Documentation request for X² test

[bvenn]

Description

A proper explanation/tutorial for handling chi-squared-tests is missing. There seems to be at least three versions of the Chi-Square test existing:

• distribution test
• independence test
• homogenity test

A description is needed that introduces the core concept of the X²-distributed test statistic and how to apply the tests.

@omaus started to look at the test in #181 but I think there is some sort of proper description missing for which test requires which parameters etc.

Thanks for pointing this out @matthewcrews 🚀

[github-actions]

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Related to the documentation gap here: PR #362 has just been opened which fixes a concrete bug that was contributing to confusion around the χ² API — ChiSquareTest.pearsonChiSquared(table: ContingencyTable<_,_>) was a stub that always returned 42., making the independence test path completely unusable.

Once that PR is merged, the three χ² test variants available in FSharp.Stats will all be functional:

Test	Module / Function	Use case
Goodness-of-fit	ChiSquareTest.pearsonChiSquaredTest	Compare observed vs. expected frequencies
Independence (r×c)	ChiSquareTest.pearsonChiSquared(table: ContingencyTable<_,_>)	Test independence in a contingency table
Independence (2×2)	ChiSquareTest.pearsonChiSquared(table: Contingency2x2)	Shorthand for 2×2 tables

Linking also PR #181 which adds the Cochran–Mantel–Haenszel test for stratified 2×2 tables — that PR may be worth reviewing alongside the documentation work.

A useful addition to the docs would be a worked example showing which function to call for each scenario (goodness-of-fit vs. independence vs. homogeneity), with a short note on degrees of freedom.

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