Critical differences can be thought of as critical regions for a priori and post hoc comparisons of pairs of means and of linear combinations of means. Critical differences can be transformed into confidence intervals. First, this entry discusses critical differences in the context of multiple comparison tests for means. Second, this entry addresses confusion surrounding applying critical differences for statistical significance and for the special case of consequential or practical significance.
Multiple comparison tests arise from parametric and nonparametric tests of means, medians, and ranks corresponding to different groups. The parametric case for modeling means can be described as
where i = 1 … p (number of treatments) and j = 1 … ni (sample size of the ith treatment). The null hypothesis is that ...
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