-data-frequency-patterns/) - Description of frequency and patterns of missing data and how to generate reports of these in Excel using functions from the Real Statistics Resource Pack.
- [Fully Conditional Specification (FCS)](https://real-statistics.com/handling-missing-data/multiple-imputation-mi/fully-conditional-specification-fcs/) - Provides an overview of the fully conditional specification (FCS) approach, also called the multivariate imputation by chained equations (MICE).
- [Multiple Imputation Overview](https://real-statistics.com/handling-missing-data/multiple-imputation-mi/multiple-imputation-overview/) - A brief overview of the multiple imputation approach for dealing with missing data. The basic concepts are described and followed up in subsequent webpages.
- [Adding constraints to Solver for FIML](https://real-statistics.com/handling-missing-data/full-information-maximum-likelihood-fiml/fiml-using-solver/adding-constraints-solver-fiml/) - Describes how to add constraints to the Solver approach to finding a Full Information Maximum Likelihood (FIML) solution to missing data.
- [FIML Real Statistics Data Analysis Tool](https://real-statistics.com/handling-missing-data/full-information-maximum-likelihood-fiml/fiml-real-statistics-data-analysis-tool/) - Describes the Real Statistics Full Information Maximum Likelihood (FIML) data analysis tool for calculating multiple regression with missing data using FIML.
- [Multiple Regression using FIML](https://real-statistics.com/handling-missing-data/full-information-maximum-likelihood-fiml/multiple-regression-using-fiml/) - Detailed description and example of how to create a multiple regression analysis in Excel even when there is missing data by using the FIML procedure.
- [FIML using Solver](https://real-statistics.com/handling-missing-data/full-information-maximum-likelihood-fiml/fiml-using-solver/) - Description of how to use Excel's Solver to deal with missing data by means of the FIML procedure. Examples and add-in software are provided.
- [Initialization of FIML](https://real-statistics.com/handling-missing-data/full-information-maximum-likelihood-fiml/initialization-fiml/) - Description of how to set up Excel to carry out the FIML procedure for dealing with missing data using Solver. Examples and software are provided.
- [FIML Basic Concepts](https://real-statistics.com/handling-missing-data/full-information-maximum-likelihood-fiml/fiml-basic-concepts/) - Brief overview of the objectives of the FIML procedure for dealing with missing data and the basic theoretical basic for the approach.
- [Multivariate Normal Properties](https://real-statistics.com/handling-missing-data/em-algorithm/multivariate-normal-properties/) - Describes various properties of multivariate normally distributed data that are useful in performing the EM algorithm when there is missing data.
- [Real Statistics support for independence testing with missing data](https://real-statistics.com/handling-missing-data/em-algorithm/independence-testing-tools-missing-data/) - Describes the Real Statistics functions and data analysis tool for performing chi-square independence testing when there is missing data using the EM algorithm.
- [Independence testing with missing data](https://real-statistics.com/handling-missing-data/em-algorithm/independence-testing-with-missing-data/) - Describes how to conduct the chi-square test of independence in Excel even when there is missing data. An example is given and free Excel software is provided.
- [Contingency tables with missing elements](https://real-statistics.com/handling-missing-data/em-algorithm/contingency-tables-with-missing-elements/) - Describes how to deal with contingency tables with missing data. Missing data is imputed using an EM algorithm. Excel examples and software is included.
- [Neural Networks](https://real-statistics.com/neural-networks/) - Tutorial on (artificial) neural networks, including implementations in Excel. Also includes several examples using Excel capabilities.
- [Full Information Maximum Likelihood (FIML)](https://real-statistics.com/handling-missing-data/full-information-maximum-likelihood-fiml/) - Tutorial on how to use the Full Information Maximum Likelihood (FIML) methodology for dealing with missing data in Excel. Includes examples and software.
- [Multiple Imputation (MI)](https://real-statistics.com/handling-missing-data/multiple-imputation-mi/) - Detailed tutorial on how to carry out multiple imputation in Excel using the FCS (aka the MICE) approach. Examples (regression) and software are described.
- [Types of Missing Data](https://real-statistics.com/handling-missing-data/types-of-missing-data/) - Describes the types of missing data: missing completely at random (MCAR), missing at random (MAR) and not missing at random
- [Handling Missing Data](https://real-statistics.com/handling-missing-data/) - Tutorial on handling missing data: traditional approaches (listwise deletion, single imputation) and advanced methods (multiple imputation, FIML EM algorithm).
- [Wordle Winning Strategy](https://real-statistics.com/wordle-strategy/) - Presents the rules of Wordle, provides a list of the 2,315 words in the dictionary and begins a tutorial on the strategy for winning the game.
- [Bayesian Statistics](https://real-statistics.com/bayesian-statistics/) - Provides a tutorial on Bayesian Statistics. Includes examples using Excel and worksheet functions and data analysis tools accessible from Excel.
- [Survival Analysis](https://real-statistics.com/survival-analysis/) - Describes how to perform Survival Analysis with censored data. Includes examples and Excel software. Topics: Cox Regression and Kaplana-Meier.
- [Time Series Analysis](https://real-statistics.com/time-series-analysis/) - Tutorial on time series analysis in Excel. Includes examples and software for moving average, exponential smoothing, Holt and Holt-Winters, ARIMA (Box-Jenkins).
- [Non-parametric Tests](https://real-statistics.com/non-parametric-tests/) - Tutorial on how to perform a variety of non-parametric statistical tests in Excel when the assumptions for a parametric test are not met.
- [Reliability](https://real-statistics.com/reliability/) - Explores internal consistency reliability, the extent to which measurements of a test remain consistent over repeated tests under identical conditions, in Excel
- [Correlation and Association](https://real-statistics.com/correlation/) - We explore the concept of correlation (especially using Pearson's correlation coefficient) and how to perform one and two sample hypothesis testing
- [Panel Data Models](https://real-statistics.com/panel-data-models/) - Tutorial on how to analyze panel data using regression. Fixed effects (FEM) and random effects models (REM) are explored using Excel.
- [Matching](https://real-statistics.com/matching/) - Tutorial on statistical matching techniques with a focus on propensity score matching (PSM) and coarsened exact matching. Examples & software in Excel provided.
- [Real Statistics Support for PSM](https://real-statistics.com/matching/propensity-score-matching/real-statistics-support-for-psm/) - Describes the various Excel worksheet functions used to perform Propensity Score Matching. These are also used by the Real Statistics PSM data analysis tool
- [PSM Example](https://real-statistics.com/matching/propensity-score-matching/psm-example/) - Describes how to use the Real Statistics Propensity Score Matching data analysis tool. This is done via an example in Excel.
- [CEM Example](https://real-statistics.com/matching/coarsened-exact-matching/cem-example/) - Describes how to use the Real Statistics Coarsened Exact Matching data analysis tool (with weights. This is done via an example in Excel.
- [CEM 1-to-1 Example](https://real-statistics.com/matching/coarsened-exact-matching/cem-1-to-1-example/) - Describes how to use the Real Statistics Coarsened Exact Matching data analysis tool (with 1-to-1 matching). This is done via an example in Excel.
- [Real Statistics Support for CEM](https://real-statistics.com/matching/coarsened-exact-matching/real-statistics-support-for-cem/) - Describes the various Excel worksheet functions used to perform Coarsened Exact Matching. These are also used by the Real Statistics CEM data analysis tool.
- [Coarsened Exact Matching](https://real-statistics.com/matching/coarsened-exact-matching/) - Describes how to use coarsened exact matcthng (CEM) to match confounding effects in treatment and control groups. Includes Excel examples and software.
- [Propensity Score Matching](https://real-statistics.com/matching/propensity-score-matching/) - Describes how to use propensity score matching (PSM) to match confounding effects in treatment and control groups. Includes Excel examples and software.
- [Double Integration Examples](https://real-statistics.com/other-mathematical-topics/integration/double-integration-examples/) - This webpage provides examples of how to use the Real Statistics INTEGRAL2 worksheet function to perform double integration in Excel using numerical analysis.
- [Numerical Integration Function](https://real-statistics.com/other-mathematical-topics/integration/numerical-integration-function/) - Describes how to perform numerical integration for any smooth function in Excel using the Real Statistics INTEGRAL function. Numerous examples are provided.
- [Numerical Double Integration](https://real-statistics.com/other-mathematical-topics/integration/numerical-double-integration/) - Describes how to estimate the value of a double integral using numerical analysis. Includes the case where the limits of the inner integral are functions.
- [Gradient and Hessian](https://real-statistics.com/other-mathematical-topics/differentiation/gradient-and-hessian/) - Describes various Excel worksheet functions for calculating the gradient and Hessian matrix for functions with two or three variables.
- [BGFS Algorithm](https://real-statistics.com/other-mathematical-topics/function-maximum-minimum/bgfs-algorithm/) - Describes the BGFS algorithm for finding local minima of a multivariate function. Examples and Excel software are provided.
- [Fraction to Decimal - Details](https://real-statistics.com/other-mathematical-topics/rational-numbers/converting-a-fraction-to-a-decimal/fraction-to-decimal-details/) - Provides a theoretical framework for calculating the fixed and repeating portions of the decimal representation of a rational number in the form of a fraction.
- [Converting a Fraction to a Decimal](https://real-statistics.com/other-mathematical-topics/rational-numbers/converting-a-fraction-to-a-decimal/) - Describes how to put a fraction in decimal form. Includes examples and Excel worksheet functions for doing this. Describes terminating and repeating decimals.
- [Converting a Decimal to a Fraction](https://real-statistics.com/other-mathematical-topics/rational-numbers/converting-decimal-to-fraction/) - Describes how to convert a rational number in decimal form to a fraction. Includes examples and Excel worksheet functions for doing this.
- [Rational Numbers in Qn](https://real-statistics.com/other-mathematical-topics/rational-numbers/rational-numbers-in-qn/) - Using properties of coprime integers, we list rational numbers in (0,1) whose numerator and denominator are less than n. Includes Excel functions and examples.
- [Coprime Numbers](https://real-statistics.com/other-mathematical-topics/rational-numbers/coprime-numbers/) - Defines coprime and describes how to determine if integers are coprime using Excel's GCD function. Also gives the probability that two integers are coprime.
- [Network Diagrams in Excel](https://real-statistics.com/other-mathematical-topics/graph-theory/network-diagrams-in-excel/) - Describes how to construct network diagrams for undirected graphs that connect pairs (x,y) of points in Excel using a Real Statistics data analysis tool.
- [MST for points in r-space](https://real-statistics.com/other-mathematical-topics/graph-theory/mst-points-in-r-space/) - Describes how to create a minimum spanning tree for points in r-space using weighted and unweighted Minkowski distance. Includes examples & software in Excel.
- [Prim Algorithm (MST)](https://real-statistics.com/other-mathematical-topics/graph-theory/prim-algorithm-mst/) - Describes the Prim algorithm for creating a minimum spanning tree (MST) of a connected graph using Excel. Examples and software are included.
- [Kruskal Algorithm (MST)](https://real-statistics.com/other-mathematical-topics/graph-theory/kruskal-algorithm-mst/) - Describes the Kruskal algorithm for creating a minimum spanning tree (MST) of a connected graph using Excel. Examples and software are included.
- [Gradient Descent Examples](https://real-statistics.com/other-mathematical-topics/function-maximum-minimum/gradient-descent/gradient-descent-examples/) - Describes how to use the Real Statistics MGRADIENT and MGRADIENTX worksheet functions to find the value X that minimizes f(X) in Excel.
- [Nelder-Mead Optimization](https://real-statistics.com/other-mathematical-topics/function-maximum-minimum/nelder-mead-optimization/) - Describes how to apply the Nelder-Mead algorithm to find a local minimum, An Excel example and Excel worksheet function are provided
- [Gradient Descent](https://real-statistics.com/other-mathematical-topics/function-maximum-minimum/gradient-descent/) - Describes the gradient descent algorithm for finding the value of X that minimizes the function f(X), including steepest descent and backtracking line search.
- [Inflection Point](https://real-statistics.com/other-mathematical-topics/function-maximum-minimum/inflection-point/) - Provides a definition of an inflection point and demonstrates how to find an inflection point in Excel using the fact that the second derivative is zero.
- [Global maximum/minimum of a multivariate function](https://real-statistics.com/other-mathematical-topics/function-maximum-minimum/global-maximum-minimum-multivariate/) - Describes how to identify global maximum and minimum values of a function f(x,y) or f(x,y,z) using Newton's method. Includes Excel worksheet functions.
- [Local maxima/minima of a multivariate function](https://real-statistics.com/other-mathematical-topics/function-maximum-minimum/local-maxima-minima-multivariate/) - Describes how to identify local maximum and minimum values of a function f(x,y) or f(x,y,z) using Newton's method. Includes Excel worksheet functions.
- [Differential Equations Analysis Tool](https://real-statistics.com/other-mathematical-topics/numerical-differential-equations/differential-equations-analysis-tool/) - Describes how to use Real Statistics data analysis tool to solve first-order and second-order differential equations in Excel.
- [Second Order Differential Equations](https://real-statistics.com/other-mathematical-topics/numerical-differential-equations/second-order-differential-equations/) - Describes how to solve second order differential equations in Excel using the Real Statistics add-in. Examples are provided to illustrate the methodology.
- [Simultaneous Differential Equations](https://real-statistics.com/other-mathematical-topics/numerical-differential-equations/simultaneous-differential-equations/) - Describes how to solve simultaneous differential equations in Excel using the Real Statistics add-in. Examples are provided to illustrate the methodology.
- [Numerical Differential Equations Support](https://real-statistics.com/other-mathematical-topics/numerical-differential-equations/numerical-differential-equations-support/) - Describes how to solve differential equations numerically in Excel using Real Statistics worksheet functions. Examples and Excel function are provided.
- [More Numerical Differential Equation Methods](https://real-statistics.com/other-mathematical-topics/numerical-differential-equations/more-numerical-differential-equation-methods/) - Describes how to solve differential equations using Euler's backward method, the trapeziod method or Runge-Kutta (RK2 and RK4). Includes Excel examples.
- [Euler's Method ODE](https://real-statistics.com/other-mathematical-topics/numerical-differential-equations/eulers-method-ode/) - Describes how to solve differential equations using Euler's forward method. An example of how to do this in Excel is given and explained.
- [Numerical Differential Equations](https://real-statistics.com/other-mathematical-topics/numerical-differential-equations/) - Tutorial on numerical differential equations. Initial focus is on first order equations. Examples using Euler, Trapezoid and Runge-Kutta methods in Excel.
- [Surface Chart](https://real-statistics.com/other-mathematical-topics/surface-chart/) - Describes how to construct a surface chart in Excel and how to plot a function in two variables using Excel-s Surface Chart and Real Statistics capabilities.
- [Numerical Differentiation](https://real-statistics.com/other-mathematical-topics/differentiation/) - Demonstrates how to perform numerical differentiation in Excel. An Excel function is provided that calculates the derivative for a specified function.
- [Rational Numbers](https://real-statistics.com/other-mathematical-topics/rational-numbers/) - Describes properties of rational numbers and their relationship to coprimes. Also repeating and terminating decimals. Includes Excel worksheet functions.
- [Prime Numbers](https://real-statistics.com/other-mathematical-topics/prime-numbers/) - Describes how to determine whether a number is prime in Excel. Also shows how to create the prime factorization of an integer.
- [Graph Theory](https://real-statistics.com/other-mathematical-topics/graph-theory/) - Provides a tutorial on some graph theory topics, especially on how to construct a minimum spanning tree for a connected undirected, weighted graph in Excel.
- [Roots of a Polynomial](https://real-statistics.com/other-mathematical-topics/roots-of-a-polynomial/) - Describes how to obtain the complex/real roots of a polynomial in Excel, especially by using Bairstow's method. An Excel function is also provided.
- [Polar Coordinates and Roots of a Complex Number](https://real-statistics.com/other-mathematical-topics/polar-coordinates-complex-roots/) - How to convert complex numbers from rectangular to polar form and vice versus in Excel. Also, how to find the nth roots of a real or complex number using Excel.
- [Geometric Series](https://real-statistics.com/other-mathematical-topics/geometric-series/) - A brief tutorial about geometric series. Describes what a geometric series is, and provides some key properties of such series.
- [Infinite Series](https://real-statistics.com/other-mathematical-topics/infinite-series/) - A brief tutorial on infinite series. Includes the alternating series test property and the divergence of the harmonic series
- [Roots of Multivariate Functions](https://real-statistics.com/other-mathematical-topics/roots-of-a-continuous-function/multidimensional-roots/) - Describes how to find roots of two functions in two unknowns or three functions in three unknowns in Excel using Newton's method, incl Excel worksheet functions
- [Roots of a Continuous Function](https://real-statistics.com/other-mathematical-topics/roots-of-a-continuous-function/) - Describes how to calculate the roots of a continuous function. Includes Brent's, Newton's, Bisection and Secant methods. Includes description of Excel functions
- [Complex Numbers](https://real-statistics.com/other-mathematical-topics/complex-numbers/) - Describes how to perform complex number operations in Excel. Examples and software are provided. Includes Excel complex number and Real Statistics formats.
- [Maximum/minimum values of a continuous function](https://real-statistics.com/other-mathematical-topics/function-maximum-minimum/) - Describes how to identify local and global maximum and minimum values of a function using Newton's method. Excel worksheet functions are described.
- [Bairstow's Method](https://real-statistics.com/other-mathematical-topics/roots-of-a-polynomial/bairstows-method/) - Describes how to carry out Bairstow's Method to find roots of a polynomial in Excel. Examples are included. We also show how to find the roots using Solver.
- [Cubic Polynomials](https://real-statistics.com/other-mathematical-topics/roots-of-a-polynomial/cubic-polynomials/) - Describes how to find the (real and complex) roots of a cubic polynomial using the cubic formula in Excel. An Excel function is also provided to get these roots
- [Real Statistics Support for Spline Fit](https://real-statistics.com/other-mathematical-topics/spline-fitting-interpolation/spline-real-statistics-support/) - Describes the Real Statistics functions and data analysis tool that support fitting a spline curve to data points in Excel. An example is provided.
- [Derivation of Spline Polynomials](https://real-statistics.com/other-mathematical-topics/spline-fitting-interpolation/derivation-spline-polynomials/) - Constructive derivation of cubic spline polynomials. Using these polynomials, we are able to show how to fit data to a spline curve.
- [Spline Fitting and Interpolation](https://real-statistics.com/other-mathematical-topics/spline-fitting-interpolation/) - Describes how to create a (cubic) spline curve that fits a series of data points. An example in given in Excel that shows how to do this in detail.
- [Complex Number Matrices](https://real-statistics.com/other-mathematical-topics/complex-matrices/) - Describes how to perform matrix operations in Excel for matrices which contain complex number values, Includes examples and Excel addin.
- [Complex Matrices in Excel Format](https://real-statistics.com/other-mathematical-topics/complex-matrices-in-excel-format/) - Describes how to perform various operations in Excel on matrices with complex entries of the form "a+bi", i.e. text versions of complex numbers used in Excel.
- [Data Analysis Tool for Other Two Sample Tests](https://real-statistics.com/students-t-distribution/problems-data-t-tests/data-analysis-tool-for-other-two-sample-tests/) - Describes how to use the Other Two Sample Tests data analysis tool to conduct the Trimmed Means t Test, Yuen-Welch's Test or Fligner-Policello test in Excel.
- [Root-finding Functions](https://real-statistics.com/other-mathematical-topics/roots-of-a-continuous-function/root-finding-functions/) - Describes how to use the bisection, secant, Newton's and Brent's approaches to finding roots of a function in Excel via Real Statistics.
- [Bayesian Two-sided Hypothesis Testing](https://real-statistics.com/bayesian-statistics/bayesian-statistics-normal-data/bayesian-hypothesis-testing-normal/bayesian-two-sided-hypothesis-testing/) - Describes how to use the unit information and JZS Cauchy priors to perform two-sided hypothesis testing for normally distributed data
- [Effect Size for ANOVA](https://real-statistics.com/one-way-analysis-of-variance-anova/effect-size-anova/) - Shows how to calculate Cohen's d and root-mean-square standardized effect (RMSSE) measures of effect size for ANOVA in Excel (including contrasts).
- [Gumbel Distribution](https://real-statistics.com/other-key-distributions/gumbel-distribution/) - Describes key properties of the Gumbel distribution, the objective of this distribution and how to use this distribution in Excel
- [Organization of the Website](https://real-statistics.com/introduction/organization-website-content/) - Describes how the Real Statistics using Excel website is organized. Tells how to get a free download of statistics software and examples.
- [Real Statistics Supplemental Capabilities](https://real-statistics.com/excel-environment/supplemental-capabilities/) - How to access & use the Real Statistics supplemental capabilities, namely worksheet functions and data analysis tools that extend Excel's built-in capabilities.
- [Other Mathematical Topics](https://real-statistics.com/other-mathematical-topics/) - Overview of various mathematical topics that are useful in statistics (complex numbers, roots of an equation, etc.). Includes examples and software
- [Real Statistics Regression/ANOVA Functions](https://real-statistics.com/real-statistics-environment/real-statistics-regression-anova-functions/) - Briefly describes all the Real Statistics worksheet functions related to regression and ANOVA. provides links for more information about each
- [Citation for the Real Statistics Software or Website](https://real-statistics.com/appendix/citation-real-statistics-software-website/) - Describes how to cite the Real Statistics software or website in a publication. Provides the latest release and copywrite information.
- [Yuen-Welch's Test](https://real-statistics.com/students-t-distribution/problems-data-t-tests/yuen-welchs-test/) - Describes how to conduct the Yuen-Welch Test in Excel. This test is useful when both the normality and equal variances assumptions for the t-test are not met.
