Generalized Linear Model Analyses for Treatment Group Equality when Data are Non-Normal

Abstract

One of the validity conditions of classical test statistics (e.g., Student’s t-test, the ANOVA and MANOVA F-tests) is that data be normally distributed in the populations. When this and/or other derivational assumptions do not hold the classical test statistic can be prone to too many Type I errors (i.e., falsely rejecting too often) and/or have low power (i.e., failing to reject when the null hypothesis is false) to detect treatment effects when they are present. However, alternative procedures are available for assessing equality of treatment group effects when data are non-normal. For example, researchers can use robust estimators instead of the usual least squares estimators to test that treatment effects are equivalent across groups. As well, recent advances in statistical methodology allow researchers to test for equality of treatment group effects by assuming other distributional shapes for the data. One class of such analyses is generalized linear model techniques. On the other hand, researchers can adopt sequential analyses where they first assess the normality assumption and then depending on the result determine the type of analysis that should be adopted. The purpose of the present study was to compare the above approaches for assessing equality of treatment group effects in the presence of non-normal data. Simulation results which were based on various non-normal distributions and the values of group variances and sample sizes revealed that sequential analysis coupled with a generalized linear model solution were just as prone to inflated or depressed rates of Type I error as the classical ANOVA F-test.