The power function and an approximation for testing variance components in the presence of interaction in two-way random effects models

In this paper we consider a two-way layout random-effects model with interaction proportional to the product of two random components and derive the distributions of the sums of squares and the F-ratio under the usual normality assumption for the random effects. Approximations to these distributions by finite series Laguerre polynomial expansions are then developed. Some numerical results are given to illustrate the applications of the theory.