- [Trimmed Means t Test](https://real-statistics.com/students-t-distribution/problems-data-t-tests/trimmed-means-t-test/) - How to conduct the Trimmed Means t Test in Excel. This test is useful when the normality assumption is not met, especially due to the presence of outliers.
- [LOESS Regression](https://real-statistics.com/regression/loess-regression/) - Describes how to perform LOESS (aka LOWESS) regression. LOESS = locally estimated scatterplot smoothing and LOWESS = locally weighted scatterplot smoothing.
- [LOESS Regression Data Analysis Tool](https://real-statistics.com/regression/loess-regression/loess-regression-data-analysis-tool/) - Describes how to use Real Statistics' LOESS Regression data analysis tool to perform LOESS regression in Excel. Two examples are also provided.
- [LOESS Regression using Excel](https://real-statistics.com/regression/loess-regression/loess-regression-using-excel/) - Describes how to perform LOESS (aka LOWESS) regression in Excel. An example is given and explained and an Excel worksheet function is provided
- [Distribution Fitting](https://real-statistics.com/distribution-fitting/) - Tutorial on distribution fitting, i.e. determining in Excel which parameters provide the best fit for a data sample; includes method of moments and MLE
- [Cox-Stuart Test](https://real-statistics.com/time-series-analysis/time-series-miscellaneous/cox-stuart-test/) - Describes how to conduct a Cox-Stuart test to determine whether a time series has an increasing or decreasing trend. Excel software and example are provided.
- [Lambda Coefficient](https://real-statistics.com/correlation/lambda-coefficient/) - Describes the lambda (asymmetric) measure of association and explains how to calculate and test it in Excel. Examples & Excel worksheet functions are provided.
- [Sample size requirements for t tests](https://real-statistics.com/students-t-distribution/sample-size-requirements-t-tests/) - Describes how to determine the sample size required to achieve a target power for the t tests. Includes examples and Excel add-in software.
- [CMH Test Basic Concepts](https://real-statistics.com/chi-square-and-f-distributions/cochran-mantel-haenszel/cmh-test-basic-concepts/) - Describes the basic concepts of the Cochran-Mantel-Haenszel (CMH) test and Woolf's Heterogeneity test. Describes the formulas and calculations required.
- [CMH Example](https://real-statistics.com/chi-square-and-f-distributions/cochran-mantel-haenszel/cmh-example/) - Describes a concrete example of the Cochran-Mantel-Haenszel test and shows how to conduct the test in Excel. Also includes Woolf’s Heterogeneity Test
- [CMH Analysis Tool](https://real-statistics.com/chi-square-and-f-distributions/cochran-mantel-haenszel/cmh-analysis-tool/) - Describes how to conduct the Cochran-Mantel-Haenszel test using the Real Statistics data analysis tool in Excel. Also outputs Woolf's heterogeneity test.
- [Bootstrapping Multivariate Regression Support](https://real-statistics.com/multivariate-statistics/multivariate-regression-analysis/multivariate-regression-bootstrapping/bootstrapping-multivariate-regression-support/) - Describes Excel worksheet functions in the Real Statistics Resource Pack to support bootstrapping for multivariate regression models. Examples are provided.
- [Bootstrapping Regression Support](https://real-statistics.com/multiple-regression/bootstrapping-regression/bootstrapping-regression-support/) - Describes Excel worksheet functions provided by the Real Statistics Resource Pack in support of bootstrapping for regression models. Examples are also provided.
- [Coding an Image](https://real-statistics.com/real-statistics-environment/coding-an-image/) - Tutorial on coding images (in color or greyscale) in Excel. Includes Excel worksheet functions and analysis tools for scanning and painting images
- [Freeform Images](https://real-statistics.com/real-statistics-environment/coding-an-image/freeform-images/) - We describe how to create an image in Excel using Excel's drawing tools. We also show how to use Excel's Pixel Art add-in to simplify the work.
- [Durbin-Watson Table](https://real-statistics.com/statistics-tables/durbin-watson-table/) - Durbin-Watson Table of critical values (lower and upper bounds) for values of alpha = .01 and .05. This table is used to test for autocorrelation.
- [Partial Least Squares (PLS) Regression](https://real-statistics.com/multivariate-statistics/multivariate-regression-analysis/partial-least-squares-pls-regression/) - Tutorial on Partial Least Squares (PLS) Regression. Explains the NIPALS algorithm & show how to use it in Excel. Provides examples and Excel worksheet functions
- [Real Statistics Support for PLS Regression](https://real-statistics.com/multivariate-statistics/multivariate-regression-analysis/partial-least-squares-pls-regression/real-statistics-support-for-pls-regression/) - Describes various Excel worksheet functions to support PLS Regression that are provided by the Real Statistics software. Examples are also provided.
- [PLS Regression Residuals and Predictions](https://real-statistics.com/multivariate-statistics/multivariate-regression-analysis/partial-least-squares-pls-regression/pls-regression-residuals-and-predictions/) - Describes how to determine the residuals and predictions based on a PLS Regression model. provides examples and worksheet functions in Excel.
- [Excel Spreadsheets](https://real-statistics.com/excel-environment/excel-spreadsheets/) - Describes Excel spreadsheets, also called worksheets, including cells, ranges, cell references, addressing (relative and absolute), formulas and functions.
- [t Distribution Basic Concepts](https://real-statistics.com/students-t-distribution/t-distribution-basic-concepts/) - Describes the basic properties of the Student's t distribution, its relationship to sampling and the Central Limit Theorem as well as key Excel formulas.
- [Holt's Linear Trend Confidence Interval](https://real-statistics.com/time-series-analysis/basic-time-series-forecasting/holt-linear-trend/holts-linear-trend-confidence-interval/) - Describes how to calculate the standard error and confidence interval of a forecast obtained via Holt's Linear Trend. Example and software are provided.
- [Confidence and Prediction Intervals Proofs](https://real-statistics.com/multiple-regression/confidence-and-prediction-intervals/confidence-and-prediction-intervals-proofs/) - Provides the proofs of the properties about confidence interval and prediction intervals for multiple linear regression models.
- [Partial Autocorrelation Function](https://real-statistics.com/time-series-analysis/stochastic-processes/partial-autocorrelation-function/) - Describes how to calculate the partial autocorrelation function in Excel. Examples are provided as well as Excel worksheet functions.
- [Autocorrelation Function](https://real-statistics.com/time-series-analysis/stochastic-processes/autocorrelation-function/) - Describes how to calculate the autocorrelation function in Excel and construct correlograms. Also explains the Bartlett's, Box-Pierce and Ljung-Box tests.
- [Using Real Statistics Functions](https://real-statistics.com/real-statistics-environment/using-real-statistics-functions/) - Describes how to obtain information about the worksheet functions provided by the Real Statistics Resource Pack. These functions augment Excel's capabilities.
- [Real Statistics ARMA Tool](https://real-statistics.com/time-series-analysis/arma-processes/real-statistics-arma-tool/) - Describes how to build an ARMA model of a time series in Excel and use this model to create a forecast. Examples and an Excel add-in are included.
- [Calculating MA Coefficients using ACF](https://real-statistics.com/time-series-analysis/moving-average-processes/ma-coefficients-acf/) - We describe how to estimate the coefficients of a Moving Average MA(q) model of a time series in Excel using the ACF. We also include examples in Excel.
- [Real Statistics Advanced Missing Data Functions](https://real-statistics.com/real-statistics-environment/real-statistics-advanced-missing-data-functions/) - Provides a summary of all the advanced missing data functions contained in the Real Statistics Resource Pack. Includes Multiple Imputation, FIML and EM.
- [Real Statistics Distribution Functions](https://real-statistics.com/real-statistics-environment/real-statistics-distribution-functions/) - Summary of worksheet functions contained in the Real Statistics Resource Pack that support distributions and parametric tests.
- [Appendix](https://real-statistics.com/appendix/) - The Appendix provides useful background information as well as some summaries of features covered elsewhere in the website.
- [Correlation and Reliability Functions](https://real-statistics.com/real-statistics-environment/correlation-and-reliability-functions/) - Summary of various correlation and reliability statistics functions that are contained in the Real Statistics Resource Pack.
- [Real Statistics Bayesian Analysis Functions](https://real-statistics.com/real-statistics-environment/real-statistics-bayesian-analysis-functions/) - Briefly describes all the Real Statistics worksheet functions related to Bayesian statistical analysis and provides links for more information about each one
- [Free Download](https://real-statistics.com/free-download/) - Access to free download of the Real Statistics Resource Pack and Real Statistics Examples Workbook. One can also purchase the Real Statistics using Excel book.
- [Real Statistics Worksheet Examples](https://real-statistics.com/real-statistics-environment/excel-worksheet-examples/) - Access to a free download of an Excel workbook containing all the worksheets that implement the various tests and analyses described in the rest of the website.
- [Synchronization of Real Statistics Examples Workbook](https://real-statistics.com/real-statistics-environment/excel-worksheet-examples/examples-synchronization/) - Describes how to install a Real Statistics examples workbook so that it synchronizes with the Real Statistics Resource pack add-in.
- [MA(q) Process Basic Concepts](https://real-statistics.com/time-series-analysis/moving-average-processes/ma-process-basic-concepts/) - Describes key properties of moving average processes and time series, and shows how to simulate an MA(q) process in Excel.
- [Correlogram](https://real-statistics.com/time-series-analysis/stochastic-processes/correlogram/) - Describes how to construct an ACF correlogram and PACF correlogram in Excel that includes confidence intervals. Examples and software are provides.
- [Time Series Testing Tools](https://real-statistics.com/time-series-analysis/stochastic-processes/time-series-testing-tools/) - Describes how to use the Real Statistics Time Series Testing data analysis tools in Excel to compute ACF/PACF, and conduct ADF, Ljung-Box and Bartlett's tests.
- [Dickey-Fuller Test](https://real-statistics.com/time-series-analysis/stochastic-processes/dickey-fuller-test/) - Describes how to perform the Dickey-Fuller test to determine whether a time series has a unit root, and so is not stationary. Example and Excel add-in included.
- [Deterministic Trend](https://real-statistics.com/time-series-analysis/stochastic-processes/deterministic-trend/) - Describes the characteristics of linear deterministic trend time series and how to detrend them in Excel to create a stationary time series.
- [Author](https://real-statistics.com/appendix/author/) - Provides a brief profile of Charles Zaiontz, the author of the website and of the Real Statistics statistical analysis program using Excel.
- [Random Walk](https://real-statistics.com/time-series-analysis/stochastic-processes/random-walk/) - Describes random walk time series and their characteristics using Excel capabilities. Explains how to test for a random walk.
- [Purely Random Time Series](https://real-statistics.com/time-series-analysis/stochastic-processes/purely-random-time-series/) - Describes purely random (white noise) time series. Shows how to test for white noise in Excel and describes their characteristics.
- [Stationary Process](https://real-statistics.com/time-series-analysis/stochastic-processes/stationary-process/) - Defines stationary stochastic processes and time series. Describes some characteristics of stationary processes. Gives examples in Excel.
- [Basic Time Series Forecasting](https://real-statistics.com/time-series-analysis/basic-time-series-forecasting/) - Tutorial on basic time series forecasting methods in Excel. Includes examples and software for moving average, exponential smoothing, Holt, Holt-Winter.
- [Forecasting Accuracy](https://real-statistics.com/time-series-analysis/forecasting-accuracy/) - Tutorial on forecasting accuracy. We describe approaches for determining the accuracy of a forecast and whether one forecast is more accurate than another.
- [Calculate ARMA(p,q) coefficients using maximum likelihood](https://real-statistics.com/time-series-analysis/arma-processes/arma-coefficients-maximum-likelihood/) - Describes how to use maximum likelihood estimation (MLE) techniques to calculate the coefficients of an autoregression moving average process, ARMA(p,q).
- [Alternative approach to multiple regression analysis](https://real-statistics.com/multiple-regression/multiple-regression-analysis/alternative-approach-multiple-regression-analysis/) - We describe an alternative approach to performing multiple regression analysis in Excel using the F-test. Includes some theory and an example.
- [Multiple Regression Analysis Theory](https://real-statistics.com/multiple-regression/multiple-regression-analysis/multiple-regression-analysis-detailed/) - Provides proofs of properties related to multiple regression analysis. Includes the proof that the usual least-squares estimate of the coefficients is unbiased.
- [Regression Analysis - Advanced](https://real-statistics.com/regression/regression-analysis/regression-analysis-advanced/) - Provides the proofs of key properties about Linear Regression Analysis.
- [Regression Analysis](https://real-statistics.com/regression/regression-analysis/) - General principles of regression analysis, including the linear regression model, predicted values, residuals and standard error of the estimate.
- [Fitting Poisson Distribution](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-poisson-distribution/) - Describes how to estimate the lambda parameter of a Poisson distribution that best fits a data set using MoM and MLE in Excel. Includes examples and software.
- [Expectation](https://real-statistics.com/general-properties-of-distributions/expectation/) - Describes the concept of mathematical expectation and its relationship to mean, variance, moments, skewness and kurtosis.
- [Normal Approximation to Binomial Distribution](https://real-statistics.com/binomial-and-related-distributions/relationship-binomial-and-normal-distributions/) - Describes how the binomial distribution can be approximated by the standard normal distribution; also shows this graphically.
- [Outliers and Influencers](https://real-statistics.com/multiple-regression/outliers-and-influencers/) - How to identify outliers anf influencers for multiple regression models in Excel, including the concepts of Cook's distance, DFFITS and studentized residuals.
- [Data Conversion and Reformatting](https://real-statistics.com/real-statistics-environment/data-conversion/) - Reformatting data in Excel (sorting, resizing, removing empty cells, deleting missing data, etc.) and converting from raw sample data to a frequency table.
- [Regression Forecasts with Seasonality](https://real-statistics.com/multiple-regression/multiple-regression-analysis/seasonal-regression-forecasts/) - Describes how to perform a forecast with seasonality using Excel. Example is given showing how it is done using categorical variables.
- [Categorical Coding for Regression](https://real-statistics.com/multiple-regression/multiple-regression-analysis/categorical-coding-regression/) - Describes how to handle categorical variables in linear regression by using dummy variables. Implements these in an Excel add-in. Examples given.
- [Comparing the slopes for two independent samples](https://real-statistics.com/regression/hypothesis-testing-significance-regression-line-slope/comparing-slopes-two-independent-samples/) - Using Excel to perform hypothesis testing to determine whether the regression lines which model two independent samples have the same slope.
- [Real Statistics Support for WLS regression](https://real-statistics.com/multiple-regression/weighted-linear-regression/real-statistics-support-for-wls-regression/) - Describes how to use the Real Statistics Weighted Linear Regression data analysis tool and Excel-based functions provided by the Real Statistics Resource Pack.
- [WLS regression and heteroskedasticity](https://real-statistics.com/multiple-regression/weighted-linear-regression/wls-regression-and-heteroskedasticity/) - Describes how to address heteroskedasticity by using weighted least-squares (WLS) regression. Numerous examples are given. Excel software is provided.
- [Real Statistics support for Mediation Analysis](https://real-statistics.com/multiple-regression/mediation-analysis/mediation-analysis-tool/) - Describes how to use the Real Statistics Mediation Analysis data analysis tool to perform Mediation Analysis in Excel based on the approach of Baron and Kenny.
- [Linear regression models for comparing means](https://real-statistics.com/regression/linear-regression-models-for-comparing-means/) - How to use the techniques of regression to perform hypothesis testing of the mean (t-test). Also provides alternative effect size measure.
- [Power Regression](https://real-statistics.com/regression/power-regression/) - Describes how to perform power regression in Excel using Excel's regression data analysis tool after a log-log transformation.
- [Using Real Statistics Tools](https://real-statistics.com/real-statistics-environment/using-real-statistics-tools/) - Describes how to use the dialog boxes to access the various data analysis tools provided in the Real Statistics Resource Pack.
- [Real Statistics Exponential Regression Capabilities](https://real-statistics.com/regression/exponential-regression-models/real-statistics-exponential-regression-functions/) - Describes the Real Statistics functions and data analysis tool that calculate the coefficients and predicted values for nonlinear exponential regression.
- [Exponential Regression using Newton's Method](https://real-statistics.com/regression/exponential-regression-models/exponential-regression-newtons-method/) - Describes how to construct a nonlinear exponential regression model using Newton's Method. Examples and software provided.
- [Exponential Regression using Solver](https://real-statistics.com/regression/exponential-regression-models/exponential-regression-using-solver/) - Describes how to use Excel's Solver to construct a nonlinear exponential regression model. Examples and software provided.
- [Exponential Regression Models](https://real-statistics.com/regression/exponential-regression-models/) - Describes three models for performing exponential regression in Excel: linear and nonlinear. Software and examples are provided.
- [Exponential Regression using a Linear Model](https://real-statistics.com/regression/exponential-regression-models/exponential-regression/) - How to perform exponential regression in Excel using built-in functions (LOGEST, GROWTH) and Excel's regression data analysis tool after a log transformation.
- [Confidence and prediction intervals for forecasted values](https://real-statistics.com/regression/confidence-and-prediction-intervals/) - Defines the confidence interval and prediction interval for a simple linear regression and describes how to calculate these values in Excel.
- [Testing the significance of the slope of the regression line](https://real-statistics.com/regression/hypothesis-testing-significance-regression-line-slope/) - How to test the significance of the slope of the regression line, in particular to test whether it is zero. Example of Excel's regression data analysis tool.
- [Fit of the Regression Line](https://real-statistics.com/regression/hypothesis-testing-regression-good-fit/) - We show how to determine in Excel whether the linear regression line is a good fit for some data. We provide an example of how this is done in Excel.
- [Method of Least Squares](https://real-statistics.com/regression/least-squares-method/) - How to apply the method of least squares in Excel to find the regression line which best fits a collection of data pairs.
- [t Distribution - Advanced](https://real-statistics.com/students-t-distribution/t-distribution-basic-concepts/t-distribution-advanced/) - Proof of Theorem 1 from Basic Concepts of t Distribution using calculus, plus another key property of t distributions and chi-square.
- [Accessing Real Statistics Data Analysis Tools](https://real-statistics.com/real-statistics-environment/accessing-supplemental-data-analysis-tools/) - How to access the Real Statistics data analysis tools via keyboard shortcut or Add-Ins ribbon. Explains how to install a new icon on the Quick Access toolbar.
- [Two within-subjects factors](https://real-statistics.com/anova-repeated-measures/two-within-subjects-factors/) - Describes how to perform in Excel ANOVA with repeated measures with two within-subjects factors, as well as planned and unplanned follow-up tests.
- [Fitting a Triangular Distribution via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-a-triangular-distribution-via-mle/) - Describes how to estimate the a, b, and c parameters of the triangular distribution that fits a set of data using the MLE approach in Excel.
- [Multivariate Regression Prediction Intervals](https://real-statistics.com/multivariate-statistics/multivariate-regression-analysis/multivariate-regression-prediction-intervals/) - Describes key properties of a multivariate regression prediction interval. Shows how to calculate this in Excel, providing examples.
- [Gaussian Mixture Models](https://real-statistics.com/multivariate-statistics/gaussian-mixture-models/) - Tutorial on Gaussian Mixture Models (GMM) and how to construct them in Excel using the EM algorithm. Examples examples and software tools are provided.
- [Cluster Analysis Proof](https://real-statistics.com/multivariate-statistics/cluster-analysis/k-means-cluster-analysis/cluster-analysis-proof/) - Provides a proof of Property 1 of k-means cluster analysis, namely providing the best choice of centroids for minimizing SSE.
- [Method of Least Squares Detailed](https://real-statistics.com/regression/least-squares-method/least-squares-method-detailed/) - Presents two proofs of the Method of Least squares. One proof uses calculus and the other proof doesn't require knowledge of calculus.
- [Linear Regression](https://real-statistics.com/regression/) - How to construct and use linear regression models in Excel. Also explores exponential regression and ANOVA based on regression, includes free software.
- [Statistical Symbols](https://real-statistics.com/mathematical-notation/statistical-symbols/) - Describes the symbols used throughout the website. Includes when we use capital and small Latin letters, as well as Greek letters. Also how do we use the tilde.
- [Exponentials and Logarithms](https://real-statistics.com/mathematical-notation/exponentials-logs/) - Presents the definition of exponential and logarithm, as well as describing the basic properties of exponentials and logs
- [Conflict between Real Statistics and Solver](https://real-statistics.com/appendix/faqs/conflict-between-real-statistics-and-solver/) - Describes how to make sure that Solver loads before Real Statistics, namely make sure that the file names are in the correct alphabetic order.
- [Sum and Product Notation](https://real-statistics.com/mathematical-notation/sigma-product-notation/) - Provides a number of examples of sum and product notation. Uses capital sigma and double sigma notation for sums and capital pi for products.
- [Combinatorial functions](https://real-statistics.com/mathematical-notation/combinatorial-functions/) - Shows how to compute the various combinatorial functions (combination, permutation, and factorial). Simple examples are provided.
- [Functions, polynomials, limits and graphs](https://real-statistics.com/mathematical-notation/functions-polynomials-limits-graphs/) - Describes basic properties of functions and their graphs, especially polynomial and linear functions, as well as limits of functions and series.
- [General Properties of Distributions](https://real-statistics.com/general-properties-of-distributions/) - Describes general characteristics of probability distributions, including expectation, estimators, moments and moment generating functions.
