Variance Component Testing in Unbalanced Nested Designs

Abstract The commonly used approximate F test for variance component testing in unbalanced nested designs was adapted from procedures developed for balanced cross classifications. However, in the unbalanced case, the analysis of variance mean squares generally are not independent or chi-square type variables, as assumed by the test procedure. Estimates of the test size disturbance introduced by employing the approximate procedure for selected unbalanced three-level nested designs indicate that the disturbances are small for a wide range of variance component ratios for extremely unbalanced design situations. Extensions to higher level unbalanced nested designs are discussed.