Assessing normality and equivariance in small multigroup samples

Abstract

A common design in biological and toxicological experimentation consists of k groups, each of sample size n. Statistical procedures for the analysis of resulting data often assume normality and equal within group variance. We examined statistical procedures based on probabilityplotting techniques for assessing these assumptions through computer simulations.. To obtain critical values, we generated 10,000 homogeneous normal samples for k=2, 3 and 4, and for n=4 to 12. Power comparisons were made using 1,000 samples each from a variety of non-normal and heterogeneous variance situations.

Our two main findings were as follows: (1) None of the procedures studied was uniformly best, but several (Shapiro-Wilk W, R² ₁ and z₂ were generally superior. (2) Critical values for some of the "standard" tests need to be adjusted for the multigroup case.

Keywords:

• normal plotting
• Shapiro-Wilk test
• test
• heterogeneity