In Pairwise t-Tests we described how to perform pairwise t-tests following a one-way ANOVA. After Kriskal-Wallis, the appropriate pairwise tests are pairwise Mann-Whitney tests.
Data Analysis Tool
Real Statistics Data Analysis Tool: The Real Statistics Resource Pack provides a data analysis tool to perform pairwise Mann-Whitney tests, as described in Example 1.
Example 1: Find all significant differences between the blemish creams of Example 1 of Kruskal-Wallis Test at the 95% significant level based on pairwise Mann-Whitney tests.
To perform this test, we proceed as in Example 1 of Nemenyi Test, except that we choose either the Pairwise MW or Pairwise Exact MW option instead of the Nemenyi option. When we press the OK button for either of these options, the results shown on the left side of Figure 1 are displayed.
Figure 1 – Pairwise MW tests
Note that cell AN6 contains the formula =MWTEST(B4:B13,C4:C13) and cell AN12 (for the exact test) contains the worksheet formula =MW_EXACT(B4:B13,C4:C13).
Following either of these tests, the Multiple Test data analysis tool can be used to determine which pairwise comparisons are significant. A number of options are available, but for purposes of illustration, we choose the Hochberg option, whose results are shown on the right side of Figure 1.
There we see that New vs. Old is the only comparison that is significant.
Reference
Midway, S. et al. (2020) Comparing multiple comparisons: practical guidance for choosing the best multiple comparisons test
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7720730/