- [Real Statistics Functions and Analysis Tools](https://real-statistics.com/free-download/real-statistics-software/) - Provides a summary of all the supplemental functions and data analysis tools contained in the Real Statistics Resource Pack.
- [License Agreement](https://real-statistics.com/free-download/license-agreement/) - Provides a link to enable the use to download the License Agreement for Real Statistics Resource Pack. Users must agree to this license to use the addin.
- [Notifications](https://real-statistics.com/free-download/notifications/)
- [Estimators - Advanced](https://real-statistics.com/general-properties-of-distributions/estimators/estimators-advanced/) - We provide a poof of Property 3 of Estimators, namely that the sample variance is an unbiased estimator of the population variance.
- [Finding Logistic Regression Coefficients using Excel’s Solver](https://real-statistics.com/logistic-regression/finding-logistic-regression-coefficients-using-excels-solver/) - Describes how to use Excel's Solver tool to find the coefficients for the logistic regression model. A example is provided to show how this is done
- [Brown-Forsythe F* Test for Two-way ANOVA](https://real-statistics.com/two-way-anova/two-factor-anova-with-replication/brown-forsythe-f-test-two-way-anova/) - Brief description of the Brown-Forsythe F* Test for two-way analysis of variances (ANOVA). The focus is on the correct degrees of freedom.
- [Names and Tables](https://real-statistics.com/excel-environment/names-and-tables/) - Brief overview of defined names and tables in Excel. Describes how to create and use defined names, tables and Pivot tables in Excel.
- [Excel Capabilities](https://real-statistics.com/excel-capabilities/) - Describes Excel functions and other capabilities that are useful for statistical analysis. Includes pure Excel substitutes for Real Statistics functions.
- [Data Transformations](https://real-statistics.com/descriptive-statistics/data-transformations/) - Describes how transformations (e.g. log, inverse, square root, square, ets.) can be used to overcome violations of test assumptions.
- [Password Prompt](https://real-statistics.com/appendix/faqs/password-prompt/) - Describes what you should do if you receive a request for a password when trying to use the Real Statistics Resource Pack.
- [Multinomial Logistic Regression](https://real-statistics.com/multinomial-ordinal-logistic-regression/) - Tutorial on multinomial logistic regression, Models are built using Excel's Solver and Newton's method. Excel examples and analysis tools are provided.
- [Multinomial regression using binary logistic regression](https://real-statistics.com/multinomial-ordinal-logistic-regression/multinomial-regression-using-binary-logistic-regression/) - Describes how to estimate the multinomial logistic regression model coefficients by using multiple binary logistic regression models. Excel example is provided.
- [Multinomial Logistic Regression Forecasts](https://real-statistics.com/multinomial-ordinal-logistic-regression/multinomial-regression-using-binary-logistic-regression/multinomial-logistic-regression-forecasts/) - Describes how to obtain forecasts based on multinomial logistic regression models. We provide examples in Excel along with explanations.
- [Sample Size for t Test based on Confidence Interval](https://real-statistics.com/students-t-distribution/sample-size-t-test-using-confidence-interval/) - Describes the sample size required for a one-sample t test based on the width of the confidence interval. Show how to do this using Excel's Goal Seek.
- [Confidence Interval for Coefficient of Variation](https://real-statistics.com/students-t-distribution/confidence-interval-coefficient-of-variation/) - Describes how to calculate a confidence interval for the coefficient of variation in Excel using the Kelley, Naive, McKay and Vangel approaches.
- [Confidence Intervals for Effect Size and Power](https://real-statistics.com/students-t-distribution/confidence-interval-effect-size-power/) - Describes how to calculate a confidence interval for effect size, noncentrality parameter and statistcial power for the t test in Excel. Examples and software.
- [Grubbs' Test Data Analysis Tool](https://real-statistics.com/students-t-distribution/identifying-outliers-using-t-distribution/grubbs-test-data-analysis-tool/) - Describes how to use the Grubbs option of the Real Statistics Descriptive Statistics data analysis tool to carry out Grubbs' test and ESD test in Excel.
- [Identifying Outliers using t Distribution](https://real-statistics.com/students-t-distribution/identifying-outliers-using-t-distribution/) - Tutorial on how to identify outliers using Grubbs' test and its extensions (i.e. the ESD test) in Excel. Software and examples.
- [Studentized Range Distribution](https://real-statistics.com/students-t-distribution/studentized-range-distribution/) - Brief introduction to the studentized range distribution and how to calculate its values and its critical values in Excel.
- [Statistical Power of the t tests](https://real-statistics.com/students-t-distribution/statistical-power-of-the-t-tests/) - Describes how to use the noncentral t distribution to compute the power of t tests. Examples and Excel add-in software are provided.
- [Fitted Parameters Confidence Interval](https://real-statistics.com/distribution-fitting/distribution-fitting-confidence-intervals/fitted-parameters-confidence-interval/) - Describes how to use bootstrapping simulation to estimate the confidence interval of estimated distribution parameters Incl. Excel examples & software.
- [Multiple t-Tests](https://real-statistics.com/students-t-distribution/two-independent-samples-t-test/multiple-t-tests/) - Describes how to perform multiple independent sample t-tests in Excel while taking care of familywise error. Examples and Excel capabilities are provided.
- [Two Sample t-Test Proof](https://real-statistics.com/students-t-distribution/two-independent-samples-t-test/two-sample-t-test-advanced/) - Provides a proof of Property 1 of Two Sample t-Test with Equal Variances, which is the basis of hypothesis testing of two independent samples.
- [T-test Analysis Tool](https://real-statistics.com/students-t-distribution/two-independent-samples-t-test/t-test-analysis-tool/) - Describes how to use the Real Statistics data analysis tool to conduct a two independent sample t-test in Excel. Examples are provided.
- [Hazard Ratio](https://real-statistics.com/survival-analysis/kaplan-meier-procedure/hazard-ratio/) - Describes how to calculate the hazard ratio for two samples based on the Kaplan-Meier procedure. Examples are provided in Excel.
- [Alternative Kaplan-Meier Comparison Tests](https://real-statistics.com/survival-analysis/kaplan-meier-procedure/kaplan-meier-comparison-tests/) - Describes how to test whether two samples have significantly different survival distributions. Includes example and Excel software.
- [Hazard Function](https://real-statistics.com/survival-analysis/kaplan-meier-procedure/hazard-function/) - Describes how to calculate the hazard function and cumulative hazard function for Kapan-Meier. We also describe the standard error of the hazard function.
- [Basic Concepts of Survival Analysis](https://real-statistics.com/survival-analysis/survival-analysis-basic-concepts/) - Describes the main concepts in Survival Analysis, including censoring (left, right, interval), survivor function, and hazard function.
- [Survival Curve](https://real-statistics.com/survival-analysis/kaplan-meier-procedure/survival-curve/) - Describes how to create a step chart in Excel containing the survival curve for S(t) from the Kaplan-Meier procedure. Provides an example.
- [Cox Regression Residuals](https://real-statistics.com/survival-analysis/cox-regression/cox-regression-residuals/) - Describes the various types of residuals that can be used with Cox Regression to identify potential outliers and test the proportional hazards assumption.
- [Cox Regression Theory](https://real-statistics.com/survival-analysis/cox-regression/cox-regression-theory/) - Provides some of the mathematical basis for Cox Regression, especially the proofs of some of the properties. Requires calculus background.
- [Real Statistics Capabilities for Cox Regression](https://real-statistics.com/survival-analysis/cox-regression/real-statistics-capabilities-for-cox-regression/) - Describes the functions and data analysis tools for performing Cox Regression in Excel. Examples and Excel software are included.
- [Cox Regression Models with Multiple Deaths per Time Period](https://real-statistics.com/survival-analysis/cox-regression/cox-regression-models-ties/) - Describes how to deal with multiple deaths in time intervals in Cox Regression, incl. Breslow and Efron estimates. Includes examples and Excel software.
- [Cox Regression](https://real-statistics.com/survival-analysis/cox-regression/) - Describes how to create a Cox proportional hazards model (Cox Regression). In Excel. Examples and Excel software are included.
- [Determining the Fit of a Cox Regression Model](https://real-statistics.com/survival-analysis/cox-regression/cox-regression-model-fit/) - Describes how to determine the goodness-of-fit of a Cox regression model using chi-square. Examples and Excel software are included.
- [Cox Regression using Newton's Method](https://real-statistics.com/survival-analysis/cox-regression/cox-regression-using-newtons-method/) - Describes how to perform Cox proportional hazard method (Cox's regression) in Excel. Includes examples and Excel add-in software.
- [Cox Regression using Solver](https://real-statistics.com/survival-analysis/cox-regression/cox-regression-solver/) - Describes how to perform Cox's proportional hazard model (Cox's regression) in Excel using Solver. Examples and Excel software are included.
- [Cox Regression Basic Concepts](https://real-statistics.com/survival-analysis/cox-regression/cox-regression-basic-concepts/) - Describes the basic concepts of Cox Proportional Hazard Regression, including concepts such as hazard ratio and relative risk.
- [Fitting GEV Distribution via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-gev-distribution-mle/) - Describes how to find GEV distribution parameters that best fit a data set using maximum likelihood estimation (MLE) in Excel. Incl. examples & software.
- [Method of Moments: GEV Distribution](https://real-statistics.com/distribution-fitting/method-of-moments/method-of-moments-gev-distribution/) - Describes how to estimate the mu, sigma and xi parameters of the GEV distribution that best fits a set of data using the method of moments in Excel.
- [Real Statistics Multinomial Logistic Regression Capabilities](https://real-statistics.com/multinomial-ordinal-logistic-regression/real-statistics-functions-multinomial-logistic-regression/) - Describes the functions and data analysis tool in the Real Statistics Resource Pack (Excel add-in) to create Multinomial Logistics Regression models in Excel.
- [Finding multinomial logistic regression coefficients using Newton's method](https://real-statistics.com/multinomial-ordinal-logistic-regression/finding-multinomial-logistic-regression-coefficients-using-newtons-method/) - Describe how to create a multinomial logistic regression model using Newton's Method. An Excel add-in is also provided to carry out the calculations.
- [Finding multinomial logistic regression coefficients using Solver](https://real-statistics.com/multinomial-ordinal-logistic-regression/finding-multinomial-logistic-regression-coefficients-using-solver/) - Describe how to calculate multinomial logistic regression coefficients and create a multinomial logistic regression model using Excel's Solver.
- [Basic Concepts of Multinomial Logistic Regression](https://real-statistics.com/multinomial-ordinal-logistic-regression/basic-concepts-of-multinomial-logistic-regression-basic-concept/) - Describes basic concepts of multinomial logistic regression, their connection to binary logistic regression, & the use of Newton's method to find coefficients.
- [Real Statistics Probit Capabilities](https://real-statistics.com/logistic-regression/probit-regression/real-statistics-probit-capabilities/) - Describes the various Probit regression functions supported by the Real Statistics add-in, as well as the Probit data analysis tool for use in Excel.
- [Logistic Regression Sample Size (Binary)](https://real-statistics.com/logistic-regression/logistic-regression-sample-size/logistic-regression-sample-size-binary/) - Describes how to estimate the minimum sample size required for logistic regression with a binary independent variable that is binomially distributed.
- [Logistic Regression Sample Size](https://real-statistics.com/logistic-regression/logistic-regression-sample-size/) - Describes how to estimate the minimum sample size required for logistic regression with a continuous independent variable that is normally distributed.
- [Two Random Factors ANOVA](https://real-statistics.com/anova-random-nested-factors/two-random-factors-anova/) - Describes how to calculate ANOVA for two random factors in Excel. Excel examples are provided as is a data analysis tool for doing this.
- [Two Mixed Factors ANOVA](https://real-statistics.com/anova-random-nested-factors/two-factor-mixed-anova/) - Describes how to calculate ANOVA for one fixed factor and one random factor (mixed model) in Excel. Examples and software provided.
- [One Random Factor ANOVA](https://real-statistics.com/anova-random-nested-factors/one-random-factor-anova/) - Describes how to calculate ANOVA for one random factor in Excel, including estimates of the population mean and between group and error variances.
- [Follow-up to Latin Squares](https://real-statistics.com/design-of-experiments/latin-squares-design/follow-up-to-latin-squares/) - Describes how to conduct follow-up testing for Latin Squares design in Excel. Includes contrasts and Tukey's HSD. Software and examples are provided.
- [Latin Squares Tools](https://real-statistics.com/design-of-experiments/latin-squares-design/latin-squares-tools/) - Describes how to analyze Latin Squares designs in Excel. A data analysis tool that carries out such calculations is included.
- [Latin Squares with Replication](https://real-statistics.com/design-of-experiments/latin-squares-design/latin-squares-with-replication/) - Describes how to analyze Latin Squares designs with replication in Excel. Examples are provided to carry out the analysis in Excel.
- [Repeated Measures ANOVA using Regression](https://real-statistics.com/anova-repeated-measures/repeated-measures-anova-using-regression/) - Tutorial on how to use regression to perform repeated measures ANOVA analyses in Excel. This is especially useful for unbalanced mixed designs. Incl. examples.
- [Latin Squares with Missing Data](https://real-statistics.com/design-of-experiments/latin-squares-design/latin-squares-missing-data/) - Describes how to analyze Latin Squares when one data element is missing. Provides an example of how to carry out the analysis in Excel.
- [Latin Squares Design](https://real-statistics.com/design-of-experiments/latin-squares-design/) - Describes when to use a Latin Squares design and how to conduct the analysis of such a design in Excel. Includes examples and software.
- [Split-plot Follow-up Tests](https://real-statistics.com/design-of-experiments/split-plot-design/split-plot-follow-up-tests/) - Describes how to perform follow-up tests to split-plot Anova in Excel: contrasts and Tukey HSD. Includes examples and software.
- [Alternative Split-plot Models](https://real-statistics.com/design-of-experiments/split-plot-design/alternative-split-plot-models/) - Describes some alternative split-plot models, including whole plots using a completely randomized design. Examples and software are included.
- [Split-plot Tools](https://real-statistics.com/design-of-experiments/split-plot-design/split-plot-tools/) - Describes how to use data analysis tools to analyze split-plot designs in Excel using ANOVA. Examples and software are provided.
- [Split-plot Design](https://real-statistics.com/design-of-experiments/split-plot-design/) - Tutorial on split-plot design. Describes how to analyze a split-plot design. Includes examples and software for the Excel environment
- [RCBD with one missing data element](https://real-statistics.com/design-of-experiments/completely-randomized-design/rcbd-one-missing-data-element/) - Describes how to perform randomized complete block design (RCBD) in Excel when there is one missing data element (handled via imputation).
- [RCBD with missing data using regression](https://real-statistics.com/design-of-experiments/completely-randomized-design/rcbd-missing-data-regression/) - Describes how to perform a randomized complete block design (RCBD) in Excel using a regression model when there is missing data. Incl. examples and software.
- [RCBD with missing data analysis tool](https://real-statistics.com/design-of-experiments/completely-randomized-design/rcbd-missing-data-analysis-tool/) - Describes how to use the Real Statistics Randomized Complete Block Design data analysis to to perform RCBD with missing data using regression.
- [RCBD with Replications](https://real-statistics.com/design-of-experiments/completely-randomized-design/rcbd-with-replications/) - Describes how to perform Randomized Complete Block Design (RCBD) with replications in Excel using Two Factor ANOVA with Replications.
- [RCBD using Regression](https://real-statistics.com/design-of-experiments/completely-randomized-design/rcbd-using-regression/) - Describes how to perform randomized complete block design using regression. Excel example and data analysis tool are provided.
- [Efficiency of RCBD vs. CRD](https://real-statistics.com/design-of-experiments/completely-randomized-design/efficiency-rcbd-vs-crd/) - Describes the greater efficiency obtained from a randomized complete block design in comparison to a completely randomized design.
- [Multivariate Regression Analysis Basic Concepts](https://real-statistics.com/multivariate-statistics/multivariate-regression-analysis/multivariate-regression-analysis-basic-concepts/) - Begins the tutorial on multivariate regression. Includes various properties and describes the relationship with multiple regression.
- [Multivariate Regression Proofs](https://real-statistics.com/multivariate-statistics/multivariate-regression-analysis/multivariate-regression-analysis-basic-concepts/multivariate-regression-proofs/) - Provides proofs of basic properties about multivariate regression. Relates many of these to properties about multiple regression.
- [Correlation - Proofs](https://real-statistics.com/correlation/basic-concepts-correlation/correlation-advanced/) - Provides an additional property of correlation and covariance, and includes proofs of properties given in Basic Concepts of Correlation
- [Introduction](https://real-statistics.com/introduction/) - Review this objectives of this website, describe briefly how the website is organized and give a quick overview of basic statistical concepts.
- [Matrix Operations](https://real-statistics.com/matrices-and-iterative-procedures/matrix-operations/) - Describes how to use various matrix operations (e.g. multiplication, addition, inverse, transpose, QR decomposition, eigenvalues and vectors, etc.) in Excel.
- [WLS regression via OLS regression through the origin](https://real-statistics.com/multiple-regression/weighted-linear-regression/wls-regression-via-ols-regression-thru-the-origin/) - Describes how to address heteroscedasticity by using a version of weighted regression based on OLS regression thru the origin. Examples & software are provided
- [Analysis of Covariance (ANCOVA)](https://real-statistics.com/analysis-of-covariance-ancova/) - Tutorial on Analysis of Covariance (ANOVA). Describes how to conduct this test in Excel and what to do when the assumptions of the test are violated.
- [Introduction to Real Statistics using Excel](https://real-statistics.com/introduction/introduction-statistics-excel/) - Tutorial on statistics and free download of Real Statistics add-in software to do statistical analysis (formulas, calculations, tools) in Excel.
- [Weighted Regression Basics](https://real-statistics.com/multiple-regression/weighted-linear-regression/weighted-regression-basics/) - Describes the basic characteristics of weighted linear regression. Explains how to perform this type of regression in Excel. Examples are provided,
- [Confidence and Prediction Intervals](https://real-statistics.com/multiple-regression/confidence-and-prediction-intervals/) - Describes how to calculate the confidence and prediction intervals for multiple regression in Excel. Software and examples included.
- [Confidence Intervals for Multivariate Regression Coefficients](https://real-statistics.com/multivariate-statistics/multivariate-regression-analysis/confidence-intervals-for-multivariate-regression-coefficients/) - Describes two approaches for calculating confidence intervals for multivariate regression coefficients: simulataneous and individual. Includes Excel examples.
- [Real Statistics Capabilities for Multiple Regression](https://real-statistics.com/multiple-regression/multiple-regression-analysis/real-statistics-capabilities-for-multiple-regression/) - Describes the capabilities provided by the Real Statistics Resource Pack in support of multiple regression. Software and examples provided.
- [Real Statistic Support for Multivariate Regression Testing](https://real-statistics.com/multivariate-statistics/multivariate-regression-analysis/multivariate-regression-hypothesis-testing/real-statistic-support-for-multivariate-regression/) - Describes various Excel worksheet functions provided by Real Statistics that support multivariate regression hypothesis testing. Excel examples are provided.
- [LASSO Regression](https://real-statistics.com/multiple-regression/ridge-and-lasso-regression/lasso-regression/) - Describes how to calculate the LASSO regression coefficients and LASSO Trace in Excel. Example and software are provided.
- [Negative Binomial and Geometric Distributions](https://real-statistics.com/binomial-and-related-distributions/negative-binomial-and-geometric-distributions/) - How to use the negative binomial and geometric distributions to solve problems related to the binomial distribution in Excel.
- [PLS Regression Bootstrapping](https://real-statistics.com/multivariate-statistics/multivariate-regression-analysis/partial-least-squares-pls-regression/pls-regression-bootstrapping/) - Describes Excel worksheet functions in the Real Statistics Resource Pack to support bootstrapping for PLS regression models. Examples are provided.
- [Matrix Operations Tool](https://real-statistics.com/matrices-and-iterative-procedures/matrix-operations/matrix-operations-tool/) - Describes how to use the Real Statistics Matrix Operations data analysis tool. Examples are provided for how to perform these operations in Excel.
- [Comparing correlation coefficients of non-overlapping dependent samples](https://real-statistics.com/correlation/two-sample-hypothesis-testing-correlation/correlations-non-overlapping-dependent-samples/) - How to perform hypothesis testing in Excel to determine whether the correlation coefficients of 2 non-overlapping dependent samples are significantly different.
- [ANOVA Analysis Tool and Confidence Intervals](https://real-statistics.com/one-way-analysis-of-variance-anova/confidence-interval-anova/) - Demonstrates the Real Statistics One-way ANOVA data analysis tool and how to calculate the confidence interval for ANOVA in the Excel environment.
- [Contrasts for ANCOVA](https://real-statistics.com/analysis-of-covariance-ancova/contrasts-ancova/) - Describes how to use planned comparisons (i.e. contrasts) to perform post hoc testing after a significant omnibus analysis of variance (ANCOVA).
- [ANCOVA Analysis Tools](https://real-statistics.com/analysis-of-covariance-ancova/ancova-analysis-tools/) - Describes how to perform ANCOVA and follow-up testing using contrasts and Tukey's HSD in Excel using the Real Statistics add-in.
- [ANOVA approach to ANCOVA](https://real-statistics.com/analysis-of-covariance-ancova/anova-approach-ancova/) - How to perform analysis of covariance (ANCOVA) in Excel using ANOVA tools built into Excel. Examples and special software provided.
- [Method of Moments: Weibull Distribution](https://real-statistics.com/distribution-fitting/method-of-moments/method-of-moments-weibull/) - Describes how to estimate the lambda parameter of the Weibull distribution that fits a set of data using the method of moments in Excel.
- [Statistical Divergence](https://real-statistics.com/distribution-fitting/statistical-divergence/) - Describes three types of divergence: Kullback-Leibler Divergence (KL), Jenson-Shannon Divergence, and the divergence statistic used for credit scoring
