Nonparametric tests for analyzing interactions among intra-block ranks in multiple group repeated measures designs

This study developed an extension of the Hollander and Sethuraman (1978) st atistic (B-2) for testing discordance among intra-block rankings of K eleme nts for. multiple groups (J greater than or equal to 2) of raters. B-2 was demonstrated to be equivalent to the Pillai-Bartlett trace (V) fi om a mult ivariate profile analysis performed on the ranks such that B-2 = V(N - 1). Results confirmed the utility of B-2 as an omnibus test of interaction (ie. , discordance) among intra-block ranks and demonstrated that it was more po werful than the multivariate approach to ranked data suggested by Serlin an d 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 invest igated. The Friedman model demonstrated adequate statistical properties onl y when covariance matrices were spherical. Results also demonstrated that t he Hollander-Sethuraman model was useful in testing interaction contrasts.