¹Universidade de São Paulo, Instituto de Matemática e Estatística, São Paulo, Brasil. Mestre em Estatística. Email: erilaniaalmeida@yahoo.com.br
²Universidade de São Paulo, Instituto de Matemática e Estatística, São Paulo, Brasil. Professor doutor. Email: selian@ime.usp.br
³Universidade Federal do Ceará, Departamento de Estatística e Matemática Aplicada, Fortaleza, Brasil. Professor adjunto I. Email: juvencio@ufc.br

Os testes usuais para comparar variâncias e médias, teste de Bartlett e teste F, supõem que as amostras sejam provenientes de populações com distribuições normais. Para o teste de igualdade de médias, a suposição de homogeneidade de variâncias também é necessária. Alguns problemas se destacam quando tais suposições básicas são violadas, como tamanho excessivo e baixo poder. Neste trabalho descrevemos inicialmente o teste de Levene para igualdade de variâncias, que é robusto à não normalidade, e o teste de Brown e Forsythe para igualdade de médias quando existe desigualdade de variâncias. Apresentamos várias modificações do teste de Levene e do teste de Brown e Forsythe, propostas por diferentes autores. Analisamos e aplicamos uma forma do teste modificado de Brown e Forsythe a um conjunto de dados reais. Este teste é uma alternativa robusta com relação a desvios de normalidade e homocedasticidade e também na presença de observações discrepantes. Na comparação de variâncias, destaca-se o teste de Levene com centralização na mediana.

Palavras chave: teste de Levene, teste de Brown e Forsythe, médias aparadas, variâncias winsorizadas, bootstrap.

The usual tests to compare variances and means (e.g. Bartletts test and F-test) assume that the sample comes from a normal distribution. In addition, the test for equality of means requires the assumption of homogeneity of variances. In some situation those assumptions are not satisfied, hence we may face problems like excessive size and low power. In this paper, we describe two tests, namely the Levenes test for equality of variances, which is robust under nonnormality; and the Brown and Forsythes test for equality of means. We also present some modifications of the Levenes test and Brown and Forsythes test, proposed by different authors. We analyzed and applied one modified form of Brown and Forsythes test to a real data set. This test is a robust alternative under nonnormality, heteroscedasticity and also when the data set has influential observations. The equality of variance can be well tested by Levenes test with centering at the sample median.

Key words: Levene's test, Brown and Forsythe's test, Trimmed Means, Winsorized variances, bootstrap.

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