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August 2009 The Impact of Levene’s Test of Equality of Variances on Statistical Theory and Practice
Joseph L. Gastwirth, Yulia R. Gel, Weiwen Miao
Statist. Sci. 24(3): 343-360 (August 2009). DOI: 10.1214/09-STS301


In many applications, the underlying scientific question concerns whether the variances of k samples are equal. There are a substantial number of tests for this problem. Many of them rely on the assumption of normality and are not robust to its violation. In 1960 Professor Howard Levene proposed a new approach to this problem by applying the F-test to the absolute deviations of the observations from their group means. Levene’s approach is powerful and robust to nonnormality and became a very popular tool for checking the homogeneity of variances.

This paper reviews the original method proposed by Levene and subsequent robust modifications. A modification of Levene-type tests to increase their power to detect monotonic trends in variances is discussed. This procedure is useful when one is concerned with an alternative of increasing or decreasing variability, for example, increasing volatility of stocks prices or “open or closed gramophones” in regression residual analysis. A major section of the paper is devoted to discussion of various scientific problems where Levene-type tests have been used, for example, economic anthropology, accuracy of medical measurements, volatility of the price of oil, studies of the consistency of jury awards in legal cases and the effect of hurricanes on ecological systems.


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Joseph L. Gastwirth. Yulia R. Gel. Weiwen Miao. "The Impact of Levene’s Test of Equality of Variances on Statistical Theory and Practice." Statist. Sci. 24 (3) 343 - 360, August 2009.


Published: August 2009
First available in Project Euclid: 31 March 2010

zbMATH: 1329.62332
MathSciNet: MR2757435
Digital Object Identifier: 10.1214/09-STS301

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.24 • No. 3 • August 2009
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