Dunn's test is the appropriate nonparametric pairwise multiple-comparison procedure when a Kruskal–Wallis test is rejected, and it is now implemented for Stata in the dunntest command. dunntest produces multiple comparisons following a Kruskal–Wallis k-way test by using Stata's built-in kwallis command. It includes options to control the familywise error rate by using Dunn's proposed Bonferroni adjustment, the Šidák adjustment, the Holm stepwise adjustment, or the Holm–Šidák stepwise adjustment. There is also an option to control the false discovery rate using the Benjamini–Hochberg stepwise adjustment.
BenjaminiY., and HochbergY.1995. Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society, Series B57: 289–300.
2.
DunnO. J.1961. Multiple comparisons among means. Journal of the American Statistical Association56: 52–64.
3.
DunnO. J.1964. Multiple comparisons using rank sums. Technometrics6: 241–252.
HolmS.1979. A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics6: 65–70.
6.
KruskalW. H., and WallisW. A.1952. Use of ranks in one-criterion variance analysis. Journal of the American Statistical Association47: 583–621.
7.
MannH. B., and WhitneyD. R.1947. On a test of whether one of two random variables is stochastically larger than the other. Annals of Mathematical Statistics18: 50–60.
8.
ŠidákZ.1967. Rectangular confidence regions for the means of multivariate normal distributions. Journal of the American Statistical Association62: 626–633.
9.
SimesR. J.1986. An improved Bonferroni procedure for multiple tests of significance. Biometrika73: 751–754.
10.
WilcoxonF.1945. Individual comparisons by ranking methods. Biometrics Bulletin1: 80–83.