- [Credit Scoring Divergence](https://real-statistics.com/descriptive-statistics/divergence/credit-scoring-divergence/) - Describes a divergence measurement used for credit scoring, and shows how to calculate this in Excel. Includes an Excel example and worksheet function.
- [Real Statistics KS Test for Normality](https://real-statistics.com/tests-normality-and-symmetry/statistical-tests-normality-symmetry/lilliefors-test-normality/real-statistics-ks-test-for-normality/) - Describes how to perform the Kolmogorov-Smirnov test for normality in Excel, especially when the mean and standard deviation are estimated from the data.
- [Measures of Variability](https://real-statistics.com/descriptive-statistics/measures-variability/) - Describes measures of variability (dispersion) of a distribution around the mean or median, including variance, standard deviation and median absolute deviation
- [Polytomous Model Fit](https://real-statistics.com/reliability/item-response-theory/polytomous-model-fit/) - Describes how to test the fit of a polytomous UCON Rasch model in Excel. Includes how to calculate the infit and outfit values.
- [Kaplan-Meier Overview](https://real-statistics.com/survival-analysis/kaplan-meier-procedure/kaplan-meier-overview/) - Describes the basic ideas behind the Kaplan-Meier non-parametric approach to Survival Analysis. Includes an example in Excel
- [LAMBDA-based Functions](https://real-statistics.com/excel-environment/lambda-functions/lambda-based-functions/) - Describes how to use the following LAMBDA-based worksheet functions in Excel: BYROW, BYCOL, REDUCE, MAP, SCAN and MAKEARRAY.
- [Kendall's Correlation Testing using a Fisher Transformation](https://real-statistics.com/correlation/kendalls-tau-correlation/kendalls-correlation-testing-using-a-fisher-transformation/) - How to test in Excel whether a population's Kendall's tau is significantly different from some value using a Fisher transformation. Incl. example and software.
- [Truncated Normal Distribution](https://real-statistics.com/normal-distribution/truncated-normal-distribution/) - Describes the truncated normal distribution and how to calculate its pdf, cdf, inverse function and key properties in Excel
- [Basic Concepts of ANCOVA](https://real-statistics.com/analysis-of-covariance-ancova/basic-concepts-ancova/) - Tutorial on analysis of covariance (ANCOVA). Includes a definition of a covariate and introduces a key example that is used throughout this part of the website.
- [Assumptions for ANCOVA](https://real-statistics.com/analysis-of-covariance-ancova/assumptions-ancova/) - Describes how to test in Excel the assumptions for the use of ANCOVA, esp. testing homogeneity of regression line slopes.
- [Regression approach to ANCOVA](https://real-statistics.com/analysis-of-covariance-ancova/regression-approach-ancova/) - How to perform ANCOVA(analysis of covariance) in Excel by using linear regression. Shows how to create partial and complete models, as well as adjusted means.
- [MANOVA Effect Size](https://real-statistics.com/multivariate-statistics/multivariate-analysis-of-variance-manova/manova-effect-size/) - Provides a description of partial eta squared, a common measure of effect size for MANOVA, esp. for Wilks Lambda, Hotelling-Lawley Trace, Pillai-Bartlett Trace.
- [Multivariate Regression Bootstrapping](https://real-statistics.com/multivariate-statistics/multivariate-regression-analysis/multivariate-regression-bootstrapping/) - How to use bootstrapping in multivariate regression modelling to estimate standard errors & confidence/prediction intervals. Provides Excel examples & software
- [Bootstrapping Regression Models](https://real-statistics.com/multiple-regression/bootstrapping-regression/) - Describes how to use bootstrapping in regression modelling to estimate standard errors and confidence/prediction intervals. Provides Excel examples and software
- [Multivariate Regression Analysis](https://real-statistics.com/multivariate-statistics/multivariate-regression-analysis/) - Tutorial on Multivariate Linear Regression. Describes how to build such models in Excel. Also explains Partial Least Squares (PLS) Regression.
- [Probit Regression](https://real-statistics.com/logistic-regression/probit-regression/) - Describes probit regression and how to perform it in Excel. Examples and software are provided.
- [ARIMA Model Coefficients](https://real-statistics.com/time-series-analysis/arima-processes/arima-model-coefficients/) - Describes how to use Excel's Solver to find model coefficients for a specified ARIMA(p,q,d) model. Software and examples are also provided.
- [Forecasting using an ARMA model](https://real-statistics.com/time-series-analysis/arma-processes/forecasting-arma/) - Describes how to build a forecast for a time series based on an ARMA model. We show how to do this using a specific example in Excel.
- [ARMA Tool Options](https://real-statistics.com/time-series-analysis/arma-processes/arma-tool-options/) - Demonstrates how to use various options of the Real Statistics ARIMA data analysis tool to build an ARMA model in Excel and use it for forecasting.
- [Calculate ARMA(p,q) coefficients using Solver](https://real-statistics.com/time-series-analysis/arma-processes/arma-coefficients-solver/) - Describes how to use Solver to calculate the coefficients of an ARMA(p,q) process or time series. Examples and software are provided.
- [Evaluating the ARMA model](https://real-statistics.com/time-series-analysis/arma-processes/evaluating-the-arma-model/) - Describes how to evaluate an ARMA model by using descriptive statistics, significance testing of model coefficients and use of AIC and BIC statistics.
- [Multivariate Regression Testing Example](https://real-statistics.com/multivariate-statistics/multivariate-regression-analysis/multivariate-regression-hypothesis-testing/multivariate-regression-testing-example/) - Provides an Example example about how to test whether a multivariate regression model provides any significant utility in predicting dependent variables
- [Multivariate Regression Hypothesis Testing](https://real-statistics.com/multivariate-statistics/multivariate-regression-analysis/multivariate-regression-hypothesis-testing/) - Tutorial on performing hypothesis testing for multivariate regression using MANOVA techniques to find if at least one regression coefficients is significant.
- [Testing a Subset of Multivariate Regression Coefficients](https://real-statistics.com/multivariate-statistics/multivariate-regression-analysis/multivariate-regression-hypothesis-testing/testing-a-subset-of-multivariate-regression-coefficients/) - Describes how to perform hypothesis testing for multivariate regression using MANOVA techniques. We test if some set of regression coefficients is significant.
- [Multivariate Normal Distribution Basic Concepts](https://real-statistics.com/multivariate-statistics/multivariate-normal-distribution/multivariate-normal-distribution-basic-concepts/) - Describes the multivariate normal distribution and various properties of this distribution. Also defines the Mahalanobis distance.
- [Eigenvectors in PLS Regression](https://real-statistics.com/multivariate-statistics/multivariate-regression-analysis/partial-least-squares-pls-regression/eigenvectors-in-pls-regression/) - We show how to apply concepts about eigenvalues/eigenvectors and SVD to creating a Partial Least Square Regression model. Excel example is provided.
- [PLS Regression Example](https://real-statistics.com/multivariate-statistics/multivariate-regression-analysis/partial-least-squares-pls-regression/pls-regression-example/) - Shows how to use the NIPALS algorithm in Excel to construct a PLS Regression model. provides a step by step example showing all the details.
- [PLS Regression: How many latent vectors?](https://real-statistics.com/multivariate-statistics/multivariate-regression-analysis/partial-least-squares-pls-regression/pls-regression-how-many-latent-vectors/) - Describes how to determine how many latent vectors to use to create a PLS Regression model: % variance explained and cross validation. Includes Excel examples.
- [Diebold-Mariano Test](https://real-statistics.com/time-series-analysis/forecasting-accuracy/diebold-mariano-test/) - Describes how to determine in Excel whether two time-series forecasts have significantly different accuracy by using the Diebold-Mariano test or HLN Test.
- [Two-Factor ART ANOVA](https://real-statistics.com/two-way-anova/aligned-rank-transform-art-anova/two-factor-art-anova/) - Describes how to perform Two-Factor Aligned Rank Transform (ART) ANOVA, a non-parametric approach to factorial ANOVA. Includes examples and software.
- [PLS Regression Basic Concepts](https://real-statistics.com/multivariate-statistics/multivariate-regression-analysis/partial-least-squares-pls-regression/pls-regression-basic-concepts/) - Describes the steps of the NIPALS (Nonlinear Iterative Partial Least Squares) algorithm used to construct a PLS Regression model.
- [Multiple Regression](https://real-statistics.com/multiple-regression/) - How to perform multiple regression in Excel, including effect size, residuals, collinearity, ANOVA via regression. Extra analyses provided by Real Statistics.
- [Multivariate Statistics](https://real-statistics.com/multivariate-statistics/) - Tutorial and software on multivariate statistics in the Excel, including multivariate normal distribution, Hotelling's test, Box's test, MANOVA, factor analysis
- [Confidence Ellipse](https://real-statistics.com/multivariate-statistics/multivariate-normal-distribution/confidence-ellipse/) - Describes how to create a confidence ellipse, using Excel charting capability, for data that follows a bivariate normal distribution. Includes examples.
- [Multiple Correlation](https://real-statistics.com/correlation/multiple-correlation/) - Shows how to calculate various measures of multiple correlation coefficient. Also reviews Excel's Correlation data analysis tool.
- [Multivariate Normality Testing (Mardia)](https://real-statistics.com/multivariate-statistics/multivariate-normal-distribution/multivariate-normality-testing/) - Describes Mardia's test for multivariate normality (both skewness and kurtosis tests) and shows how to carry out the test in Excel. Incl. example and software
- [Calculating MA Coefficients using Solver](https://real-statistics.com/time-series-analysis/moving-average-processes/calculating-ma-coefficients-solver/) - Describes how to build an MA(q) model of a time series in Excel using Solver. An example is given of how to calculate the model coefficients
- [Fitting Lognormal Distribution Details](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-lognormal-distribution-via-mle/fitting-lognormal-distribution-details/) - Explains the derivation of the formulas for the log-likelihood function for a log-normal distribution, and how to estimate the mu and sigma parameters using MLE
- [Brown-Forsythe F* Test](https://real-statistics.com/one-way-analysis-of-variance-anova/brown-forsythe-f-test/) - How to perform Brown-Forsythe F* Test in Excel using the Real Statistics Single Factor ANOVA data analysis tool.
- [Fitting Lognormal Distribution via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-lognormal-distribution-via-mle/) - How to estimate lognormal distribution parameters that best fits a data set using maximum likelihood estimation (MLE) in Excel. Incl. examples and software.
- [Welch’s ANOVA Test](https://real-statistics.com/one-way-analysis-of-variance-anova/welchs-procedure/) - How to perform Welch's test for analysis of variances,when the homogeneity of variances assumption is not met, esp. with unequal sample sizes. Example. S/W.
- [Interactions for 4-level Taguchi Designs](https://real-statistics.com/design-of-experiments/taguchi-design-of-experiments/interactions-for-4-level-taguchi-designs/) - Provides a table with how to construct interactions of main effects factors for 4-level Taguchi design in Excel. Also provides examples
- [MANOVA Basic Concepts](https://real-statistics.com/multivariate-statistics/multivariate-analysis-of-variance-manova/manova-basic-concepts/) - Tutorial on how to perform mulativariate analysis of variance (MANOVA) in Excel, including Wilks lambda, Pillai-Bartlett Trace, Hotelling-Lawley Trace and Roy's
- [Taguchi Worksheet Functions and Analysis Tool](https://real-statistics.com/design-of-experiments/taguchi-design-of-experiments/taguchi-worksheet-functions-and-analysis-tool/) - Describes the Taguchi DOE data analysis tool provided by the Real Statistics Resource Pack plus the TOptimize and TInteract worksheet functions.
- [Taguchi Designs with Replication](https://real-statistics.com/design-of-experiments/taguchi-design-of-experiments/taguchi-designs-with-replication/) - Describes how to perform Taguchi DOE when output data is replicated (using means of replications). Provides examples in Excel.
- [Signal-to-Noise Ratio](https://real-statistics.com/design-of-experiments/taguchi-design-of-experiments/signal-to-noise-ratio/) - Describe the Signal-to-Noise Ratio and how to use it in Taguchi designs. An example in Excel in provided along with the formulas to calculate the S/N Ratio.
- [5-level Taguchi Designs](https://real-statistics.com/design-of-experiments/taguchi-design-of-experiments/5-level-taguchi-designs/) - Describes briefly how to perform Taguchi DOE in Excel using designs with 5 factors. The two supported designs are displayed.
- [4-level Taguchi Designs](https://real-statistics.com/design-of-experiments/taguchi-design-of-experiments/4-level-taguchi-designs/) - Describes the 4-level Taguchi designs supported by the Real Statistics Taguchi DOE data analysis tool. Includes basic characteristics of these designs
- [Taguchi 3-level Designs](https://real-statistics.com/design-of-experiments/taguchi-design-of-experiments/taguchi-3-level-designs/) - This webpage provides a list of all the supported 3-level Taguchi designs and the acceptable interactions between pairwise factors.
- [Taguchi Design of Experiments](https://real-statistics.com/design-of-experiments/taguchi-design-of-experiments/) - Tutorial on Taguchi Design of Experiments. Includes design examples, as well as software to implement the analysis in Excel.
- [Taguchi 2-level Designs](https://real-statistics.com/design-of-experiments/taguchi-design-of-experiments/taguchi-2-level-designs/) - Lists all the 2-level Taguchi designs used in the Real Statistics website along with the table of acceptable interactions for 2-level factors.
- [2-level Taguchi Design](https://real-statistics.com/design-of-experiments/taguchi-design-of-experiments/2-level-taguchi-design/) - Describes the supported Taguchi 2-level designs and provides an example of how to perform DOE using the L8 design in Excel.
- [One-Sample Anderson-Darling Test Table](https://real-statistics.com/statistics-tables/anderson-darling-test-table/) - A table of critical values for the one-sample Anderson-Darling test for generic, normal, gamma, Weibull, Gumbel, logistic, lognormal, exponential distributions.
- [Sorting and Filtering](https://real-statistics.com/excel-environment/sorting-filtering/) - A brief tutorial on how to sort, remove duplicates and filter in Excel. Numerous examples are provided which describe how these activities are carried out.
- [Sample Size Requirements for Multiple Regression](https://real-statistics.com/multiple-regression/multiple-regression-analysis/sample-size-multiple-regression/) - Describes how big a sample is required to achieve 80% power at various values for R-square when doing multiple regression
- [Regression using Solver](https://real-statistics.com/multiple-regression/multiple-regression-analysis/regression-using-solver/) - Describes how to use the Solver option of the Real Statistics Multiple Regression data analysis tool with certain types of data.
- [Multiple Regression Analysis in Excel](https://real-statistics.com/multiple-regression/multiple-regression-analysis/multiple-regression-analysis-excel/) - Describes the multiple regression capabilities provided in standard Excel. Explains the output from Excel's Regression data analysis tool in detail.
- [Multiple Regression Basic Concepts](https://real-statistics.com/multiple-regression/multiple-regression-analysis/multiple-regression-basic-concepts/) - Describes some of the theoretical foundations for multiple linear regression. Includes a list of the assumptions for multiple regression,
- [Multiple Regression using Matrices](https://real-statistics.com/multiple-regression/multiple-regression-analysis/multiple-regression-using-matrices/) - Describes how to perform multiple linear regression using matrix operations in Excel. Also defines the hat matrix and regression residuals.
- [Method of Least Squares for Multiple Regression](https://real-statistics.com/multiple-regression/least-squares-method-multiple-regression/) - How to find the regression coefficients in Excel for the multiple regression line which is the best fit for data using the method of least squares.
- [Tukey HSD for Two Factor ANOVA w/o Replications](https://real-statistics.com/two-way-anova/follow-up-analyses-for-two-factor-anova-w-o-replications/tukey-hsd-for-two-factor-anova-w-o-replications/) - Describes how to use the Real Statistics Two Factor ANOVA w/o Repl. Follow-up data analysis tool to perform Tukey HSD for main effects or interactions in Excel.
- [Follow-up Analyses for Two Factor ANOVA w/o Replications](https://real-statistics.com/two-way-anova/follow-up-analyses-for-two-factor-anova-w-o-replications/) - Describes how to conduct follow-up analyses after a significant two factor ANOVA without Replications. Examples and software included.
- [Contrasts for Two Factor ANOVA w/o Replications](https://real-statistics.com/two-way-anova/follow-up-analyses-for-two-factor-anova-w-o-replications/contrasts-two-factor-anova-no-replications/) - Describes how to perform contrast analysis in Excel after a significant Two Factor ANOVA w/o Replications result. Examples are provided.
- [Tukey HSD after Two Factor ANOVA with Replications](https://real-statistics.com/two-way-anova/follow-up-analyses-for-two-factor-anova/tukey-hsd-after-two-factor-anova/) - Describes how to use the Real Statistics Two Factor ANOVA w/ Repl. Follow-up data analysis tool to perform Tukey HSD for main effects or interactions in Excel.
- [Indexed Values and Counts](https://real-statistics.com/real-statistics-environment/data-conversion/indexed-values-and-counts/) - Describes a way to reformat an array in Excel based on an index value. Examples are provided in Excel as well as Excel worksheet functions
- [Gage R&R](https://real-statistics.com/two-way-anova/gage-rr/) - Brief tutorial about Gage R&R studies and a description of how to conduct such studies using Excel. Examples and software are provided.
- [Scheirer-Ray-Hare Test](https://real-statistics.com/two-way-anova/scheirer-ray-hare-test/) - Describes how to perform the Scheirer-Ray-Hare Test, a non-parametric version of two-way ANOVA based on ranks. Excel examples and software are provided.
- [Contrasts for Two Factor ANOVA with Replications](https://real-statistics.com/two-way-anova/follow-up-analyses-for-two-factor-anova/contrasts-two-factor-anova/) - Describes how to analyze the main and simple effects and contrasts for two-way ANOVA with replication. Excel examples and software are included.
- [M/M/s Queueing Model with pre-emptive priority queueing](https://real-statistics.com/probability-functions/queueing-theory/m-m-s-queueing-model-with-pre-emptive-priority-queueing/) - Describes the M/M/s model with preemptive priority queueing and provides formulas for characteristics of this model, and explains how to calculate them in Excel
- [M/M/1 with non-preemptive priority queueing and variable service means](https://real-statistics.com/probability-functions/queueing-theory/m-m-s-non-preemptive-priority-queueing-variable-service/) - Describes the M/M/1 non-preemptive priority queueing model with variable service, and shows how to calculate L, Lq, W, and Wq for each priority class in Excel.
- [M/M/1 Queueing Model with preemptive priority queueing](https://real-statistics.com/probability-functions/queueing-theory/m-m-1-preemptive-priority-queueing/) - Describes the M/M/1 model with preemptive priority queueing and provides formulas for characteristics of this model, and explains how to calculate them in Excel
- [M/M/s Non-Preemptive Priority Queueing Model](https://real-statistics.com/probability-functions/queueing-theory/m-m-s-non-preemptive-priority-queueing-model/) - Describes the M/M/s queueing model with non-preemptive priority, and shows how to calculate L, Lq, W, and Wq for each priority class in Excel.
- [Single Factor Follow-up to Two Factor ANOVA](https://real-statistics.com/two-way-anova/follow-up-analyses-for-two-factor-anova/single-factor-follow-up-to-two-factor-anova/) - Describes how to use Single Factor ANOVA for follow-up analysis after a two-factor ANOVA. Examples and software included.
- [M/M/1 Non-Preemptive Priority Queueing Model](https://real-statistics.com/probability-functions/queueing-theory/m-m-1-non-preemptive-priority-queueing-model/) - Describes the M/M/1 queueing model with non-preemptive priority, and shows how to calculate L, Lq, W, and Wq for each priority class in Excel.
- [Follow-up Analyses for Two Factor ANOVA with Replications](https://real-statistics.com/two-way-anova/follow-up-analyses-for-two-factor-anova/) - Describes how to conduct follow-up analyses in Excel after a significant two-factor ANOVA. Examples and software included.
- [More about two multivariate within-subjects factors (2W+0B)](https://real-statistics.com/multivariate-statistics/multivariate-repeated-measures-tests/more-two-multivariate-within-subjects-factors-2w0b/) - Describes how to perform a two within-subjects repeated measures test using multivariate techniques (Hotelling's Test) in Excel. Incl. data analysis tool.
- [Two multivariate within-subjects factors (2W+0B)](https://real-statistics.com/multivariate-statistics/multivariate-repeated-measures-tests/two-within-subjects-factors-multivariate-repeated-measures-2w0b/) - Describes how to perform a two within-subjects repeated measures test using multivariate techniques (Hotelling's Test) in Excel.
- [Real Statistics Support for Two Factor Anova](https://real-statistics.com/two-way-anova/real-statistics-support-for-two-factor-anova/) - Describes the various Two Factor ANOVA supplemental functions and data analysis tools provided in the Real Statistics software, which is an Excel add-in.
- [Two Factor ANOVA with Replication](https://real-statistics.com/two-way-anova/two-factor-anova-with-replication/) - Provides a tutorial on how to perform Two Factor ANOVA with Replication in Excel. Examples are provided as well as an explanation of Excel's analysis tool.
- [Two Factor ANOVA without Replication](https://real-statistics.com/two-way-anova/two-factor-anova-without-replication/) - Describes how to perform two-way ANOVA in Excel using the standard Excel data analysis tool and worksheet functions. Also describes Real Statistics' tool.
- [Assumptions for ANOVA](https://real-statistics.com/one-way-analysis-of-variance-anova/assumptions-anova/) - Describe the assumptions for use of analysis of variance (ANOVA) and the tests to checking these assumptions (normality, heterogeneity of variances, outliers).
- [Contrasts post KW](https://real-statistics.com/one-way-analysis-of-variance-anova/kruskal-wallis-test/contrasts-post-kw/) - Describes how to conduct the contrasts tests after a significant Kruskal-Wallis test. Excel examples and software are included.
- [Table Lookup](https://real-statistics.com/excel-capabilities/table-lookup/) - Describes various table lookup procedures that can be used in Excel, as well as additional functions provided by the Real Statistics Resource Pack.
- [Creating Box Plots with Outliers in Excel](https://real-statistics.com/excel-capabilities/creating-box-plot-outliers-manually/) - Describes how to manually, step-by-step, create box plots with outliers in Excel. An example is provided to make the steps clearer
- [Creating Simple Box Plots in Excel](https://real-statistics.com/excel-capabilities/special-charting-capabilities/) - Describes how to create simple box plots using standard Excel charting capabilities. Examples are given to demonstrate the step-by-step process.
- [Creating Dot Plots in Excel](https://real-statistics.com/excel-capabilities/creating-dot-plots-in-excel/) - Describes how to create a dot plot manually in Excel using Excel's charting capabilities. Provides step-by-step instructions.
- [Keyboard Shortcuts](https://real-statistics.com/excel-capabilities/keyboard-shortcuts/) - Provides a list of Excel keyboard shortcuts that are useful for statistical analysis, along with a description of what the shortcut does
