The impact of sample non-normality on ANOVA and alternative methods

Area of Science:

• Statistics
• Statistical Methods

Background:

• Traditional methods for comparing locations often assume data normality.
• Preliminary tests to select methods when normality is doubtful can lead to uncertain statistical power and significance due to potential errors at multiple stages.

Purpose of the Study:

• To investigate the relationship between population and sample non-normality.
• To evaluate the performance of ANOVA, Brown-Forsythe, Welch, and Kruskal-Wallis tests under varying degrees of non-normality, sample sizes, and effect sizes.

Main Methods:

• Simulated data sets were ranked based on their degree of normality, following Schmider et al. (2010).
• Performance of four statistical tests (ANOVA, Brown-Forsythe, Welch, Kruskal-Wallis) was assessed across different distributions, sample sizes, and effect sizes.

Main Results:

• The Kruskal-Wallis test demonstrated significantly less sensitivity to sample normality compared to other tested methods when populations were distinctly non-normal.
• Performance variations were observed across different distributions, sample sizes, and effect sizes for all tested tests.

Conclusions:

• The Kruskal-Wallis test is recommended as the primary method for comparing locations when populations are known to be non-normal.
• Researchers should consider the Kruskal-Wallis test to avoid potential type I and type II errors associated with preliminary normality testing and subsequent method selection.