Pairwise multiple comparisons: a model comparison approach versus stepwise procedures.

Abstract

Researchers in the behavioural sciences have been presented with a host of pairwise multiple comparison procedures that attempt to obtain an optimal combination of Type I error control, power, and ease of application. However, these procedures share one important limitation: intransitive decisions. Moreover, they can be characterized as a piecemeal approach to the problem rather than a holistic approach. Dayton has recently proposed a new approach to pairwise multiple comparisons testing that eliminates intransitivity through a model selection procedure. The present study compared the model selection approach (and a protected version) with three powerful and easy-to-use stepwise multiple comparison procedures in terms of the proportion of times that the procedure identified the true pattern of differences among a set of means across several one-way layouts. The protected version of the model selection approach selected the true model a significantly greater proportion of times than the stepwise procedures and, in most cases, was not affected by variance heterogeneity and non-normality.