Appendix A - Common Statistical Tests Embraced by the MRPP Command in Blossom Statistics

Multiresponse permutation procedures (MRPP) can duplicate many common statistical tests (the parametric tests listed below are all permutation versions).

Two-sample t-test
One-way analysis of variance
Multivariate analysis of variance
Hotelling's T ²
Median test (2 and k-sample)
Wilcoxon-Mann-Whitney test
Kruskal-Wallis test
Goodman and Kruskal contingency table tests of association (tau-a, tau-b)
Generalized runs tests (including Wald-Walfowitz runs test)
Durbin-Watson for univariate first-order autoregression
Schoener's t²/r² for bivariate first-order autoregression

The multiresponse permutation procedures for randomized block data (MRBP) and permutation tests for matched pairs (PTMP) can duplicate the following tests (the parametric tests listed below are all permutation versions).

Matched pairs and 1-sample t-test
Analysis of variance for complete randomized blocks
Sign test
Wilcoxon signed rank test
Pearson correlation coefficient
Spearman rank correlation
Kendall tau (correlation)
Friedman's test for randomized blocks
Spearman's footrule and multi-block extension
Cochran's Q and McNemar's tests
Cohen's kappa

Other less familiar tests are also known to be special cases of MRPP and MRBP. Be aware, too, that many of the above tests are strictly univariate or bivariate, but MRPP and MRBP often generalize to the multivariate case as well. Further, most of the above listed tests use the square of Euclidean distance in the definition of the test statistic, whereas MRPP and MRBP have the option of choosing a distance measure commensurate with the data space. The generalized distance function in MRPP yields alternative, often more powerful versions of these tests.