On the Multivariate Analysis of Three Dichotomous Variables

Taking Yule's coefficient, Q, as a measure of the intensity of association in a 2 X 2 contigency table, Costner and Wager recommend in a recent article in this Journal that the statistical significance of the difference between the values of Q calculated for two different 2 X 2 tables can be tested using the usual x test for the second-order interaction in a 2 X 2 X 2 contingency table. They note that the calculation of this test is tedious and time-consuming when a desk calculator is used, and they recommend the use of high speed electronic computers for carrying out this test. In the present paper, we shall present a much simpler test of the statistical significance of the difference between two Q's. The test presented herein can be calculated rapidly even by hand. In addition, we shall present other statistical methods particularly suited to the analysis of the difference between the intensity of association in two (or more) contigency tables. The methods presented here can be used to study the relationship between two dichotomous variables when a third dichotomous variables is taken into account, or more generally the relationship between two polytomous variables when a third dichotomous when a third polytomous variable is taken into account.