On Approximating the Null and Nonnull Distributions of theFRatio in Unbalanced Random-Effect Models from Nonnormal Universes

Abstract

Abstract In this article we consider the unbalanced random-effects model as given in (1.1) with random variables from nonormal universes. Assuming that the αi 's are independently distributed of the eij 's, an approximation to the joint distribution of the mean squares (and hence the F ratio) by using Laguerre polynomials is derived. These results are then used to examine the effects of departure from normality on the traditional F-ratio distribution.