Post Hoc Analysis

Post hoc analysis, or a posteriori analysis, generally refers to a type of statistical analysis that is conducted following the rejection of an omnibus null hypothesis. Post hoc analysis can be conducted for a variety of statistics including proportions and frequencies, but post hoc analysis is most commonly used for testing mean differences. This entry focuses primarily on post hoc analysis for investigating mean differences. Following are brief discussions of the omnibus test under a one-way analysis of variance (ANOVA), Tukey honestly significant difference test for pairwise contrasts, Scheffé’s procedure for pairwise or complex contrasts, other available post hoc procedures, and considerations for using post hoc analysis.