Comparing Between- and Within-Group Variances in a Two-Level Study: A Latent Variable Modeling Approach to Evaluating Their Relationship.

This note is concerned with examining the relationship between within-group and between-group variances in two-level nested designs. A latent variable modeling approach is outlined that permits point and interval estimation of their ratio and allows their comparison in a multilevel study. The procedure can also be used to test various hypotheses about the discrepancy between these two variances and assist with their relationship interpretability in empirical investigations. The method can also be utilized as an addendum to point and interval estimation of the popular intraclass correlation coefficient in hierarchical designs. The discussed approach is illustrated with a numerical example.