The impact of Levene’s test of equality of variances on statistical theory and practice
By Joseph L. Gastwirth, Yulia R. Gel, Weiwen Miao. 2009
622 citations recorded by the source corpus.
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.
Subfields: Economics and Econometrics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/4f41cba6bc2d28369f159cf92c380bae6f91b00a
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Citations in the corpus
- Observations on the use of statistical methods in Food Science and Technology (2014, background): “More details about tests to check for homogeneity of variances can be found in Levene (1960), Brownand Forsythe (1974), Limand Loh (1996), Keselman and Wilcox (1999) and Gastwirth, Gel, and Miao (2009).”