NONPARAMETRIC HYPOTHESES AND RANK STATISTICS FOR UNBALANCED FACTORIAL-DESIGNS

Factorial designs are studied with independent observations, fixed num ber of levels, and possibly unequal number of observations per factor level combination. In this context, the nonparametric null hypotheses introduced by Akritas and Arnold are considered. New rank statistics a re derived for testing the nonparametric hypotheses of no main effects , no interaction, and no factor effects in unbalanced crossed classifi cations. The formulation of all results includes tied observations. Ex tensions of these procedures to higher-way layouts are given, and the efficacies of the test statistics against nonparametric alternatives a re derived. A modification of the test statistics and approximations t o their finite-sample distributions are also given. The small-sample p erformance of the procedures for two factors is examined in a simulati on study. As an illustration, a real dataset with ordinal data is anal yzed.