Robustness of the ANOVA and Tukey-Kramer statistical tests

Analysis of variance (ANOVA) allows one to compare the means of μ1, μ2,…,μm of m populations. For a randomized block single-factor design of experiments with m treatments, the analyst uses ANOVA to test the null hypothesis H0 : {μ1 = μ2 = … = μm}. If H0 is rejected, the Tukey-Kramer procedure may be used to determine which pairs of means have statistically significant differences. Unfortunately, ANOVA and the Tukey-Kramer procedures both depend upon the use of data from normal populations. Departure from normality may cause errors. These errors cannot be determined analytically; however, they can be estimated via simulation. This paper reports on the use of computer simulation to estimate the errors that attend the use of ANOVA with Tukey-Kramer to test for differences of population means.