Tests of statistical hypotheses in the case of unequal or disproportionate numbers of observations in the subclasses

General solutions of the analysis of variance in the case of unequal numbers of observations in the subclasses are presented. If we havek criteria for the classification, there will bek! solutions in making a complete analysis and 2^k–1 answers, bearing different meanings, for the sum of squares between subclasses of each criterion. The sum of squares for the interaction of any order, however, will be identical in different solutions of same problem.