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Bernstein fits implemented into R allow another route for Kruskal-Wallispower-study tool development. Monte-Carlo Kruskal-Wallis power studies werecompared with measured power, with Monte-Carlo ANOVA equivalent and with ananalytical method, with or without normalization, using four simulated runseach with 60-100 populations (each population with N=30000 from a set ofPearson-type ranges): random selection gave 6300 samples analysed forpredictive power. Three medical-study datasets (Dialysis/systolic bloodpressure; Diabetes/sleep-hours; Marital-status/high-density-lipoproteincholesterol) were also analysed. In three from four simulated runs (run_one,run_one_relaxed, and run_three) with Pearson types pooled, Monte-CarloKruskal-Wallis gave predicted sample sizes significantly slightly lower thanmeasured but more accurate than with ANOVA methods; the latter gave highsample-size predictions. Populations (run_one_relaxed) with ANOVA assumptionsinvalid gave Kruskal-Wallis predictions similar to those measured. In two fromthree medical studies, Kruskal-Wallis predictions (Dialysis: similarpredictions; Marital: higher than measured) were more accurate than ANOVA (bothhigher than measured) but in one (Diabetes) the reverse was found(Kruskal-Wallis: lower; Monte-Carlo ANOVA: similar to measured). Thesepreliminary studies appear to show that Monte-Carlo Kruskal-Wallis powerstudies based on Bernstein fits might perform better than ANOVA equivalents inmany settings (and provide reasonable results when ANOVA cannot be used); andboth Monte-Carlo methods appeared considerably more accurate than the analysedanalytical version.

Kruskal-Wallis Power Studies Utilizing Bernstein Distributions; preliminary empirical studies using simulations/medical studies