Information criteria for pairwise comparisons

A new approach is presented for the interpretation of differences among means and proportions. Post hoc techniques, such as Tukey's honestly significant difference procedure, have interpretive problems related to intransitive decisions and technical issues arising from unequal sample sizes or heterogeneity of variance. These concerns can be avoided by considering ordered subsets of means and by using information criterion to select among competing models. This paired-comparisons information-criterion (PCIC) approach is wholistic in nature and does not depend on interpreting a series of statistical tests. Simulation results suggest that a protected version of the PCIC procedure is desirable to minimize failures to detect the null case. This technique is illustrated for independent means, proportions, and means from repeated measures.