- [Arrays as an argument in an Excel formula](https://real-statistics.com/excel-capabilities/array-arguments-in-excel-formulas/) - Describes how Excel treats arrays that are not cell ranges when they are used as an argument in an Excel worksheet formula
- [Table Lookup Functions](https://real-statistics.com/excel-capabilities/table-lookup-functions/) - Describes how to perform table lookup in Excel using the worksheet functions INDEX, MATCH, OFFSET, and XLOOKUP. Examples are provided.
- [Miscellaneous Built-in Functions](https://real-statistics.com/excel-capabilities/built-in-excel-functions/) - Description of Excel functions useful in statistics, including mathematical, summation, matrix, combinatorial, table lookup and dynamic array functions.
- [Excel Conditional Functions](https://real-statistics.com/excel-capabilities/excel-conditional-functions/) - Brief description of Excel's conditional worksheet functions useful in statistics, including IF, IFS, SUMIF, SUMIFS, COUNTIF, COUNTIFS, SWITCH, MINIFS, MAXIFS.
- [Real Statistics Lambda Capabilities](https://real-statistics.com/real-statistics-environment/real-statistics-lambda-capabilities/) - Describes how to specify and evaluate formulas using Real Statistics capabilities similar to those supplied by Excel's LAMBDA function.
- [Excel Data Analysis Tools](https://real-statistics.com/excel-environment/data-analysis-tools/) - Provides an overview of Excel's data analysis tools. Shows how to select an Excel data analysis tool from a menu and how to fill in the resulting dialog box..
- [Worksheet Functions](https://real-statistics.com/excel-environment/excel-worksheet-functions/) - Describes Excel's built-in worksheet functions as well as the supplementary functions provided in the Real Statistics Resource Pack.
- [Excel Environment](https://real-statistics.com/excel-environment/) - Review of basic Excel capabilities, with special emphasis on those topics which are especially important to do statistical analysis. Examples provided.
- [Multivariate two within-subjects and one between-subjects factors (2W+1B)](https://real-statistics.com/multivariate-statistics/multivariate-repeated-measures-tests/multivariate-two-within-subjects-and-one-between-subjects-factors-2w1b/) - How to perform a repeated measures test for one between-subjects and two within-subjects factors using multivariate techniques (via MANOVA) in Excel
- [Two Factor Multivariate Repeated Measures](https://real-statistics.com/multivariate-statistics/multivariate-repeated-measures-tests/two-factor-multivariate-repeated-measures/) - Describes how to perform two a two factor repeated measures test using multivariate techniques (MANOVA) in Excel without the sphericity assumption.
- [More about One Factor Multivariate Repeated Measures](https://real-statistics.com/multivariate-statistics/multivariate-repeated-measures-tests/more-one-factor-multivariate-repeated-measures/) - Provides additional information about performing a one-factor repeated measures test using multivariate techniques (Hotelling's Test) in Excel.
- [One Factor Multivariate Repeated Measures](https://real-statistics.com/multivariate-statistics/multivariate-repeated-measures-tests/one-factor-multivariate-repeated-measures/) - Describes how to perform a one-factor repeated measures test using multivariate techniques (Hotelling's Test) in Excel without the sphericity assumption.
- [Descriptive Multivariate Statistics](https://real-statistics.com/multivariate-statistics/descriptive-multivariate-statistics/) - Brief tutorial on descriptive multivariate descriptive statistics in Excel, including description of random vectors, mean vectors, covariance matrices, etc.
- [Friedman-Rafsky Test](https://real-statistics.com/multivariate-statistics/multivariate-normal-distribution/friedman-rafsky-test/) - Describes how to perform the Friedman-Rafsky Test to determine in Excel whether two samples of random vectors come from populations with the same distributions.
- [Multivariate Normality Testing (FRSJ)](https://real-statistics.com/multivariate-statistics/multivariate-normal-distribution/multivariate-normality-testing-frsj/) - Describes the Friedman-Rafsky-Smith-Jain test for multivariate normality and how to perform this test in Excel. Example and software are included
- [Confidence Hyper-ellipse and Eigenvalues](https://real-statistics.com/multivariate-statistics/multivariate-normal-distribution/confidence-hyper-ellipse-eigenvalues/) - Tutorial on how to calculate the length of the axes in Excel of the confidence hyper-ellipse (ellipsoid) from the eigenvalues of the covariance matrix.
- [Discriminant Analysis](https://real-statistics.com/multivariate-statistics/discriminant-analysis/) - Tutorial on Discriminant Analysis, including how to carry out the analysis in Excel. Examples and free software are provided.
- [Hotelling T-Square Power](https://real-statistics.com/multivariate-statistics/hotellings-t-square-statistic/hotelling-t-square-power/) - Describes how to determine the statistical power and sample size of the one sample and two sample Hotelling's T-square tests in Excel.
- [Hotelling's T-square: Real Statistics Capabilities](https://real-statistics.com/multivariate-statistics/hotellings-t-square-statistic/hotellings-t-square-real-statistics-functions/) - Description of the Hotelling's T-square tests data analysis tool and worksheet functions supplied by the Real Statistics Resource Pack.
- [Hotelling's T-square Test with Unequal Covariance Matrices](https://real-statistics.com/multivariate-statistics/hotellings-t-square-statistic/hotellings-t-square-unequal-covariance-matrices/) - Tutorial on how to perform Hotelling's T-square test for two independent samples in Excel using Real Statistics where the covariance matrices are unequal,
- [Hotelling's T-square Test Additional Topics](https://real-statistics.com/multivariate-statistics/hotellings-t-square-statistic/hotellings-t-square-independent-samples/hotellings-t-square-additional/) - Tutorial on the following topics re Hotelling's T2 test for independent samples: simultaneous and Bonferroni confidence intervals, effect size and assumptions
- [Hotelling's T-square Test for Two Independent Samples](https://real-statistics.com/multivariate-statistics/hotellings-t-square-statistic/hotellings-t-square-independent-samples/) - Tutorial on how to perform multivariate Hotelling's T-square test for two independent samples in Excel using the Real Statistics Resource Pack.
- [Paired Sample Hotelling's T-square](https://real-statistics.com/multivariate-statistics/hotellings-t-square-statistic/paired-sample-hotellings-t-square/) - Tutorial on how to perform multivariate paired sample Hotelling's T-square test in Excel using Real Statistics. Also describes two types of post-hoc tests.
- [One Sample Hotelling's T-square](https://real-statistics.com/multivariate-statistics/hotellings-t-square-statistic/one-sample-hotellings-t-square/) - Tutorial on how to use Hotelling's T-square test to analyze whether the mean vector is equal to some value, i.e. the multivariate one sample test of the mean.
- [Cluster Analysis](https://real-statistics.com/multivariate-statistics/cluster-analysis/) - Describes how to perform the k-means++ cluster analysis and Jenks Natural Breaks analysis in Excel. Examples and software are provided.
- [Real Statistics support for k-means cluster analysis](https://real-statistics.com/multivariate-statistics/cluster-analysis/real-statistics-k-means/) - Describes the Real Statistics functions and data analysis tool to calculate k-means and k-means++ cluster analysis in Excel.
- [Jenks Natural Breaks](https://real-statistics.com/multivariate-statistics/cluster-analysis/jenks-natural-breaks/) - Describes how to perform Jenks Natural Breaks in Excel. Determines goodness of variance fit (GVF). Includes examples and software.
- [CA Data Analysis Tool](https://real-statistics.com/multivariate-statistics/correspondence-analysis/ca-data-analysis-tool/) - Describes how to use the Real Statistics Correspondence Analysis data analysis tool in Excel. An example is demonstrated. Reports and charts are shown.
- [Supplementary CA Profiles](https://real-statistics.com/multivariate-statistics/correspondence-analysis/supplementary-ca-profiles/) - Describes how to add supplementary row and column profiles to correspondence analysis plots in Excel. An example is employed to illustrate how this is done.
- [Correspondence Plots](https://real-statistics.com/multivariate-statistics/correspondence-analysis/correspondence-plots/) - Describes how to create correspondence analysis plots (for rows and columns) in Excel. Examples and software are provided.
- [Correspondence Analysis Basic Concepts](https://real-statistics.com/multivariate-statistics/correspondence-analysis/correspondence-analysis-basic-concepts/) - Describes the objectives of Correspondence Analysis and how to perform these analyses in Excel. Examples and software are included.
- [Quadratic Discriminant Analysis](https://real-statistics.com/multivariate-statistics/discriminant-analysis/quadratic-discriminant-analysis/) - Describes how to conduct quadratic discriminant analysis (QDA) in Excel. Includes examples and software. Used when equal covariance matrix assumption is not met
- [Classification using Discriminant Analysis](https://real-statistics.com/multivariate-statistics/discriminant-analysis/classification-using-discriminant-analysis/) - Describes how to build a classification table (aka a confusion table) based on discriminant analysis. Includes misclassification probabilities.
- [Confidence Ellipse Analysis Tool](https://real-statistics.com/multivariate-statistics/multivariate-normal-distribution/confidence-ellipse-analysis-tool/) - Describes how to use the Real Statistics Confidence Ellipse data analysis tool to create a plot of a confidence ellipse in Excel.
- [Linear Discriminant Analysis](https://real-statistics.com/multivariate-statistics/discriminant-analysis/linear-discriminant-analysis/) - Describes how to perform Linear Discriminant Analysis (LDA) in Excel. Examples are given and free software is also provided.
- [Real Statistics MANOVA Capabilities](https://real-statistics.com/multivariate-statistics/multivariate-analysis-of-variance-manova/real-statistics-manova-features/) - Overview of the MANOVA data analysis tool and MANOVA supplemental functions supplied by the Real Statistics Excel add-in software.
- [MANOVA Assumptions](https://real-statistics.com/multivariate-statistics/multivariate-analysis-of-variance-manova/manova-assumptions/) - Tutorial on the assumptions for MANOVA, including multivariate normality, lack of outliers, homogeneity of covariance matrices and lack of collinearity.
- [Real Statistics Support for PERMANOVA](https://real-statistics.com/multivariate-statistics/multivariate-analysis-of-variance-manova/permutational-manova/real-statistics-permanova/) - Describes how to perform Permutational MANOVA in Excel using Real Statistics. Permutational MANOVA is a non-parametric substitute for MANOVA.
- [Permutational MANOVA Example](https://real-statistics.com/multivariate-statistics/multivariate-analysis-of-variance-manova/permutational-manova/permutational-manova-example/) - Describes how to perform Permutational MANOVA in Excel via a specific example. Permutational MANOVA is a non-parametric substitute for MANOVA.
- [MANOVA Power and Sample Size](https://real-statistics.com/multivariate-statistics/multivariate-analysis-of-variance-manova/manova-power-and-sample-size/) - Describes how to calculate the statistical power and sample size for a one-way MANOVA. Provides examples in Excel and worksheet functions and data analysis tool
- [Two-way MANOVA Power and Sample Size](https://real-statistics.com/multivariate-statistics/multivariate-analysis-of-variance-manova/two-way-manova-power-and-sample-size/) - Describes how to calculate the statistical power of a two-way MANOVA. It also calculates the minimum sample size required for two-way MANOVA.
- [Discrete Probability Distributions](https://real-statistics.com/probability-functions/discrete-probability-distributions/) - Describes the basic characteristics of discrete probability distributions, including probability density functions and cumulative distribution functions.
- [3-level Taguchi Examples](https://real-statistics.com/design-of-experiments/taguchi-design-of-experiments/3-level-taguchi-examples/) - Provides two example for how to build 3-level Taguchi designs in Excel. The first has not interactions and the section has interactions.
- [Taguchi Design Optimization](https://real-statistics.com/design-of-experiments/taguchi-design-of-experiments/taguchi-design-optimization/) - Describes how to determine the result in the 2-level Taguchi design for each combination of main effects factor and level. Provides an example in Excel.
- [TLS Regression Confidence Interval](https://real-statistics.com/regression/total-least-squares/tls-regression-confidence-interval/) - Describes how to estimate the standard errors and confidence intervals for TLS regression coefficients in Excel. Incl. example of comparison with gold standard.
- [Distribution Fitting via MLE: Real Statistics Support](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/distribution-fitting-mle-real-statistics/) - Describes Excel worksheet functions found in the Real Statistics Resource Pack for distribution fitting using the maximum likelihood approach.
- [Fitting Geometric Parameter via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-geometric-parameter-via-mle/) - Describes how to find geometric distribution parameter that best fit a data set using maximum likelihood estimation (MLE) in Excel. Incl. examples & software.
- [LAD Regression Analysis Tool](https://real-statistics.com/multiple-regression/lad-regression/lad-regression-analysis-tool/) - Describes how to calculate LAD regression coefficients and their standard errors and confidence intervals in Excel using the Real Statistics data analysis tool.
- [Total Least Squares](https://real-statistics.com/regression/total-least-squares/) - Describes how total least squares regression in two variables and how to calculate the linear regression coefficients in Excel. Includes examples and software.
- [Fitting a Weibull Distribution via Regression](https://real-statistics.com/distribution-fitting/fitting-weibull-regression/) - Describes how to use regression to estimate Weibull parameter values that fit a data set. Excel examples are provided as well as Excel worksheet function.
- [Fitting Logistic Parameters via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-logistic-parameters-via-mle/) - Describes how to find logistic distribution parameters that best fit a data set using maximum likelihood estimation (MLE) in Excel. Incl. examples & software.
- [ROC Curve and Classification Table](https://real-statistics.com/descriptive-statistics/roc-curve-classification-table/) - Describes how to construct a ROC curve and classification table (aka a comfusion matrix) in Excel. Software and examples are given.
- [Multivariate Analysis of Variance (MANOVA)](https://real-statistics.com/multivariate-statistics/multivariate-analysis-of-variance-manova/) - Tutorial on one.way Multivariate Analysis of Variance (MANOVA) using Excel, including effect size, follow-up with ANOVA and Contrasts
- [Hotelling’s T-square and Analysis of Mean Vectors](https://real-statistics.com/multivariate-statistics/hotellings-t-square-statistic/) - Tutorial on how to use Hotelling's T-squared statistical analysis to compare mean vectors. Excel examples and software are provided.
- [Correspondence Analysis](https://real-statistics.com/multivariate-statistics/correspondence-analysis/) - Tutorial on Correspondence Analysis, a multivariate technique similar to factor analysis or principal component analysis for categorical data.
- [Multivariate Normal Distribution](https://real-statistics.com/multivariate-statistics/multivariate-normal-distribution/) - Tutorial on the multivariate normal distribution, includes pdf and cdf, key properties, and how to test in Excel if data is multivariate normally distributed
- [Box’s Test for Equality of Covariance Matrices](https://real-statistics.com/multivariate-statistics/boxs-test/) - Tutorial on how to perform Box's test in Excel to determine whether the covariance matrices from multiple populations are statistically equivalent.
- [Real Statistics Box's Test Support](https://real-statistics.com/multivariate-statistics/boxs-test/real-statistics-boxs-test-support/) - Describes how to use the Real Statistics software add-in to perform Box's Test in Excel. Various worksheet functions and a data analysis tool are described.
- [AUC Confidence Interval](https://real-statistics.com/descriptive-statistics/roc-curve-classification-table/auc-confidence-interval/) - Describes how to calculate a confidence interval for AUC (area under the curve for a ROC curve) in Excel. Example and software are included.
- [Fitting Uniform Parameters via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-uniform-parameters-via-mle/) - Describes how to find uniform distribution parameters that best fit a data set using maximum likelihood estimation (MLE) in Excel. Incl. examples and software.
- [Equivalence Testing (TOST)](https://real-statistics.com/students-t-distribution/equivalence-testing-tost/) - Describes how to conduct two one-sided t tests (TOST) in Excel to determine whether two populations are equivalent. Examples are included.
- [ROC and Classification Table Data Analysis Tool](https://real-statistics.com/descriptive-statistics/roc-curve-classification-table/roc-and-classification-table-data-analysis-tool/) - Describes the Real Statistics data analysis tool that calculates the ROC table and classification table and creates the ROC curve.
- [Fitting Weibull Parameters using MLE and Newton's Method](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-weibull-parameters-mle-newtons-method/) - Describes how to fit a Weibull distribution to a data set using maximum likelihood estimation (MLE) based on Newton's method. We show how this is done in Excel.
- [Collinearity](https://real-statistics.com/multiple-regression/collinearity/) - How to identify in Excel when collinearity occurs, i.e. when one independent variable is a non-trivial linear combination of the other independent variables.
- [Proportional Multivariate Distribution](https://real-statistics.com/binomial-and-related-distributions/multinomial-distribution/proportional-multivariate-distribution/) - Describes the proportional multinomial distribution, which is the proportion version of the multinomial distribution. Provides confidence intervals for the mean
- [Box’s M Test Basic Concepts](https://real-statistics.com/multivariate-statistics/boxs-test/boxs-test-basic-concepts/) - Tutorial on how to perform Box's test in Excel to determine whether the covariance matrices from multiple populations are statistically equivalent.
- [Polynomial Regression](https://real-statistics.com/multiple-regression/polynomial-regression/) - Describes how to use the multiple regression model to investigate whether data fits a polynomial model. Examples using Excel are provided.
- [Comparing slopes and intercepts](https://real-statistics.com/multiple-regression/comparing-slopes-and-intercepts/) - Describes how to determine whether the slopes and intercepts for two or more regressions are equal. Gives an example in Excel.
- [Effect Size for Factorial ANOVA](https://real-statistics.com/multiple-regression/effect-size-factorial-anova/) - We explore measures of effect size for Factorial ANOVA based on the correlation coefficient (in addition to Cohen's d studied elsewhere).
- [Other measures of effect size for ANOVA](https://real-statistics.com/multiple-regression/other-measures-effect-size-anova/) - We explore measures of effect size for One-way ANOVA based on the correlation coefficient (in addition to Cohen's d studied elsewhere).
- [ANOVA using Regression](https://real-statistics.com/multiple-regression/anova-using-regression/) - Describes how to use Excel's tools for regression to perform analysis of variance (ANOVA). Shows how to use dummy (aka categorical) variables to accomplish this
- [Three Factor ANOVA using Regression](https://real-statistics.com/multiple-regression/three-factor-anova-using-regression/) - How to use regression models in Excel to perform three factor analysis of variance (ANOVA) for both balanced and unbalanced models
- [Unbalanced Factorial ANOVA](https://real-statistics.com/multiple-regression/unbalanced-factorial-anova/) - How to use regression models in Excel to perform analysis of variance (ANOVA) for samples of different sizes (unbalanced models).
- [Breusch-Godfrey and Newey-West Tool](https://real-statistics.com/multiple-regression/autocorrelation/breusch-godfrey-and-newey-west-tool/) - Describes how to perform the Breusch-Godfrey test and calculate the Newey-West standard errors in Excel using a Real Statistics data analysis tool.
- [Cochrane-Orcutt Tool](https://real-statistics.com/multiple-regression/autocorrelation/cochrane-orcutt-tool/) - Describes how to perform Cochrane-Orcutt regression to correct for autocorrelation using a Real Statistics data analysis tool; also includes Durbin-Watson test.
- [Cochrane-Orcutt Regression](https://real-statistics.com/multiple-regression/autocorrelation/cochrane-orcutt-regression/) - Describes how to carry out the Cochrane-Orcutt procedure in Excel to address autocorrelation in linear regression. Example and software are provided.
- [Newey-West Standard Errors](https://real-statistics.com/multiple-regression/autocorrelation/newey-west-standard-errors/) - Describes how to calculate the Newey-West standard errors in Excel for multiple linear regression where autocorrelation is present. Includes a detailed example.
- [FGLS Method for Autocorrelation](https://real-statistics.com/multiple-regression/autocorrelation/fgls-method-for-autocorrelation/) - Describes the feasible general least squares (FGLS) regression and how to implement this approach in Excel. This is useful when there is autocorrelation.
- [ROC Curve](https://real-statistics.com/descriptive-statistics/roc-curve-classification-table/roc-curve/) - Describes how to construct the Receiver Operating Characteristic (ROC) Curve table and ROC curve in Excel. Software and examples are given.
- [Fitting Weibull Parameters via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-weibull-parameters-mle/) - Describes how to find the Weibull parameters that best fit a data set using maximum likelihood estimation (MLE) in Excel. Examples and software are provided.
- [Breusch-Godfrey Test](https://real-statistics.com/multiple-regression/autocorrelation/breusch-godfrey-test/) - Describes how to conduct the Breusch-Godfrey (BG) Test in Excel to detect autocorrelation up to any predesignated order p. Example and software are provided.
- [GLS Method for Autocorrelation](https://real-statistics.com/multiple-regression/autocorrelation/gls-method-for-autocorrelation/) - Describes the general least squares (GLS) approach to regression. This is useful when there is autocorrelation. Includes the Prais-Winsten transformation.
- [Autocorrelation](https://real-statistics.com/multiple-regression/autocorrelation/) - Describes the consequences of autocorrelation (aka serial correlation) on linear regression. Describes how to detect autocorrelation and how to address it.
- [Durbin-Watson Test](https://real-statistics.com/multiple-regression/autocorrelation/durbin-watson-test/) - Describes how to use the Durbin-Watson statistic for testing first-order autocorrelation in regression models in Excel. Examples and software are provided.
- [Autocorrelation Introduction](https://real-statistics.com/multiple-regression/autocorrelation/autocorrelation-introduction/) - Provides a brief introduction to autocorrelation, including the definition and the sources for it, as well as the problems for the regression model.
- [Detecting Autocorrelation Graphically](https://real-statistics.com/multiple-regression/autocorrelation/detecting-autocorrelation-graphically/) - Describes how to detect autocorrelation by creating a graph of the residuals against a time-lagged version of these residuals. We show this in Excel.
- [Interaction](https://real-statistics.com/multiple-regression/interaction/) - How to perform multiple regression analysis in Excel where interaction between variables is modeled.
- [Multiple Regression with Logarithmic Transformations](https://real-statistics.com/multiple-regression/multiple-regression-log-transformations/) - Provides examples in Excel of how to use log transformations to create better fitting regression models. Incl. log-log, log-level, level-log transformations
