Two tests of variance homogeneity for clustered data where group size is informative

To evaluate variance homogeneity among groups for clustered data, Iachine et al. (Robust tests for the equality of variances for clustered data. J Stat Comput Simul 2010;80(4):365–377) introduced an extension of the well-known Levene test. However, this method does not account for informative cluster size (ICS) or informative within-cluster group size (IWCGS), which can occur in clustered data when cluster and group sizes are random variables. This article introduces two tests of variance homogeneity that are appropriate for data with ICS and IWCGS, one extending the Levene-style transformation method and one based on a direct comparison of estimates of variance. We demonstrate the properties of our tests in a detailed simulation study and show that they are resistant to the potentially biasing effects of ICS and IWCGS. We illustrate the use of these tests by applying them to a data set of x-ray diffraction measurements collected from a specimen of duplex steel.