Power derivation in an ANOVA model which is intermediate between the "fixed-effects" and the "random-effects" models

Some ANOVA models are presented where the "treatments effects" can assume, under the alternative, a few discrete values with prescribed probabilities. The power function, of the test that all treatment effects are zero, is approximated by a Laguerre series using the methods of Tiku (1965). Some comparisons are shown between this approximation, a direct computation and the normal approximation to the direct computation. Finally, a description of some genetical problems is given where such models are appropriate and where the power calculation may improve the planning of experiments.