Comparison of Kruskal-Wallis and Anova Power Studies Utilizing Bernstein Distributions (with simulations/medical studies)

Background. There are few freely-available methods for power studies using Kruskal-Wallis tests. Previous studies include: extended average X and Y, AdjGeneric and shift-g methods. Bernstein fits have been implemented into R and provide another route for development of power study tools. Methods. Monte Carlo (M.C.) Kruskal-Wallis power studies were compared with measured power and ANOVA equivalents (M.C. plus analytical), with or without normalization, using simulated datasets with a range of Pearson types; and with three medical study datasets (systolic blood pressure, hours of sleep and high-density-lipoprotein cholesterol, HDL-C). Results. With three from four simulated runs (Pearson types pooled), M.C. Kruskal-Wallis gave predicted sample sizes significantly slightly lower than that measured and more accurate than M.C. ANOVA (which gave significantly higher predictions; with run_two both gave significantly lower predictions than measured with M.C. ANOVA more accurate). M.C. Kruskal-Wallis or ANOVA results were not significantly different. With run_one populations where ANOVA could not be used, Kruskal-Wallis predictions were similar to that measured. In two from three medical studies, Kruskal-Wallis predictions (with "dialysis" with similar predictions and "marital" higher than measured) were more accurate than M.C. ANOVA (both higher than measured) but in one ("diabetes") the reverse was the case (Kruskal-Wallis giving lower; ANOVA similar; to measured). Conclusions. M.C. Kruskal-Wallis power studies based on Bernstein fits can be used with continuous variables (regardless of ties) to predict power and sample size. Overall they do not seem less accurate than M.C. ANOVA where the latter can be used, and have a much wider range of applicability. Further testing is needed to define accuracy limitations. M.C. Kruskal-Wallis will be useful for sample size prediction with three groups.