Nonparametric Tests for Analyzing Interactions Among Intra-Block Ranks in Multiple Group Repeated Measures Designs

Abstract

This study developed an extension of the Hollander and Sethuraman (1978) statistic (B² ) for testing discordance among intra-block rankings of K elements for multiple groups (J ≥ 2) of raters. B² was demonstrated to be equivalent to the Pillai-Bartlett trace (V) from a multivariate profile analysis performed on the ranks such that B² = V (N - 1) Results confirmed the utility of B² as an omnibus test of interaction (i.e., discordance) among intra-block ranks and demonstrated that it was more powerful than the multivariate approach to ranked data suggested by Serlin and Marascuilo (1983). An extension of the Friedman (1937) two-way ANOVA for intra-block ranks was also developed. The adequacy of these procedures for testing interactions in multiple group repeated measures designs was investigated. The Friedman model demonstrated adequate statistical properties only when covariance matrices were spherical. Results also demonstrated that the Hollander-Sethuraman model was useful in testing interaction contrasts.