I want to allow users of GraphPad Prism to use the False Discovery Rate (FDR) approach to multiple comparisons after nonparametric one-way ANOVA (Kruskal-Wallis). The idea is first to compute an exact (not corrected for multiple comparisons) P value for each comparison, and then to use a standard FDR algorithm to decide which of those P values are small enough for the associated comparison to be designated a "discovery".
How to compute the P value for each comparison?
- Use the Mann-Whitney test.
- Use the Dunn's test, usually used for multiple comparisons, adapted to give an uncorrected P value for each comparison.
Dunn's method uses the rankings from all the groups (and the sample size from all the groups) even when just comparing two groups. Does this add power over doing the Mann-Whitney test for each pair?
In another CV case, Alexis posted "Dunn's test preserves a pooled variance for the tests implied by the Kruskal-Wallis null hypothesis.". But I don't understand how pooled variance is a concern with nonparametric tests.