COMPARAÇÃO DE TESTES PARA IGUALDADES DE MÉDIAS SOB HETEROCEDASTICIDADE: SIMULAÇÃO E APLICAÇÃO - OLIVEIRA, Helen Maria Pedrosa de; FERREIRA, Eric Batista (Brazilian Journal of Biometrics, 2017)
Generally, comparison of several means is made by testing to detect the existence of differences between treatments. One of the most widely used tests in this case is the F test, within the Analysis of Variance. However, your credibility is linked to the fulfillment of four assumptions: additivity of the terms of the model, errors should follow a normal distribution, be independent and possess homogeneous variances. However, in the literature there are alternative tests to F, when you break any of those assumptions. The aim of this study was to provide the comparison of seven tests for equality of means under heteroscedasticity. The evaluation of the tests was done by analyzing rates of type I error and power over scenarios resulting from the combination of treatments numbers repetitions degree of heterogeneity and standard error difference between means. Overall, the tests showed little sensitiveness to the increasing of heterogeneity, which it was not observed with the Welch test. Based on the evaluated conditions, the tests that presented the best performance were Kruskal-Wallis and F, followed by the parametric bootstrap Krishnamoorthy, Lu and Mathew. The tests with the worst performances were the bootstrap nonparametric Reddy, Kumar and Ramu and the Zhow and Wong.