Abstract

DE ALMEIDA, ANTÔNIA; ELIAN, SILVIA  and  NOBRE, JUVÊNCIO. Modifications and Alternatives to the Tests of Levene and Brown & Forsythe for Equality of Variances and Means. Rev.Colomb.Estad. [online]. 2008, vol.31, n.2, pp.241-260. ISSN 0120-1751.

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.

Keywords : Levene's test; Brown and Forsythe's test; Trimmed Means; Winsorized variances; bootstrap.

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