Analysis of Variance of Proportions with Unequal Frequencies

Abstract

For dichotomous data based on unequal frequencies, the formulae for analysis of variance, estimates and confidence bounds are presented in detail, along with the corresponding χ 2 and χ 1 2 test statistics. A theorem is given which relates the formulae for analysis of heteroscedastic observations to those of homoscedastic observations. The formulae presented in this paper may be justified by this theorem. Advantages of analysis of variance techniques over χ 2 tests are pointed out because of the possibility that data do not obey the binomial law.