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

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.