Time for some a priori thinking about post hoc testing

Researchers are commonly in a situation, often after an experiment, where they want to compare the central tendency of some measure across a number of groups. If the number of groups is simply 2, then there is little controversy as to the appropriate analysis, with normally a t-test or a nonparametric equivalent being adopted. If the number of groups is greater than 2, most elementary statistical textbooks suggest performing an analysis of variance (ANOVA) to test the null hypothesis that all the groups are the same and, if this null hypothesis is rejected, implementing some post hoc testing to identify which groups are significantly different from which other groups. However, as readers and reviewers of scientific papers in behavioral science, we have noted a great diversity of approaches when comparing more than 2 groups often with little or no justification for the adoption of a specific approach. Hence, our aim in this note is to briefly survey current practice in this regard and to provide clear guidance on how such testing might most appropriately be carried out in different instances.