- [Standardized Regression Coefficients](https://real-statistics.com/multiple-regression/standardized-regression-coefficients/) - How to calculate standardized regression coefficients and how to calculate unstandardized regression coefficients from standardized coefficients in Excel.
- [Multiple Regression without Intercept](https://real-statistics.com/multiple-regression/multiple-regression-without-intercept/) - Explains how to perform multiple linear regression without a constant term in Excel. Includes examples, theory and software.
- [Stepwise Regression](https://real-statistics.com/multiple-regression/stepwise-regression/) - Describes how to perform stepwise regression in Excel. Various worksheet functions are described as well as a data analysis tool. Examples are included.
- [Confidence intervals of effect size and power for regression](https://real-statistics.com/multiple-regression/confidence-intervals-effect-size-power-regression/) - Describes how to calculate confidence intervals for effect size and power for regression in Excel. Software and examples are provided.
- [Statistical Power and Sample Size for Multiple Regression](https://real-statistics.com/multiple-regression/statistical-power-sample-size-multiple-regression/) - Describes how to calculate the statistical power and sample size requirements for multiple regression in Excel. Software and examples are included.
- [Regression through Origin in Excel](https://real-statistics.com/multiple-regression/multiple-regression-without-intercept/regression-wo-constant-in-excel/) - Explains how to perform multiple linear regression without a constant term in Excel (i.e. regression through the origin). Includes examples and software.
- [White Test for Heteroskedasticity](https://real-statistics.com/multiple-regression/heteroskedasticity/white-test-for-heteroskedasticity/) - Describes the White test and how to use it to test the homoskedasticity assumption of linear regression. We provide an example and Excel worksheet functions.
- [Breusch-Pagan Test](https://real-statistics.com/multiple-regression/heteroskedasticity/breusch-pagan-test/) - Describes how to conduct the Breusch-Pagan test in Excel to test for homoskedasticity. We also provide an example and Excel worksheet functions.
- [Graphical Tests for Heteroskedasticity](https://real-statistics.com/multiple-regression/heteroskedasticity/graphical-tests-for-heteroskedasticity/) - Describes how to determine whether data meets the homoskedasticity assumption for linear regression using graphical techniques. Excel example is provided.
- [Heteroskedasticity Data Analysis Tool](https://real-statistics.com/multiple-regression/heteroskedasticity/heteroskedasticity-data-analysis-tool/) - Describes how to use the Real Statistics Heteroskedasticity data analysis tool in Excel to perform the Breusch-Pagan and White tests.
- [Heteroskedasticity](https://real-statistics.com/multiple-regression/heteroskedasticity/) - Tutorial on the Heteroskedasticity assumption in multiple least-squares linear regression. Deals with testing and what to do when this assumption is not met.
- [Polynomial Regression Analysis Tool](https://real-statistics.com/multiple-regression/polynomial-regression/polynomial-regression-analysis-tool/) - Describes how to use the Real Statistics software to create polynomial regression models in Excel. Software and examples are provided.
- [LAD Regression using IRLS Method](https://real-statistics.com/multiple-regression/lad-regression/lad-regression-irls-method/) - Describes how to calculate the coefficients of a LAD regression model in Excel using iteratively reweighted least squares (IRLS). Examples are provided.
- [LAD Regression using Simplex Method](https://real-statistics.com/multiple-regression/lad-regression/lad-regression-simplex-method/) - Describes how to calculate the coefficients of a LAD regression model in Excel using Solver's Simplex capability. Examples are provided.
- [Testing the significance of extra variables on the model](https://real-statistics.com/multiple-regression/testing-significance-extra-variables-regression-model/) - Testing the significance of adding or subtracting variables from the regression model (reduced vs complete model). Also Akaike’s information criterion, AIC.
- [Robust Standard Errors](https://real-statistics.com/multiple-regression/robust-standard-errors/) - Describes how to calculate robust standard errors in Excel using the techniques of Huber-White to address heteroscedasticity. Includes examples and software.
- [Shapley-Owen Decomposition](https://real-statistics.com/multiple-regression/shapley-owen-decomposition/) - Describes how to calculate the Shapley-Owen decomposition of the R-square parameter from multiple regression. Includes examples and Excel add-in.
- [Lp Regression](https://real-statistics.com/multiple-regression/lp-regression/) - Describes how to conduct Lp regression in Excel based on the Lp norm for values of p between 1 and 2. When p = 1 Lp regression is equivalent to LAD regression.
- [Cross Validation](https://real-statistics.com/multiple-regression/cross-validation/) - Describes cross validation and the related concepts of predictive sum of squares and predictive R-square. Example and software are provided.
- [Sobel Test](https://real-statistics.com/multiple-regression/mediation-analysis/sobel-test/) - Describes how to execute the Sobel test in Excel to perform Mediation Analysis based on the work of Baron and Kenny. An example and software are provided.
- [Mediation Analysis Basics](https://real-statistics.com/multiple-regression/mediation-analysis/mediation-analysis-basics/) - Describes the basic approach to Mediation Analysis, and how to carry out the analysis in Excel. Example and software are provided.
- [Negative Binomial Regression](https://real-statistics.com/negative-binomial-regression/) - Tutorial on how to perform Negative Binomial regression in Excel. Examples and free software are provided. Neg Binomial regression is used with count data.
- [Basic Concepts of Matrices](https://real-statistics.com/matrices-and-iterative-procedures/basic-concepts-of-matrices/) - Describe some basic properties of a matrix, including square matrix, identity matrix, triangular matrix, vector, scalar, length.
- [Spectral Decomposition](https://real-statistics.com/linear-algebra-matrix-topics/spectral-decomposition/) - Tutorial on spectral decomposition theorem and the concepts of algebraic multiplicity. Includes its relationship to eigenvalues and eigenvectors.
- [Fitting 3-Parameter Weibull Distribution using MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-3-parameter-weibull-distribution-using-mle/) - Describes how to fit a 3 parameter Weibull distribution to a data set using maximum likelihood estimation (MLE). We show how this is done in Excel.
- [Distribution Fitting via Maximum Likelihood](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/) - Tutorial on how to use the maximum likelihood method for estimating the parameters of a distribution that fits a data set. Examples in Excel.
- [Zero-Truncated Poisson Distribution](https://real-statistics.com/binomial-and-related-distributions/poisson-distribution/zero-truncated-poisson-distribution/) - Describes the Zero-truncated Poisson distribution, and how to calculate its pdf, cdf, and inverse cdf in Excel. This also includes how to generate random values
- [Miscellaneous Real Statistics Capabilities](https://real-statistics.com/real-statistics-environment/miscellaneous-real-statistics-capabilities/) - Describes miscellaneous Real Statistics functions: e.g. Real Statistics release number, Excel release number, first cell with non-numeric value.
- [Method of Moments: Real Statistics Support](https://real-statistics.com/distribution-fitting/method-of-moments/method-of-moments-real-statistics-support/) - Describes Excel worksheet functions found in the Real Statistics Resource Pack for distribution fitting using the method of moments
- [Spearman's Correlation Testing using a Fisher Transformation](https://real-statistics.com/correlation/spearmans-rank-correlation/spearmans-correlation-testing-fisher-transformation/) - How to test in Excel whether a population's Spearman's correlation coefficient is significantly different from some value using a Fisher transformation
- [Kendall’s Tau Correlation](https://real-statistics.com/correlation/kendalls-tau-correlation/) - Tutorial on Kendall's tau non-parametric correlation coefficient. Including definition, properties, hypothesis testing, examples and Excel software
- [Resolve error when choosing any option from main dialog box](https://real-statistics.com/appendix/faqs/resolve-error-when-choosing-any-option-from-main-dialog-box/) - Describes how to resolve a 404 error that appears no matter which option I choose from the main dialog box. Requires changing the Trust Center setting.
- [Fitting Zero-Truncated Poisson Distribution](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-poisson-distribution/fitting-zero-truncated-poisson-distribution/) - How to estimate the lambda parameter of a Zero-truncated Poisson distribution that best fits a data set using MoM & MLE in Excel. Includes examples & software.
- [Dunnett's Table](https://real-statistics.com/statistics-tables/dunnetts-table/) - Provides the table of critical values for Dunnett's test (two-tailed test). This test is used for comparisons with a control (post-hoc test after ANOVA).
- [Regression Models](https://real-statistics.com/regression-models/) - Tutorials on linear regression, logistic regression and log-linear regression in Excel, including free downloadable software to create the regression models.
- [Fitting Data to a Cauchy Distribution](https://real-statistics.com/distribution-fitting/fitting-data-to-a-cauchy-distribution/) - Describes how to use weighted order statistics to estimate the mu and sigma parameters of a Cauchy distribution that fits data.
- [Method of Moments: 3 Parameter Weibull Distribution](https://real-statistics.com/distribution-fitting/method-of-moments/method-of-moments-weibull/method-of-moments-3-parameter-weibull-distribution/) - Describes how to estimate the parameter of the 3 parameter Weibull distribution that fits a set of data using the method of moments in Excel.
- [Weibull Distribution](https://real-statistics.com/other-key-distributions/weibull-distribution/) - Describes the use of the Weibull distribution to calculate the mean time to failure (MTTF) and mean time between failures (MTBF) using Excel. Includes example.
- [Spearman’s Rank Correlation Hypothesis Testing](https://real-statistics.com/correlation/spearmans-rank-correlation/spearmans-rank-correlation-detailed/) - Describes how to use Spearman's Rank Correlation for hypothesis testing in Excel to determine whether two samples are independent. Example and software provided
- [Generalized Extreme Value Distribution](https://real-statistics.com/other-key-distributions/generalized-extreme-value-distribution/) - Describes the Generalized Extreme Value (GEV) distribution and how to use it in Excel, esp. for determining the risk of extreme events.
- [Three-parameter Weibull Distribution](https://real-statistics.com/other-key-distributions/weibull-distribution/three-parameter-weibull-distribution/) - Describes the key characteristics (mean, mode, pdf, cdf, etc.) of the three-parameter Weibull distribution and how to use this distribution in Excel.
- [Chart standard errors of the mean](https://real-statistics.com/excel-capabilities/chart-standard-errors/) - Describes how to create graphs that show vertical bars to depict the interval around the mean of one standard error using Excel’s charting capabilities.
- [Trend Analysis using Polynomial Contrast Coefficients](https://real-statistics.com/one-way-analysis-of-variance-anova/trend-analysis-polynomial-contrast-coefficients/) - Tutorial on using polynomial contrast coefficients to perform various trend analyses (linear, quadratic, cubic, quartic, quintic). Includes Excel example.
- [Bayesian Mann-Whitney Support](https://real-statistics.com/bayesian-statistics/bayesian-non-parametric-testing/bayesian-mann-whitney-test/bayes-mann-whitney-support/) - Provides an example of how to perform the Bayesian Mann-Whitney test in Excel, using both the small and large sample methods. Also provides worksheet functions.
- [Cohen's Kappa Sample Size](https://real-statistics.com/reliability/interrater-reliability/cohens-kappa/cohens-kappa-sample-size/) - Describes how to calculate the power and minimum sample size required for Cohen's kappa in the case where there are two categories.
- [Calculating Orthogonal Polynomial Contrast Coefficients](https://real-statistics.com/one-way-analysis-of-variance-anova/trend-analysis-polynomial-contrast-coefficients/calculating-orthogonal-polynomial-contrast-coefficients/) - Describes how to calculate the orthogonal polynomial contrast coefficients for equally-spaced groups in Excel. Shows hoe to build coefficient tables
- [Two-way MANOVA Follow-up Tests](https://real-statistics.com/multivariate-statistics/multivariate-analysis-of-variance-manova/two-way-manova-follow-up-tests/) - Describes how to use contrasts for follow-up testing after Two Factor MANOVA. Also provides an Excel example. Software is also provided.
- [MANOVA Follow up using Contrasts](https://real-statistics.com/multivariate-statistics/multivariate-analysis-of-variance-manova/manova-follow-up-contrasts/) - Tutorial on following up on MANOVA by performing multivariate contrasts and then using simultaneous and Bonferroni confidence intervals.
- [Real Statistics Support for Two-way MANOVA](https://real-statistics.com/multivariate-statistics/multivariate-analysis-of-variance-manova/real-statistics-support-for-two-way-manova/) - Describes the Real Statistics worksheet functions that support two-way MANOVA for the row factor, column factor and interaction.
- [Two-way MANOVA](https://real-statistics.com/multivariate-statistics/multivariate-analysis-of-variance-manova/two-way-manova/) - Describes the theoretical basis for two-way MANOVA. Includes Wilk's Lambda, Hotelling-Lawley Trace, Pillai-Bartlett Trace and Roy's Largest Root.
- [Two-way MANOVA Example](https://real-statistics.com/multivariate-statistics/multivariate-analysis-of-variance-manova/two-way-manova-example/) - Provides an example of how to perform two-way MANOVA in Excel. An Excel-based data analysis tool is also provided to make it easier to do this.
- [Polynomial Regression Models based on Trend Analysis](https://real-statistics.com/one-way-analysis-of-variance-anova/trend-analysis-polynomial-contrast-coefficients/polynomial-regression-models-trend-analysis/) - Describes how to create polynomial regression models using orthogonal contrast coefficients. Also shows how to construct tables of such coefficients in Excel.
- [FAQs](https://real-statistics.com/appendix/faqs/) - Provides the answers to a variety of frequently asked questions regarding the Real Statistics software, especially about how to resolve problems.
- [Multivariate Normal Distribution and GHK Algorithm](https://real-statistics.com/multivariate-statistics/multivariate-normal-distribution/multivariate-normality-functions/multivariate-normal-distribution-ghk-algorithm/) - Describes how to use the GHK algorithm to calculate the multivariate normal cumulative distribution function. Includes Excel examples and worksheet functions.
- [Ranking Functions in Excel](https://real-statistics.com/descriptive-statistics/ranking-function-excel/) - Describes how to calculate the ranking, percentile, percent rank, and quartile functions in Excel via RANK.AVG, PERCENTILE.EXC, QUARTILE.EXC, etc.
- [Bayesian Mixed Model Contrasts](https://real-statistics.com/bayesian-statistics/bayesian-non-parametric-testing/bayesian-contrasts/bayesian-mixed-model-contrasts/) - How to create contrasts for models with both between-subjects and within-subjects factors. Provides Bayesian analysis examples in Excel and Excel functions.
- [More Bayesian Non-parametric Tests](https://real-statistics.com/bayesian-statistics/bayesian-non-parametric-testing/more-bayesian-non-parametric-tests/) - Describes how to perform the Bayesian versions of the McNemar, Sign, and Median tests in Excel. Examples and Excel worksheet functions are provided.
- [Power and Sample Size for Two-Sample Correlation Testing](https://real-statistics.com/correlation/two-sample-hypothesis-testing-correlation/power-and-sample-size-for-two-sample-correlation-testing/) - Describes how to calculate the power of a two-sample correlation test in Excel as well as the minimum sample size. Excel examples and functions are provided.
- [Multi-sample Correlation Test Support](https://real-statistics.com/correlation/two-sample-hypothesis-testing-correlation/multi-sample-correlation-test-support/) - Describes how to conduct hypothesis testing for 3 or more correlations in Excel. Includes Tukey HSD & Dunnett's post hoc tests, plus contrasts.
- [Bayesian Contrasts](https://real-statistics.com/bayesian-statistics/bayesian-non-parametric-testing/bayesian-contrasts/) - How to extend the Bayesian versions of the Signed Ranks and Mann-Whitney non-parametric tests using contrasts. Provides examples in Excel and Excel functions.
- [Student's t Distribution](https://real-statistics.com/students-t-distribution/) - Tutorial on the t distribution and how to perform the various t-tests in Excel. Also includes other tests that rely on the t distribution (e.g. Grubbs' test).
- [Assumptions for Statistical Tests](https://real-statistics.com/descriptive-statistics/assumptions-statistical-test/) - Typical assumptions for statistical tests, including normality, homogeneity of variances and independence. When these are not met use non-parametric tests.
- [Descriptive Statistics](https://real-statistics.com/descriptive-statistics/) - Common statistics (e.g. mean, standard deviation, variance, percentile, kurtosis) and common graphical ways (histogram, box plot, QQ plot) for describing data.
- [Basics](https://real-statistics.com/basics/) - Tutorials on the basics of statistics in the Excel environment using Real Statistics, including hypothesis testing, descriptive statistics and probability.
- [Hypothesis Testing using the Central Limit Theorem](https://real-statistics.com/sampling-distributions/one-sample-hypothesis-testing-central-limit-theorem/) - How to perform on sample hypothesis testing of the mean using the Central Limit Theorem in Excel. Uses ZTEST, CONFIDENCE as well as Real Statistics functions.
- [Central Limit Theorem](https://real-statistics.com/sampling-distributions/central-limit-theorem/) - Describes the Central Limit Theorem and the Law of Large Numbers. These are some of the most important properties used throughout statistical analysis.
- [Sample Size Requirements for Tolerance Intervals](https://real-statistics.com/sampling-distributions/tolerance-interval/sample-size-requirements-for-tolerance-intervals/) - Describes how to estimate the sample size requirements to produce a tolerance interval with given characteristics in Excel using Goal Seek.
- [Tolerance Interval Example](https://real-statistics.com/sampling-distributions/tolerance-interval/tolerance-interval-example/) - Shows how to calculate a one-sided and two-sided tolerance interval in Excel. Two examples are presented to show how this is done.
- [Identifying Outliers and Missing Data](https://real-statistics.com/sampling-distributions/identifying-outliers-missing-data/) - Identifies potential outliers and missing data in Excel using a data analysis tool found in the Real Statistics Resource Pack
- [Power and Sample Size using Real Statistics](https://real-statistics.com/sampling-distributions/power-sample-size-real-statistics/) - Describes how to calculate power and sample size for one-sample and two-sample testing using the normal distribution. Excel software and examples are included.
- [Power & Sample Size Two-Sample Test](https://real-statistics.com/sampling-distributions/statistical-power-sample/power-sample-size-two-sample-test/) - Describes how to calculate power and sample size for two-sample testing using the normal distribution. Excel software and examples are included.
- [Power & Sample Size Two-tailed Test](https://real-statistics.com/sampling-distributions/statistical-power-sample/power-sample-size-two-tailed-test/) - Describes how to calculate power and sample size for two-tailed, one-sample testing using the normal distribution. Excel software and examples are included.
- [Statistical Power and Sample Size](https://real-statistics.com/sampling-distributions/statistical-power-sample/) - How to use Excel's Goal Seek to determine the statistical power of a sample or determine how big a sample is needed to obtain a given power. Includes examples.
- [Sampling using Real Statistics Capabilities](https://real-statistics.com/sampling-distributions/sampling/sampling-using-real-statistics/) - Shows how to use Real Statistics capabilities to create a random sample in Excel. Both sampling with and without replacement are explored.
- [Simulation](https://real-statistics.com/sampling-distributions/simulation/) - Describes how to use random number generation techniques in Excel to simulate various distributions. Examples and software are provided.
- [Paired Sample t-Test](https://real-statistics.com/students-t-distribution/paired-sample-t-test/) - Describes how to use the t-test in Excel to determine whether two paired samples have equal means. We provide examples using standard Excel and Real Statistics.
- [One-Sample t-Test](https://real-statistics.com/students-t-distribution/one-sample-t-test/) - Describes the one-sample t-test and how to carry it out in Excel. Includes assumptions, confidence intervals, power, and sample size requirements.
- [Sequential Randomness](https://real-statistics.com/sampling-distributions/sequential-randomness/) - Describes how to test whether a series is random using the mean of successive squared differences (MSSD). Examples and software are included.
- [Runs Test Table](https://real-statistics.com/statistics-tables/runs-test-table/) - Provides a table of critical values for the two-tailed version of the Runs Test, restricted to a significance level of alpha = 5%.
- [Comparing ARIMA Models](https://real-statistics.com/time-series-analysis/arima-processes/comparing-arima-models/) - Describes how to compare ARIMA (Box-Jenkins) models in Excel using Akaike Information Criterion (AIC) and Bayesian Information Criteria (BIC). Incl. example.
- [ARIMA Forecasting](https://real-statistics.com/time-series-analysis/arima-processes/arima-forecasting/) - Describes how to use the Real Statistics data analysis tool to perform ARIMA forecasts based on Excel's Solver. Software and examples are included.
- [Invertibility of MA(q) Processes](https://real-statistics.com/time-series-analysis/moving-average-processes/invertibility-ma-processes/) - Describes what it means for a moving averages process to be invertible. Shows how to calculate the roots of the characteristic equation in Excel.
- [Iterative Proportional Fitting Procedure (IPFP)](https://real-statistics.com/matrices-and-iterative-procedures/iterative-proportional-fitting-procedure-ipfp/) - How to use the Iterative Proportional Fitting Procedure (IPFP) to solve problems of independence testing. We provide examples for both 2 and 3 dimension cases.
- [Real Statistics Power Data Analysis Tool](https://real-statistics.com/hypothesis-testing/real-statistics-power-data-analysis-tool/) - Describes how to use the Real Statistics data analysis tool to calculate the statistical power and sample size requirements for statistical tests in Excel.
- [Central Limit Theorem - Proof](https://real-statistics.com/sampling-distributions/central-limit-theorem/central-limit-theorem-advanced/) - We provide a proof of the Central Limit Theorem. This proof employs the moment/generating function of the normal distribution.
- [Confidence Intervals for Sampling Distributions](https://real-statistics.com/sampling-distributions/confidence-intervals-sampling-distributions/) - Describes how to calculate confidence interval for the sample mean. Provides some simple examples in Excel for how to accomplish this.
- [Single Sample Hypothesis Testing](https://real-statistics.com/sampling-distributions/single-sample-hypothesis-testing/) - Describes how to perform one sample hypothesis testing using the normal distribution and standard normal distribution (via z-score).
- [Sampling Distributions - Advanced](https://real-statistics.com/sampling-distributions/basic-concepts-sampling-distributions/sampling-distribution-advanced/) - Provides the proof of Theorem 1 in Basic Concepts of Sampling Distributions, relating sample mean to the mean of a normal population.
- [Half-Normal Distribution](https://real-statistics.com/normal-distribution/half-normal-distribution/) - Describes the half-normal distribution and how to calculate its pdf, cdf, inverse function and a number of properties in Excel.
