  Bernstein fits implemented into R allow another route for Kruskal-Wallis
power-study tool development. Monte-Carlo Kruskal-Wallis power studies were
compared with measured power, with Monte-Carlo ANOVA equivalent and with an
analytical method, with or without normalization, using four simulated runs
each with 60-100 populations (each population with N=30000 from a set of
Pearson-type ranges): random selection gave 6300 samples analysed for
predictive power. Three medical-study datasets (Dialysis/systolic blood
pressure; Diabetes/sleep-hours; Marital-status/high-density-lipoprotein
cholesterol) were also analysed. In three from four simulated runs (run_one,
run_one_relaxed, and run_three) with Pearson types pooled, Monte-Carlo
Kruskal-Wallis gave predicted sample sizes significantly slightly lower than
measured but more accurate than with ANOVA methods; the latter gave high
sample-size predictions. Populations (run_one_relaxed) with ANOVA assumptions
invalid gave Kruskal-Wallis predictions similar to those measured. In two from
three medical studies, Kruskal-Wallis predictions (Dialysis: similar
predictions; Marital: higher than measured) were more accurate than ANOVA (both
higher than measured) but in one (Diabetes) the reverse was found
(Kruskal-Wallis: lower; Monte-Carlo ANOVA: similar to measured). These
preliminary studies appear to show that Monte-Carlo Kruskal-Wallis power
studies based on Bernstein fits might perform better than ANOVA equivalents in
many settings (and provide reasonable results when ANOVA cannot be used); and
both Monte-Carlo methods appeared considerably more accurate than the analysed
analytical version.
