A NOTE ON CHI-SQUARED APPROXIMATIONS FOR TESTS OF RANK INTERACTION WITH ORDERED CATEGORICAL-DATA

The idea of rank interaction in factorial experiments when the response is only measured on an ordinal scale was introduced by de Kroon and van der Laan (1981). In this paper, the exact null distributions of test statistics for main effects and rank interaction are compared with their independent asymptotic chi(2) distributions, in particular for experiments with an ordered categorical response using an arbitrary score. Expressions' are derived for the exact null variances and covariance of the two statistics for balanced experiments. Simulation is used to make further comparisons between the exact and the asymptotic distributions, and to consider experiments which are not balanced. Some recommendations are made as to when the asymptotic distributions may safely be used.