Comparação de testes para a igualdade de média sob heterocedasticidade: simulação e aplicações

Abstract

In experimentation, usually several comparison means is made by testing to detect the existence of differences among treatments. One of the most widely used tests for comparison of averages is the F test in the context of analysis of variance. However, the credibility of this test is directly linked to compliance with four assumptions which are: additivity of the terms of the model, errors should follow a normal distribution, be independent and possess homogeneous variances. According to some researchers, the assumption that most affects test performance F is breaking the homogeneity. However, in the literature there are several alternative tests to F, when you break any of the assumptions. The objective of this study was the comparison of eight tests for equality of means under heteroskedasticity. The evaluation of the tests was made by Monte Carlo simulation analyzing the error rates of type I and power over scenarios resulting from the combination of different numbers of treatments (5, 10, 15 and 20) repeats (3 and 20) , degree of heterogeneity (1, 2, 4, 8, 16, 32, 64, 128, 256) and standard error of the difference between the mean (0.5, 1, 2, 4 and 8). In general, the tests proved insensitive to increased heterogeneity of variance, which did not occur withWelch test. The evaluated conditions, improved performance tests were Kruskal-Wallis and F in the context of ANOVA, followed by parametric bootstrap Krishnamoorthy, Lu and Mathew. Already the worst performance tests were non-parametric bootstrap Reddy, Kumar and Ramu and the non-parametric bootstrap Zhow and Wong.