The Effects of Non-Normality on Type III Error for Comparing Independent Means.

Abstract: The major objective of this study was to investigate the effects of non-normality on Type III error rates for ANOVA F its three commonly recommended parametric counterparts namely Welch, Brown-Forsythe, and Alexander-Govern test. Therefore these tests were compared in terms of Type III error rates across the variety of population distributions, mean difference (effect size), and sample sizes. At the end of 100,000 simulation trials it was observed that the Type III error rates for four tests were affected by the effect size (δ) and sample size, whereas Type III errors were not affected from distribution shapes. Results of the simulation also indicated that increases in sample size and population mean difference decreased Type III error, and increased statistical test power. Across the all distributions, sample sizes and population mean differences (δ), the Alexander-Govern test obtained higher estimates for power, lower estimates of Type III error (γ). Key words: Type I error rates, power of test, Type III error rates, normality, ANOVA 1.