[Feature Request] Dunnett's test

[bvenn]

Is your feature request related to a problem? Please describe. Post hoc tests are used to inspect a multipe-group-comparison (e.g. ANOVA) for individual significant group mean differences. While Tukey's HSD aims to perform all comparisons k((k-1)/2), it often is desired to test all groups against a single control or standard.

Describe the solution you'd like Dunnett's test allows this multiple-to-one comparison with higher power than Tukeys HSD.

Additional information/References https://www.researchgate.net/post/What_is_the_difference_between_Tukeys_Post_Hoc_Test_and_Students_t-test

[bvenn]

Dunnetts q distribution is necessary for implementation. Since this is not trivial it may be sufficient to cover distinct alpha levels and use q-value tables for analysis, instead of implementing the distribution

• Suggestion: alpha levels 0.05 and 0.01

[bvenn]

Additional references for exact p value calculation:

• New Tables for Multiple Comparisons with a Control, C. W. Dunnett, Biometrics , Sep., 1964, Vol. 20, No. 3 (Sep., 1964), pp. 482-491 Chapter 3

• On a statistic which arises in selection and ranking problems, Gupta, Ann. Math. Statist. 28, 957-67, 1957, Formula 7.2

[bvenn]

Dunnetts test was implemented with unit tests and documentation. A table for two sided tests with a significance threshold of 0.05 is provided and should be extended for a higher sample count and various significance thresholds.