A Comparison of Random Normal Scores Test Under the F and Chi-Square Distributions to the 2x2x2 ANOVA Test

Abstract

The use of the parametric ANOVA Test when the underlying population is non-normally distributed is a violation of the test’s assumption of normality. Alternatives include the use of nonparametric procedures. However, to date, useful procedures have not been developed to detect interactions, especially those of the higher order. Based on the rank transform, theRandomNormalScoresTest has been suggested as a powerful alternative to the ANOVATest. The major support rests upon asymptotic theory. This study is an empirical analysis of the Random Normal Scores Test performed under the F and Chi-square distributions. In the balanced 2x2x2 layout, for various population distributions, sample sizes, and nominal alpha levels selected, the Random Normal Scores Tests- were shown to be non-robust and not powerful alternatives to the ANOVA Test.