- [Rectified Normal Distribution](https://real-statistics.com/normal-distribution/rectified-normal-distribution/) - Describes the rectified normal distribution and how to calculate its pdf, cdf, inverse function, mean and variance in Excel
- [Split Normal Distribution](https://real-statistics.com/normal-distribution/split-normal-distribution/) - Describes the split normal distribution and how to calculate its pdf, cdf, inverse function and a number of properties using Excel.
- [Order statistics from continuous uniform population](https://real-statistics.com/other-key-distributions/uniform-distribution/distribution-of-order-statistics-from-continuous-population/) - Describes order statistics from a uniform population and how they are distributed. Includes properties and provides a number of examples using Excel.
- [Joint and Range Distribution from a Continuous Population](https://real-statistics.com/order-statistics/joint-and-range-distribution-from-a-continuous-population/) - Describes the joint and range distribution of order statistics from a continuous population. Includes Excel functions and a variety of examples.
- [Distribution of Order Statistics from a Continuous Population](https://real-statistics.com/order-statistics/distribution-order-statistics-continuous-population/) - Describes the cdf and pdf of the distribution of order statistics from a continuous population. Includes Excel functions and a variety of examples.
- [Statistical Power for the Binomial Distribution](https://real-statistics.com/binomial-and-related-distributions/statistical-power-binomial-distribution/) - Description of how to calculate the power of a one-sample and two-sample hypothesisi testing using the binomial distribution. Examples are given.
- [Runs](https://real-statistics.com/binomial-and-related-distributions/runs/) - Explains how to calculate the probability of a run of at least r (or at least r heads) in n tosses of a coin using recursion in Excel.
- [Binomial Distribution and Random Walks](https://real-statistics.com/binomial-and-related-distributions/binomial-distribution-and-random-walks/) - Describes the average dispersion from the mean, which is based on random walks and the binomial distribution. We can obtain an estimate using Excel.
- [Skellam Distribution](https://real-statistics.com/binomial-and-related-distributions/poisson-distribution/skellam-distribution/) - Described the Skellam distribution and its relationship to the Poisson distribution. Shows how to use this distribution to find the odds for sporting games.
- [Poisson Distribution](https://real-statistics.com/binomial-and-related-distributions/poisson-distribution/) - Describes how to use the Poisson distribution as well as the relationship with the binomial and normal distributions. Also describes key functions in Excel
- [Multinomial Distribution](https://real-statistics.com/binomial-and-related-distributions/multinomial-distribution/) - Describes how to use the multinomial function and multinomial distribution in Excel. Examples and a new Excel worksheet function are provided.
- [Beta Prime Distribution](https://real-statistics.com/binomial-and-related-distributions/beta-distribution/beta-prime-distribution/) - Describes the probability of the odds of success on a single trial in Excel for a specific sample size & number of successes using the beta prime distribution.
- [Hypergeometric Distribution](https://real-statistics.com/binomial-and-related-distributions/hypergeometric-distribution/) - How to use the hypergeometric distribution in Excel to solve problems similar to those using the binomial distribution but with sampling without replacement.
- [Proportion Testing Analysis Tools](https://real-statistics.com/binomial-and-related-distributions/proportion-distribution/proportion-testing-analysis-tools/) - How to use Real Statistics data analysis tools & functions to perform one- and two-sample proportion testing in Excel. Incl. confidence interval & effect size.
- [Proportion Parameter Confidence Interval](https://real-statistics.com/binomial-and-related-distributions/proportion-distribution/proportion-parameter-confidence-interval/) - Describes various estimates of a confidence interval for the proportion parameter and how to calculate them in Excel. Includes an Excel example.
- [One-sample Proportion Testing](https://real-statistics.com/binomial-and-related-distributions/proportion-distribution/one-sample-proportion-testing/) - Describes how to perform a one-sample proportion test in Excel. Includes examples. Also explains how to estimate the confidence interval.
- [Hypothesis Testing for Binomial Distribution](https://real-statistics.com/binomial-and-related-distributions/hypothesis-testing-binomial-distribution/) - Provides various examples demonstrating how to use Excel functions to perform hypothesis testing using the binomial distribution.
- [Goodness-of-Fit to a Distribution](https://real-statistics.com/chi-square-and-f-distributions/goodness-of-fit/goodness-of-fit-to-a-distribution/) - Describes how to use the chi-square test for goodness of fit of observeddata to a distribution using Excel. Also explores the Poisson index of dispersion.
- [Extreme Value Applications and Theory](https://real-statistics.com/other-key-distributions/generalized-extreme-value-distribution/extreme-value-applications-theory/) - Describes how the Generalized Extreme Value (GEV) distribution is used to predict extreme events. Also, some properties of the GEV distribution are explained.
- [Distribution Property Functions](https://real-statistics.com/other-key-distributions/distribution-property-functions/) - Describes the Real Statistics functions that output the mean and variance of various distributions in the Excel environment.
- [Bayesian Distributions](https://real-statistics.com/other-key-distributions/miscellaneous-distributions/) - Describes the inverse gamma and (scaled) inverse chi-square distributions, which are useful in Bayesian statistics, and how to calculate them in Excel.
- [Frechet Distribution](https://real-statistics.com/other-key-distributions/frechet-distribution/) - Describes key properties of the Frechet distribution (pdf, cdf, mean, median, standard deviation, etc.) and how to use this distribution in Excel.
- [Generalized Pareto Distribution](https://real-statistics.com/other-key-distributions/pareto-distribution/generalized-pareto-distribution/) - Provides the formulas for the pdf, cdf, and inverse of the Generalized Pareto distribution and shows how to calculate these in Excel. Includes key properties.
- [Pareto Distribution](https://real-statistics.com/other-key-distributions/pareto-distribution/) - Describes key properties of the Pareto distribution (pdf, cdf, mean, median, standard deviation, etc.) and how to use this distribution in Excel.
- [Uniform Distribution Proofs](https://real-statistics.com/other-key-distributions/uniform-distribution/uniform-distribution-proofs/) - Provides the proofs of various properties about the uniform distribution and related distributions. Calculus is required for this webpage.
- [Exponential Distribution Proofs](https://real-statistics.com/other-key-distributions/exponential-distribution/exponential-distribution-proofs/) - The proof that the exponential distribution is memoryless and the proof of the connection between the exponential and Poisson distributions.
- [Exponential Distribution](https://real-statistics.com/other-key-distributions/exponential-distribution/) - Brief description of the exponential distribution, which describes the inter-arrival times in a Poisson process and is useful in statistics.
- [Gamma Function](https://real-statistics.com/other-key-distributions/gamma-function/) - Describes the gamma function, which is used to define a number of common probability distribution functions. It also described how to use this function in Excel
- [Correlation Testing for more than two samples](https://real-statistics.com/correlation/two-sample-hypothesis-testing-correlation/correlation-testing-more-than-two-samples/) - Describes how to conduct hypothesis testing for 3 or more correlations. Includes Tukey HSD & Dunnett's post hoc tests, plus contrasts. Includes Excel examples.
- [Two Sample Hypothesis Testing for Correlation](https://real-statistics.com/correlation/two-sample-hypothesis-testing-correlation/) - How to perform hypothesis testing in Excel to determine whether the correlation coefficients of two independent samples are significantly different.
- [Ability and Difficulty Measurements](https://real-statistics.com/reliability/item-response-theory/ability-difficulty-measurements/) - Provides an expanded definition of subject ability and item difficulty for Rasch IRT models, especially with Likert scores and non-dichotomous scoring.
- [Polytomous Model Tools](https://real-statistics.com/reliability/item-response-theory/polytomous-model-tools/) - Describes how to use Real Statistics functions and a data analysis tool to build and analyze the fit of a polytomous Rasch model using the UCON method in Excel.
- [Building a Polytomous Model](https://real-statistics.com/reliability/item-response-theory/building-a-polytomous-model/) - Describes how to manually construct a polytomous Rasch model using the UCON method. How this is done is demonstrated via a step-by-step example in Excel.
- [Polytomous Model Basic Concepts](https://real-statistics.com/reliability/item-response-theory/polytomous-model-basic-concepts/) - Describes the basic concepts of the UCON method of Rasch analysis for polytomous data (i.e. scores 0, 1, 2, …, m where m > 0). Key formulas are described.
- [PROX Model Example](https://real-statistics.com/reliability/item-response-theory/prox-model-example/) - Describes how to build a PROX model for Rasch item response analysis in Excel using a specific example. The formulas in the spreadsheet are explained.
- [PROX Model for Rasch Analysis](https://real-statistics.com/reliability/item-response-theory/prox-model-rasch/) - Describes how to build a PROX model (ability & difficulty are normally distributed) for Rasch item response theory analysis Examples and software are included.
- [Building a Rasch Model](https://real-statistics.com/reliability/item-response-theory/building-rasch-model/) - Describes how to build a Rasch model in Excel and how to interpret the results. Also explains how good a fit the model is.
- [Rasch Analysis Motivation](https://real-statistics.com/reliability/item-response-theory/rasch-analysis-motivation/) - Describes the motivation for performing Rasch analysis and the benefits obtained. This is the first of a series of tutorials on Rasch item response analysis.
- [Power and Sample Size for Correlation Testing](https://real-statistics.com/correlation/one-sample-hypothesis-testing-correlation/power-sample-size-correlation-testing/) - Describes how to determine the power and sample size requirements for one sample correlation testing in Excel. Includes examples and software.
- [Correlation and Chi-square Test for Independence](https://real-statistics.com/correlation/dichotomous-variables-chi-square-independence-testing/) - How to perform a correlation test on dichotomous variables to get the same results as can be obtained by using the chi-square test for independence.
- [Comparing correlation coefficients of overlapping samples](https://real-statistics.com/correlation/two-sample-hypothesis-testing-correlation/comparing-correlation-coefficients-two-dependent-samples/) - How to perform hypothesis testing in Excel to determine whether the correlation coefficients of two overlapping dependent samples are significantly different.
- [Correlation Data Analysis Tool](https://real-statistics.com/correlation/correlation-data-analysis-tool/) - Describes how to use the Real Statistics Correlation data analysis tool to calculate Pearson's, Spearman's and Kendall's correlation and do hypothesis testing.
- [Correlation in Relationship to t-test](https://real-statistics.com/correlation/dichotomous-variables-t-test/) - Correlation of dichotomous variables and relation to t-test. In this way two sample comparison of means t-testing can be turned into a correlation problem.
- [Correlation as t-test proofs](https://real-statistics.com/correlation/dichotomous-variables-t-test/correlation-as-t-test-proofs/) - Provides proofs of properties linking correlations and t-tests. Includes properties about the point-biserial correlation and r-effect size
- [Kendall's Correlation Testing with Ties](https://real-statistics.com/correlation/kendalls-tau-correlation/kendalls-correlation-testing-with-ties/) - Describes how to perform hypothesis testin for Kendall's tau correlation coefficient when there are a large number of ties.
- [Kendall's Tau Hypothesis Testing](https://real-statistics.com/correlation/kendalls-tau-correlation/kendalls-tau-hypothesis-testing/) - Describes how to do hypothesis testing for Kendall's tau correlation coefficient for small samples using a table of critical vales. Example is given.
- [Spearman’s Rank Correlation](https://real-statistics.com/correlation/spearmans-rank-correlation/) - Provides a description of Spearman’s rank correlation, also called Spearman's rho, and how to calculate it in Excel. This is a non-parametric measure.
- [Resampling for Correlation](https://real-statistics.com/correlation/resampling-correlation/) - Describing how to perform resampling (bootstrapping, randomization) for correlation testing and confidence interval. Examples and software are included.
- [Polychoric Correlation Tool](https://real-statistics.com/correlation/polychoric-correlation/polychoric-correlation-tool/) - Describes the Real Statistics Polychoric Correlation data analysis tool and various Excel worksheet functions in support of the polychoric correlation.
- [Polychoric Correlation Basic Concepts](https://real-statistics.com/correlation/polychoric-correlation/polychoric-correlation-basic-concepts/) - Describes the basic ideas underlying the polychoric correlation, including the tetrachoric correlation coefficient. These correlations are compared to Pearson's
- [Correlation Testing via Exact Test](https://real-statistics.com/correlation/one-sample-hypothesis-testing-correlation/correlation-testing-via-exact-test/) - Describes the distribution of the correlation coefficient and hypothesis testing using this distribution. Includes examples and software.
- [Correlation testing via Fisher transformation](https://real-statistics.com/correlation/one-sample-hypothesis-testing-correlation/correlation-testing-via-fisher-transformation/) - How to perform one sample correlation hypothesis testing in Excel using the Fisher transformation; includes examples and software.
- [Correlation testing via t test](https://real-statistics.com/correlation/one-sample-hypothesis-testing-correlation/correlation-testing-via-t-test/) - Describes how to perform a one-sample correlation test using the t-test in Excel. Includes examples and software. Also provides Excel functions for the test.
- [One Sample Hypothesis Testing for Correlation](https://real-statistics.com/correlation/one-sample-hypothesis-testing-correlation/) - How to perform one sample correlation hypothesis testing in Excel using t test or Fisher transformation; includes examples, sample size and power calculation.
- [Markov-Chain Monte Carlo](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/markov-chain-monte-carlo/) - Introduction to Markov-Chain Monte Carlo (MCMC) for data that follows a binomial distribution. An example of a Markov chain is presented.
- [Basic Concepts for ANOVA](https://real-statistics.com/one-way-analysis-of-variance-anova/basic-concepts-anova/) - Review of the basic concepts behind the analysis of variance (ANOVA) and how to perform ANOVA tests in Excel. Numerous examples are provided.
- [Probability Functions](https://real-statistics.com/probability-functions/) - Brief overview of concepts in probability theory that are useful in statistics, as well as basic concepts of discrete and continuous probability distributions.
- [Advanced Multiple Correlation](https://real-statistics.com/multiple-regression/multiple-correlation-advanced/) - How to use regression to calculate the correlation coefficient in Excel. Includes the partial correlation coefficient and the partial correlation matrix.
- [Schur's Factorization](https://real-statistics.com/linear-algebra-matrix-topics/schur-factorization/) - Describes how to find the Schur's decomposition for a square matrix, which will be used to calculate real eigenvectors for non-symmetric matrices in Excel
- [Singular Value Decomposition](https://real-statistics.com/linear-algebra-matrix-topics/singular-value-decomposition/) - Tutorial on the Singular Value Decomposition and how to calculate it in Excel. Also describes the pseudo-inverse of a matrix and how to calculate it in Excel.
- [Positive Definite Matrices](https://real-statistics.com/linear-algebra-matrix-topics/positive-definite-matrices/) - Tutorial on positive definite and semidefinite matrices and how to calculate the square root of a matrix in Excel. Provides theory and examples.
- [Hessenberg Decomposition](https://real-statistics.com/linear-algebra-matrix-topics/hessenberg-decomposition/) - Describes how to identify a Hessenberg decomposition of a square matrix in Excel based on an upper triangular matrix, tridiagonal matrix for a symmetric matrix.
- [Orthogonal Vectors and Matrices](https://real-statistics.com/linear-algebra-matrix-topics/orthogonal-vectors-matrices/) - Tutorial on orthogonal vectors and matrices, including the Gram-Schmidt Process for constructing an orthonormal basis. Also Gram Schmidt calculator in Excel.
- [Eigenvalues and Eigenvectors](https://real-statistics.com/linear-algebra-matrix-topics/eigenvalues-eigenvectors/) - Tutorial on eigenvalues and eigenvectors, plus access to functions that calculate the eigenvalues and eigenvectors of a square matrix in Excel.
- [Rank of a Matrix](https://real-statistics.com/linear-algebra-matrix-topics/matrix-rank/) - Review of rank of a matrix and its relationship to solutions to linear equations (and Gaussian elimination), dimension, null space and range.
- [Linear Independent Vectors](https://real-statistics.com/linear-algebra-matrix-topics/linear-independent-vectors/) - Describes fundamental properties of linear independence and the basis of a set of vectors. Describes concepts such as span and dimension as well.
- [Determinant of a Square Matrix](https://real-statistics.com/matrices-and-iterative-procedures/determinants-and-simultaneous-linear-equations/) - Describes how to calculate the determinant of a square matrix by hand, and also how to do it in Excel. Examples are given and a worksheet function is explained.
- [Kolmogorov Distribution](https://real-statistics.com/tests-normality-and-symmetry/statistical-tests-normality-symmetry/kolmogorov-smirnov-test/kolmogorov-distribution/) - Description of the Kolmogorov distribution and how it can be used to calculate the p-value and critical value for the Kolmogorov-Smirnov test; incl. examples.
- [Chi-square Test for Normality](https://real-statistics.com/tests-normality-and-symmetry/statistical-tests-normality-symmetry/chi-square-test-for-normality/) - How to use the chi-square goodness of fit test to determine in Excel whether sample data comes from a population which is normally distributed.
- [Analysis of Skewness and Kurtosis](https://real-statistics.com/tests-normality-and-symmetry/analysis-skewness-kurtosis/) - Explains how to use the values of skewness (SKEW) and kurtosis in Excel to determine whether data is normally distributed, incl. Jarque-Bera test.
- [Graphical Tests for Normality and Symmetry](https://real-statistics.com/tests-normality-and-symmetry/graphical-tests-normality-symmetry/) - Describes how to use graphs (histogram, QQ plot and box plot) to determine whether data are normally distributed and/or symmetric. Excel examples are provided.
- [GoF ICF Multivariate Normal Distribution](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/goodness-of-fit-tests-characteristic-function/gof-icf-multivariate-normal-distribution/) - Tutorial on goodness-of-fit tests in Excel based on the characteristic function. Examples are provided for multivariate normal distributions.
- [GoF ICF Logistic Distribution](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/goodness-of-fit-tests-characteristic-function/gof-icf-logistic-distribution/) - Tutorial on goodness-of-fit tests in Excel based on the characteristic function. Examples are provided for the logistic distribution
- [GoF ICF Gumbel & Weibull](https://real-statistics.com/non-parametric-tests/goodness-of-fit-tests/goodness-of-fit-tests-characteristic-function/gof-icf-gumbel-weibull/) - Tutorial on goodness-of-fit tests in Excel based on the characteristic function. Examples are provided for the Gumbel and Weibull distributions.
- [Runs Test with more than two categories](https://real-statistics.com/non-parametric-tests/one-sample-runs-test/runs-test-with-more-than-two-categories/) - Describes how to perform a one-sample runs test in Excel when there are more than two categories. Examples and new Excel worksheet functions are provided
- [One-Sample Runs Test](https://real-statistics.com/non-parametric-tests/one-sample-runs-test/) - Describes several methods for performing a one-sample runs test in Excel. Examples are provided as well as new Excel worksheet functions.
- [McNemar Test Effect Size and Power](https://real-statistics.com/non-parametric-tests/mcnemars-test/mcnemar-test-effect-size-and-power/) - Describes how to calculate the effect size, power, and minimum sample size for McNemar's test. Provides examples using Excel.
- [Multiple Mann-Whitney Tests](https://real-statistics.com/non-parametric-tests/mann-whitney-test/multiple-mann-whitney-tests/) - Describes how to perform multiple Mann-Whitney tests in Excel while taking care of familywise error. Examples and Excel capabilities are provided
- [Bayesian Non-parametric Testing](https://real-statistics.com/bayesian-statistics/bayesian-non-parametric-testing/) - Tutorial on Bayesian non-parametric testing. Includes the Wilcoxon Signed-Ranks and Mann-Whitney tests. Provides examples in Excel and Excel tools.
- [Assumptions for Two-Sample t-Test](https://real-statistics.com/students-t-distribution/two-independent-samples-t-test/assumptions-for-two-sample-t-test/) - Provides information about the assumptions for the two-sample t-test; in particular, the impact of violations on the type I error.
- [Runs Up/Down Test](https://real-statistics.com/non-parametric-tests/one-sample-runs-test/runs-up-down-test/) - Describes how to perform a one-sample runs up/down test in Excel. Examples are provided as well as a new Excel worksheet function.
- [Statistical Power and Sample Size](https://real-statistics.com/hypothesis-testing/statistical-power/) - How to determine power of a test based on specific sample size, effect size and alpha. Also determine the sample size needed to achieve required power target.
- [Hypothesis Testing](https://real-statistics.com/hypothesis-testing/) - Review of hypothesis testing (via null and alternative hypotheses) and the related topics of confidence intervals, effect size and statistical power.
- [Null and Alternative Hypothesis](https://real-statistics.com/hypothesis-testing/null-hypothesis/) - Describes how to test the null hypothesis that some estimate is due to chance vs the alternative hypothesis that there is some statistically significant effect.
- [Distribution Fitting Tool](https://real-statistics.com/distribution-fitting/distribution-fitting-tool/) - How to use the Distribution Fitting analysis tool to find the best-fit parameters for the normal, Weibull, exponential, beta, gamma, and uniform distribution.
- [Bayesian Binomial Testing Tools](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/analytic-approach-binomial-data/bayesian-binomial-testing-tools/) - Describes how to perform hypothesis testing for binomially distributed data in Excel using special software. Examples are provided.
- [Bayesian Mann-Whitney Test](https://real-statistics.com/bayesian-statistics/bayesian-non-parametric-testing/bayesian-mann-whitney-test/) - Describes the Bayesian version of the Mann-Whitney non-parametric test for two independent samples. Provides examples in Excel and Excel tools.
- [Gibbs Sampler Normal Distribution](https://real-statistics.com/bayesian-statistics/bayesian-statistics-normal-data/gibbs-sampler-normal-distribution/) - Describes how to use Gibbs Sampler to create a sample for the bivariate normal distribution. An example in Excel is provided.
- [Credible Interval and HDI](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/bayesian-grid-approximation/credible-interval-hdi/) - Defines a credible interval and the high-density interval (HDI) and shows how to calculate an HDI in Excel from a Bayesian grid
