Post - Hoc Comparisons

The F test used in analysis of variance (ANOVA) is called an omnibus test because it can detect only the presence or the absence of a global effect of the independent variable on the dependent variable. However, in general we want to draw specific conclusions from the results of an experiment. Specific conclusions are derived from focused comparisons which are, mostly, implemented as contrasts between experimental conditions. When these comparisons are decided after the data are collected, they are called post-hoc or a posteriori analyses. These comparisons are performed after an ANOVA has been performed on the experimental data of interest. In the ANOVA framework, post-hoc analyses take two general forms: (1) comparisons that involves all possible contrasts, and (2) comparisons which are restricted to comparing pairs of means (called pariwise comparisons).