A Monte Carlo study of the Friedman test and some competitors in the single factor, repeated measures design with unequal covariances

Abstract

Single factor, repeated measures designs are employed in a variety of research settings. Assumptions about the form of the covariance matrix of the repeated measures have traditionally been applied only to parametric tests, yet the classical nonparametric alternative, the Friedman test, also possesses an implicit assumption of equal covariances of the measures. The results of a Monte Carlo study suggest that neither the Friedman rank test or other nonparametric competitors are robust to extreme departures from equal covariances when population distributions are symmetric, or to mild departures when population distributions are skewed. Surprisingly, the type I error rate of the parametric F test was less sensitive to an asymmetric⧸heavy-tailed distribution for unequal covariances than the nonparametric tests.