Performs hybrid multiple testing that incorporates method selection and assumption evaluations into the analysis using empirical Bayes probability (EBP) estimates obtained by Grenander density estimation. For instance, for 3-group comparison analysis, Hybrid Multiple testing considers EBPs as weighted EBPs between F-test and H-test with EBPs from Shapiro Wilk test of normality as weigth. Instead of just using EBPs from F-test only or using H-test only, this methodology combines both types of EBPs through EBPs from Shapiro Wilk test of normality. This methodology uses then the law of total EBPs.