- [Creating a Grid using Real Statistics](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/bayesian-grid-approximation/creating-grid-using-real-statistics/) - Describes how to create a grid for Bayesian analysis in Excel using a Real Statistics data analysis tool. Includes an example and software
- [Bayesian Grid Approximation](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/bayesian-grid-approximation/) - Describes how to construct a grid in Bayesian analysis for binomially distributed data using triangular distribution priors. Includes Excel examples
- [High Density Interval (HDI)](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/analytic-approach-binomial-data/high-density-interval-hdi/) - Describes how to calculate a high-density interval (HDI) in Excel for a conjugate beta distribution when the data follow a binomial distribution
- [Effective Sample Size for Metropolis Algorithm](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/markov-chain-monte-carlo/ess-metropolis-algorithm/) - Describes how to calculate the effective sample size (ESS) for the Metropolis algorithm using a binomial data example in Excel.
- [Bayesian Analysis using Grids](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/bayesian-grid-approximation/bayesian-analysis-using-grids/) - Describes how to estimate the mean, median, mode, HDI, equal-tailed CI, and Bayesian Factor for Bayesian analysis in Excel based on a grid.
- [Bayesian Signed-Rank Test Support](https://real-statistics.com/bayesian-statistics/bayesian-non-parametric-testing/bayesian-signed-ranks-test/bayesian-signed-rank-test-support/) - Describes various Excel worksheet functions to perform the Bayesian version of the Wilcoxon Signed-Ranks non-parametric test. Also explains a data analysis tool
- [Bayesian Gamma Test](https://real-statistics.com/bayesian-statistics/bayesian-non-parametric-testing/bayesian-gamma-test/) - How to conduct a non-parametric Gamma correlation test using a Bayesian approach in Excel. Provides worksheet functions, data analysis tool and examples.
- [Bayesian Kendall’s Tau Test](https://real-statistics.com/bayesian-statistics/bayesian-non-parametric-testing/bayesian-kendalls-tau/) - How to conduct a non-parametric Kendall's tau correlation test using a Bayesian approach in Excel. Provides worksheet functions, data analysis tool & examples.
- [Bayesian Independence Testing Support](https://real-statistics.com/bayesian-statistics/bayesian-independence-testing/bayesian-independence-testing-support/) - Describes Excel worksheet functions and data analysis tools provided by the Real Statistics Resource Pack to perform Bayesian independence testing.
- [Bayesian Correlation Testing](https://real-statistics.com/bayesian-statistics/bayesian-correlation-testing/) - Describes how to conduct a correlation hypothesis test using a Bayesian approach in Excel. Worksheet functions, data analysis tools and examples are provided.
- [Bayesian Beta Test Sample and Effect Sizes](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/analytic-approach-binomial-data/bayesian-beta-sample-and-effect-sizes/) - Determine the beta effect size needed to achieve a given level of support for a hypothesis for a given sample size. Also find the sample size needed in Excel.
- [Bayesian Characterization of a Beta Distribution](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/analytic-approach-binomial-data/bayesian-characterization-of-a-beta-distribution/) - Describes how to estimate the mean, median, mode, HDI, equal-tailed CI, and Bayesian Factor for Bayesian analysis in Excel based on a beta distribution.
- [Bayesian Hypothesis Testing](https://real-statistics.com/bayesian-statistics/bayesian-statistics-introduction/bayesian-hypothesis-testing/) - Describes how to perform hypothesis testing in the Bayes context. Also describes the Bayes Factor and provides an example of hypothesis testing.
- [Analytic Approach for Binomial Data](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/analytic-approach-binomial-data/) - Describes how to calculate the posterior pdf for binomially distributed data with a beta prior, as well as the HDI. Includes Excel examples and software.
- [Wakeby Distribution](https://real-statistics.com/other-key-distributions/wakeby-distribution/) - Describes how to calculate the cdf, pdf, and inverse cdf for the Wakeby distribution in Excel. Provides Excel worksheet functions
- [Other Key Distributions](https://real-statistics.com/other-key-distributions/) - Review of the uniform distribution, exponential distribution, gamma function, gamma distribution Weibull distribution, etc. in the Excel environment.
- [Bayesian Signed Ranks Test](https://real-statistics.com/bayesian-statistics/bayesian-non-parametric-testing/bayesian-signed-ranks-test/) - Describes the Bayesian version of the Wilcoxon Signed-Ranks non-parametric test. Provides examples in Excel and Excel tools.
- [Disappearing Addins ribbon](https://real-statistics.com/appendix/faqs/disappearing-addins-ribbon/) - Describes what to do if the Addins ribbon does not appear or the Real Statistics add-in disappears from the Addins ribbon.
- [Calling Real Statistics Functions in VBA](https://real-statistics.com/real-statistics-environment/calling-real-statistics-functions-in-vba/) - Describes how to call Real Statistics functions from other VBA programs, including the code and the references that need to be used.
- [Real Statistics Time Series Analysis Functions](https://real-statistics.com/real-statistics-environment/real-statistics-time-series-analysis-functions/) - A summary of all the time series functions contained in the Real Statistics Resource Pack. A link is provided for each function to get further information.
- [Seasonality for Time Series](https://real-statistics.com/time-series-analysis/seasonal-arima-sarima/seasonality/) - Describes seasonality for time series. Extends notions of random walk, drift, etc. to time series with seasonality. Three approaches are described
- [Moving Average Proofs](https://real-statistics.com/time-series-analysis/moving-average-processes/moving-average-proofs/) - Provides the proofs of various properties about finite Moving Average (MA) Processes, as well as infinite Moving Average processes.
- [Ordinal Regression](https://real-statistics.com/ordinal-regression/) - Tutorial on ordinal logistic regression, Models are built using Excel's Solver and Newton's method. Excel examples and analysis tools are provided.
- [Real Statistics Ordinal Regression Support](https://real-statistics.com/ordinal-regression/real-statistics-ordinal-regression-support/) - Describes how to use Real Statistics functions and data analysis tools to create an ordinal regression model in Excel and use it to make predictions.
- [Proportional Odds Model Proofs](https://real-statistics.com/ordinal-regression/proportional-odds-model/proportional-odds-model-proofs/) - Provides the proofs of Properties 1 and 2 which show how to calculate the ordinal regression coefficients for the proportional odds model using Newton's method.
- [Proportional Odds Model](https://real-statistics.com/ordinal-regression/proportional-odds-model/) - Describes how to build an ordinal logistic regression model using the proportional odds model via Newton's method for minimizing the log-likelihood function.
- [Real Statistics Support for SARIMA](https://real-statistics.com/time-series-analysis/seasonal-arima-sarima/real-statistics-support-for-sarima/) - Describes how to to use the Real Statistics SARIMA data analysis tool to create a SARIMA model and forecast in Excel. The process is illustrated via an example.
- [SARIMA Forecast Example](https://real-statistics.com/time-series-analysis/seasonal-arima-sarima/sarima-forecast-example/) - Shows how to create a SARIMA forecast based on Amazon quarterly revenues. The webpage shows how to build the forecast, step-by-step in Excel.
- [SARIMA Model Example](https://real-statistics.com/time-series-analysis/seasonal-arima-sarima/sarima-example/) - Shows how to create a SARIMA model (for Amazon revenues), step by step, in Excel using ordinary differencing as well as seasonal differencing.
- [SARIMA Models](https://real-statistics.com/time-series-analysis/seasonal-arima-sarima/sarima-models/) - Defines a seasonal ARIMA (SARIMA) model and describes the formulas used to create a forecast based on this type of time series model.
- [Infinite Moving Average Processes](https://real-statistics.com/time-series-analysis/moving-average-processes/infinite-moving-average-processes/) - Describes how to calculate the psi coefficients in Excel for an infinite moving averages process which represents an ARMA process. Incl. examples and software.
- [Autoregressive Processes](https://real-statistics.com/time-series-analysis/autoregressive-processes/) - Tutorial on autoregressive processes and time series, including examples in Excel and software. Describes how to build AR(p) models and create forecasts.
- [Sorting and Removing Duplicates](https://real-statistics.com/real-statistics-environment/data-conversion/sorting-and-removing-duplicates/) - Describes how to sort data and sort data removing duplicates using the Real Statistics Resource Pack. Duplicates SORT and UNIQUE available from Excel 365.
- [Seasonal ARIMA (SARIMA)](https://real-statistics.com/time-series-analysis/seasonal-arima-sarima/) - This part of the Real Statistics website provides a tutorial on Seasonal ARIMA modelling and forecasting. Excel examples and software are provided.
- [Moving Average Processes](https://real-statistics.com/time-series-analysis/moving-average-processes/) - Tutorial on moving average (MA) process. Describes how to find ACF and MA coefficients in Excel. Excel worksheet functions and examples are provided.
- [Stochastic Processes](https://real-statistics.com/time-series-analysis/stochastic-processes/) - Tutorial on stochastic processes, including stationary processes, white noise, random walk, autocorrelation, etc. Includes examples and Excel software.
- [Miscellaneous Time Series Topics](https://real-statistics.com/time-series-analysis/time-series-miscellaneous/) - Describes additional topics for Time Series analysis, including Mann-Kendall test, Sen's slope, Granger causality, cointegration, cross-correlations, ARIMAX.
- [ARMA(1,1) Processes](https://real-statistics.com/time-series-analysis/arma-processes/arma11-processes/) - Describes the basic characteristics of an ARMA(1,1) process, including mean, variance and autocorrelation (ACF). Examples and software is provided.
- [ARMA Processes](https://real-statistics.com/time-series-analysis/arma-processes/) - Tutorial on autoregressive moving average processes, including how to build ARMA models in Excel and use them for forecasting. Software and examples included.
- [ARIMA Processes](https://real-statistics.com/time-series-analysis/arima-processes/) - Describes how to find an ARIMA process in Excel which best fits time series data. Includes Box-Jenkins approach, examples and software.
- [Plots of Regression Confidence and Prediction Intervals](https://real-statistics.com/regression/confidence-and-prediction-intervals/plots-regression-confidence-prediction-intervals/) - Shows how to create plots of the confidence and prediction intervals in Excel for a regression line. The sequence of steps is described and examples given
- [Dunn's Test after KW](https://real-statistics.com/one-way-analysis-of-variance-anova/kruskal-wallis-test/dunns-test-after-kw/) - Describes how to conduct Dunn's test after a significant Kruskal-Wallis test. Excel examples are included and Excel functionality described.
- [Biserial Correlation](https://real-statistics.com/correlation/biserial-correlation/) - Shows how to calculate the biserial correlation coefficient in Excel, as well as the p-value and confidence interval. Example included.
- [Monte Carlo Integration](https://real-statistics.com/bayesian-statistics/monte-carlo-integration/) - Describes Monte Carlo techniques for calculating integrals, expected values and cumulative distribution functions useful in Bayesian analysis
- [Fitting Laplace Parameters via MLE](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-laplace-parameters-via-mle/) - Describes how to find Laplace distribution parameters that best fit a data set using maximum likelihood estimation (MLE) in Excel. Incl. examples & software.
- [Weighted Variance, Standard Deviation, and Covariance](https://real-statistics.com/descriptive-statistics/measures-variability/weighted-variance-standard-deviation-and-covariance/) - Describes how to calculate the weighted variance, standard deviation, and covariance in Excel for both reliability and frequency weights.
- [Cross Correlations](https://real-statistics.com/time-series-analysis/time-series-miscellaneous/cross-correlations/) - Describes how to create cross correlations, i.e. correlation between one data set and another with a lag. Example, chart and Excel software are provided.
- [Fitting Binomial Distribution](https://real-statistics.com/distribution-fitting/distribution-fitting-via-maximum-likelihood/fitting-binomial-distribution/) - Describes how to find binomial distribution parameter p that best fit a data set using MoM and MLE techniques in Excel. Includes examples & worksheet functions.
- [Bayesian Statistics for Binomial Distributed Data](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/) - Tutorial on Bayesian Statistics in the context of data that has a binomial distribution: beta conjugate priors, grids, MCMC. Includes Excel examples & software
- [Bayesian Independence Testing](https://real-statistics.com/bayesian-statistics/bayesian-independence-testing/) - How to determine whether the two variables defined in a contingency table are independent using a Bayesian approach. Incl. Excel examples & worksheet functions
- [Other Multivariate Normal Properties](https://real-statistics.com/multivariate-statistics/multivariate-normal-distribution/other-multivariate-normal-properties/) - Describes a variety of basic properties about the multivariate normal distribution (incl. the Multivariate Central Limit Theorem), and the Wishart distribution.
- [Multivariate Central Limit Theorem](https://real-statistics.com/multivariate-statistics/multivariate-normal-distribution/multivariate-central-limit-theorem/) - Describes the multivariate central limit theorem and the multivariate law of large numbers as extensions to the univariate versions.
- [Random Multivariate Normal Vectors](https://real-statistics.com/multivariate-statistics/multivariate-normal-distribution/random-multivariate-normal-vectors/) - Describes how to generate multivariate normal random vectors in Excel based on the Cholesky decomposition. Software and examples are included.
- [Bayesian Hypothesis Testing for Normal Data](https://real-statistics.com/bayesian-statistics/bayesian-statistics-normal-data/bayesian-hypothesis-testing-normal/) - Describes how to perform hypothesis testing for normally distributed data using a Bayesian approach. Here we describe one-sided tests.
- [Bayesian Statistics for Normal Data](https://real-statistics.com/bayesian-statistics/bayesian-statistics-normal-data/) - Tutorial on how to use Bayesian statistics techniques where the data follows a normal distribution. Examples are provided using Excel
- [Beta Distribution](https://real-statistics.com/binomial-and-related-distributions/beta-distribution/) - How to find the probability of success on any single trial in Excel for a specific sample size and total number of successes using the beta distribution.
- [Bayesian Binomial Hypothesis Testing](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/analytic-approach-binomial-data/bayesian-binomial-hypothesis-testing/) - Describes how to conduct hypothesis testing for binomially distributed data using a Bayesian approach. Provides examples in Excel.
- [Two-way Repeated Measures Anova Tool](https://real-statistics.com/anova-repeated-measures/two-within-subjects-factors/two-way-repeated-measures-anova-tool/) - Describes in detail how to perform ANOVA repeated measures with two within-subjects factors. Describes Real Statistics data analysis tool.
- [Statistics Tables](https://real-statistics.com/statistics-tables/) - Provides links to various statistics tables. These tables correspond to tests for which Excel doesn't provide built-in functions.
- [Beta Conjugate Prior](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/analytic-approach-binomial-data/beta-conjugate-prior/) - Describes how to calculate the (beta) posterior pdf for binomially distributed data with a beta prior. Includes Excel examples and software.
- [Multivariate Repeated Measures Tests](https://real-statistics.com/multivariate-statistics/multivariate-repeated-measures-tests/) - Describes how to use multivariate techniques to perform repeated measures analyses 8in Excel without assuming sphericity. Software and examples are included.
- [One-Sample Kolmogorov-Smirnov Table](https://real-statistics.com/statistics-tables/kolmogorov-smirnov-table/) - Kolmogorov-Smirnov Table of critical values for alpha = .01, .02., .05, .10, .15, .20. Used with the one-sample Kolmogorov-Smirnov test.
- [Spearman’s Rho Table](https://real-statistics.com/statistics-tables/spearmans-rho-table/) - Provides a table of critical values for the Spearman’s Rho Test for significance levels alpha = .01, .02, .05, .10 and sample size up to 30.
- [Augmented Dickey-Fuller Table](https://real-statistics.com/statistics-tables/augmented-dickey-fuller-table/) - Provides a table of critical values for the Augmented Dickey Fuller test based on work by MacKinnon. This table is used by Real Statistics.
- [Testing for Normality and Symmetry](https://real-statistics.com/tests-normality-and-symmetry/) - How to test for symmetry and normality in Excel using histograms, box plots, QQ plots, Chi-square, Kolmogorov-Smironov, Shapiro-Wilk, skewness and kurtosis.
- [Real Statistics Univariate GMM Support](https://real-statistics.com/multivariate-statistics/gaussian-mixture-models/real-statistics-univariate-gmm-support/) - Describes the worksheet functions and data analysis tools provided by the Real Statistics software to create and utilize univariate GMM models in Excel.
- [Rasch Analysis Basic Concepts](https://real-statistics.com/reliability/item-response-theory/rasch-analysis-basic-concepts/) - Tutorial on Rasch item response analysis. Includes how to build a Rasch model for dichotomous data and how to interpret the model.
- [One Sample Effect Size](https://real-statistics.com/students-t-distribution/one-sample-t-test/one-sample-effect-size/) - Describes the effect size for a one-sample t-test and how to calculate a 1-alpha confidence interval for Cohen effect size d using the Hedges and Olkin method.
- [Two Sample (Equal Variances) Effect Size](https://real-statistics.com/students-t-distribution/two-independent-samples-t-test/two-sample-effect-size/) - Describes how to calculate a 1-alpha confidence interval for Cohen effect size d for a two-sample test using the Hedges and Olkin method.
- [Excel's Data Table Facility](https://real-statistics.com/excel-environment/excels-data-table-facility/) - Describes how to use Excel's Data Table capability based on a formula f(x) in one variable. Examples are provided to illustrate key points.
- [Non-standardized t distribution](https://real-statistics.com/students-t-distribution/non-standardized-t-distribution/) - Describes the key properties of the non-standardized (aka three-parameter) t distribution and how to calculate the pdf and cdf in Excel.
- [CI Functions for Effect Sizes d and g](https://real-statistics.com/students-t-distribution/confidence-interval-effect-size-power/ci-functions-effect-size-d/) - Describes Real Statistics functions that calculate confidence intervals for Cohen's effect size d associated with the t test in Excel.
- [Independence Testing Follow-up](https://real-statistics.com/chi-square-and-f-distributions/independence-testing/independence-testing-follow-up/) - Describes how to perform post-hoc testing after a significant chi-square test of independence. Examples and software are provided.
- [Multivariate Normality Functions](https://real-statistics.com/multivariate-statistics/multivariate-normal-distribution/multivariate-normality-functions/) - Describes how to calculate the cdf and pdf of the bivariate normal distribution in Excel as well as the Mahalanobis distance between two vectors
- [Bayesian Hypothesis Testing Theory](https://real-statistics.com/bayesian-statistics/bayesian-statistics-normal-data/bayesian-hypothesis-testing-normal/bayesian-hypothesis-testing-theory/) - Provides the theoretical basis for hypothesis testing for normally distributed data using a Bayesian approach. Uses calculus.
- [Jeffreys' Priors](https://real-statistics.com/bayesian-statistics/non-informative-priors/jeffreys-priors/) - Describes what a Jeffreys' prior is and what are the Jeffreys' priors for binomially distributed and normally distributed data.
- [Non-informative Priors](https://real-statistics.com/bayesian-statistics/non-informative-priors/) - Provides a description on non-informative priors, including improper priors and Jefferies priors. These are used when we don't have useful prior information.
- [Confidence Interval for the Survival Function](https://real-statistics.com/survival-analysis/kaplan-meier-procedure/confidence-interval-for-the-survival-function/) - Describes how to calculate the standard error and confidence intervals for the survival function S(t) from Kaplan-Meier. Includes examples and Excel software.
- [Conjugate Priors Normal Distribution](https://real-statistics.com/bayesian-statistics/bayesian-statistics-normal-data/conjugate-priors-normal-distribution/) - Describes the conjugate priors for normal data: (1) mean unknown and variance known, (2) variance unknown and mean known and (3) mean and variance are unknown.
- [Real Statistics Capabilities for Kaplan-Meier](https://real-statistics.com/survival-analysis/kaplan-meier-procedure/real-statistics-kaplan-meier/) - Describes how to perform Kaplan-Meier survival analysis in Excel, as well as the logrank test. Excel examples are provided as well as Excel tools.
- [Monte Carlo Simulation Normal Data](https://real-statistics.com/bayesian-statistics/bayesian-statistics-normal-data/monte-carlo-simulation-normal-data/) - Provides step-by-step examples of using Monte Carlo simulation in Excel based on conjugate priors for normally distributed data.
- [Gibbs Sampler Two Sample Binomial](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/bayesian-approach-for-two-binomial-samples/gibbs-sampler-two-sample-binomial/) - Describes how to apply Gibbs Sampler to the two independent, binomially distributed samples case. Excel examples and software are included.
- [Two Sample Binomial Metropolis Algorithm](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/bayesian-approach-for-two-binomial-samples/two-sample-binomial-metropolis/) - Shows how to apply the Metropolis algorithm to the case where there are two independent, binomially distributed samples. Excel example and software are included
- [Two Sample Binomial Grid](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/bayesian-approach-for-two-binomial-samples/two-sample-binomial-grid/) - Describes how to estimate the posterior distribution for two samples that are binomially distributed using a grid in Excel.
- [Bayesian Approach for Two Binomial Samples](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/bayesian-approach-for-two-binomial-samples/) - Describes how to apply various Bayesian techniques (grid, MCMC, beta conjugate prior) to two samples whose data follows a binomial distribution. Excel examples.
- [Two Binomial Samples Beta Prior](https://real-statistics.com/bayesian-statistics/bayesian-statistics-for-binomial-distributed-data/bayesian-approach-for-two-binomial-samples/two-binomial-samples-beta-prior/) - Describes how to determine the posterior distribution for two samples that are binomially distributed assuming a beta prior in Excel.

## Categories

- [Uncategorized](https://real-statistics.com/category/uncategorized/)
- [New Release](https://real-statistics.com/category/new-release/)
- [Hint](https://real-statistics.com/category/hint/)
- [Announcement](https://real-statistics.com/category/anouncement/)
- [Game](https://real-statistics.com/category/game/)
Stored receipt and evidence

Inspect the site's MCP endpoint

Offer samples

Action samples

Product samples

robots.txt

llms.txt

llms-full.txt

Top Sites>Rreal-statistics.com

Stored receipt and evidence

Inspect the site's MCP endpoint

Offer samples

Action samples

Product samples

robots.txt

llms.txt

llms-full.txt

Top Sitesreal-statistics.com
