Robust Tests for the Equality of Variances for Clustered Data

• Activity Number: 54
• Type: Contributed
• Date/Time: Sunday, August 8, 2004 : 4:00 PM to 5:50 PM
• Sponsor: General Methodology
• Author(s): Ivan Iachine*+ and Hans C. Petersen
• Companies: University of Southern Denmark and University of Southern Denmark
• Keywords: equality of variances ; non-normality ; robust tests ; Levene's test ; clustered data ; twins

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 (1960) suggested a method which was surprisingly robust under non-normality, and the procedure was further improved by Brown and Forsythe (1974). 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 we replaced the ANOVA step with a regression analysis with standard errors computed using a clustered version of the Huber-White sandwich estimator, followed by a pseudo-t-test. We studied the properties of our procedure using simulated non-normal clustered data and obtained Type I error rates close to nominal and reasonable power.