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

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 α_i 's are independently distributed of the e_ij '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.

Key Words:

• Departure from normality
• Laguerre polynomial expansion
• Mixture of normals
• F test
• Unbalanced random-effects models