SRH_TEST: Stata module for computing the Scheirer-Ray-Hare nonparametric two-way analysis of variance test

srh_test performs the Scheirer-Ray-Hare (SRH) test, a nonparametric alternative to two-way factorial ANOVA. The test was introduced by Scheirer, Ray, and Hare (1976) as an extension of the Kruskal-Wallis one-way test to designs with two crossed factors and their interaction. The command displays the standard ANOVA table augmented with two additional columns, H, the Scheirer-Ray-Hare test statistic for each term, and Prob>chi2, the p-value for H based on the chi-squared distribution with degrees of freedom equal to those of the term. Like the Kruskal-Wallis test, the SRH test does not require normality. It assumes that observations are independent and that the response variable is at least ordinal. The chi-squared approximation improves with larger sample sizes; results should be interpreted cautiously in small samples. The SRH test is intended for balanced factorial designs, where every combination of factor_var1 and factor_var2 levels contains the same number of observations. With unbalanced designs the test may produce unreliable results, because the sums of squares and MS(total) are distorted when cell sizes differ. If the design is unbalanced, alternative approaches should be considered. The SRH test has lower statistical power than parametric two-way ANOVA and is considered conservative relative to the parametric alternative (Dytham 2003). When the normality assumption of parametric ANOVA is plausible, that test is preferred. Post-hoc pairwise comparisons should be performed separately if significant effects are found.