| Abstract: | Tests for the equality of variances are often needed in applications. In genetic studies the assumption of equal variances of continuous traits, measured in identical and fraternal twins, is crucial for heritability analysis. To test the equality of variances of traits, which are non-normally distributed, Levene H. Levene, Robust tests for equality of variances, in Contributions to Probability and Statistics, I. Olkin, ed. Stanford University Press, Palo Alto, California, 1960, pp. 278–292] suggested a method that was surprisingly robust under non-normality, and the procedure was further improved by Brown and Forsythe M.B. Brown and A.B. Forsythe, Robust tests for the equality of variances, J. Amer. Statis. Assoc. 69 (1974), pp. 364–367]. These tests assumed independence of observations. However, twin data are clustered – observations within a twin pair may be dependent due to shared genes and environmental factors. Uncritical application of the tests of Brown and Forsythe to clustered data may result in much higher than nominal Type I error probabilities. To deal with clustering we developed an extended version of Levene's test, where the ANOVA step is replaced with a regression analysis followed by a Wald-type test based on a clustered version of the robust Huber–White sandwich estimator of the covariance matrix. We studied the properties of our procedure using simulated non-normal clustered data and obtained Type I error rates close to nominal as well as reasonable powers. We also applied our method to oral glucose tolerance test data obtained from a twin study of the metabolic syndrome and related components and compared the results with those produced by the traditional approaches. |
