The classical parametric analysis of covariance (ANCOVA) is frequently used when comparing an ordinal outcome variable between two groups, while adjusting for a continuous covariate. However, the normality assumption might be crucial and assuming an underlying additive model might be questionable. Therefore, in the present manuscript, we consider the outcome as truly ordinal and dichotomize the covariate by a median split, in order to transform the testing problem to a nonparametric factorial setting. We propose using either a permutation-based Anderson–Darling type approach in conjunction with the nonparametric combination method or the pseudo-rank version of a nonparametric ANOVA-type test. The results of our extensive simulation study show that both methods maintain the type I error level well, but that the ANOVA-type approach is superior in terms of power for location-shift alternatives. We also discuss some further aspects, which should be taken into account when deciding for the one or the other method. The application of both approaches is illustrated by the analysis of real-life data from a randomized clinical trial with stroke patients.
