On the Non-Null Distribution of Anova F-Ratio in One Way Unbalanced Random Model

Abstract

Expressions for the non-null distribution of analysis of variance F-ratio and the power of F-test in the unbalanced one-way random model have been obtained. The exact values of power of the test have been worked out, numerically, and compared with those obtained by using ( i) the Laguerre polynomial and (ii) the two moments approximations. The computed results reveal that the two moments approximation, for the non-null distribution of F-ratio, is quite good and there is no need for the Laguerre polynomial approimation, which is computationally very tedious for practical applications.