Robustness of power in analysis of variance for various designs.

Robustness of power of the analysis of variance technique to the departures from the underlying assumptions of homoskedasticity and independence of error has been considered in various designs, including the mixed and non-orthogonal designs. Distribution of the ratio of two independent quadratic forms is modified with arbitrary scale, parameter g and has been used extensively. The choice of g is also discussed. The results, in general., indicate that the power of the test of equal means is seriously affected when the assumption of homoskedasticity is violated, but'for moderate degree of heteroskedasticity, the actual type I error is not seriously affected. Also, the power of the test of homogeneity of means is highly sensitive to the departure from the fixed effects model to the corresponding random effects model. The problem of design of experiments to optimise power of the test under the constraint of cost is discussed with reference to the one-way classification for both cases of homogeneous and heterogeneous group error variances.