Analysis of Variance of Disproportionate Data When Interaction is Present

The disturbance to the level of significance of additive sums of squares methods of analyzing disproportionate data is studied for several patterns of subclass numbers in the two-way classification. These methods yield too many significant results for main effects under the null hypothesis although this disturbance is judged to be moderate for the method of unweighted means. Factors to remove the bias in the method of expected subclass numbers are given. A procedure for computing the power of the exact methods, similar to the computations for equal subclass numbers, and approximate procedures for determining the power of the method of unweighted means are described.