Effects of the heterogeneity of variance and probability distribution of the data on the power and size of the F test

Abstract

The effect of the heterocedasticity of treatments and the distribution of probability over the size and power of the F test was studied, in two experimental designs: complete randomized blocks (with 3, 5, 7, 9 e 11 treatments) and latin square (from sizes 3 x 3 to 7 x 7). Data were generated from seven probability distributions, to wit, normal, uniform, logistic, Laplace, Weibull, exponential and Cauchy. In each case 10,000 experiments were generated and it was counted the number of times the F test was significant, for the null hipotheses either true or false. Based on this counting, it could be concluded that non-normality does not affect the size and the power of the F test, which were affected only when heterocedasticity of the treatments occurred. Transformation of the data is recommended only when there is heterogeneity of variance mainly when associated to normal distribution, in which case the F test was not efficient and had a very bad test-size.