Simple Methods for Analyzing Three-Factor Interaction in Contingency Tables

Interfaith Dating: Religion, Social Class and Premarital Sexual Attitudes

“…This is a way of telling the researcher whether two partial tables are "really" different or just appear to be different. The distribution of this test for interaction is very similar to the chi square distribution and its statistic called y2 (Goodman, 1964).…”

“…Catholic females who were permissive in their sexual attitudes (those who accept coitus before marriage) were more Iikely to be inteffaith-daters than those who were not permissive in their attitudes (those who do not accept coitus before marriage). ThŸ prediction was substantiated with 94 percent of the Catholic females who are high-permissive on sexual attitudes being inteffaith-daters, compared with 69 percent of the Catholie females who are low-permissive on sexual atti-12 The Goodman test for interaetion, developed by Leo Goodman (1964), determines whether interaction is present between two or more contingency tables. This is a way of telling the researcher whether two partial tables are "really" different or just appear to be different.…”

A Note on the Minimum χ21Estimate and a L.A.M.S.T. χ2in the “No Interaction” Problem

“…For the 2 X 2 x 2 table it is given by xi = ( 9 1 -9 2 ) ' / n c 1 / 8 t j k = (91 -9 2 ) ' c l / g r j k (6) where g 1 is computed for layer k = 1 and g2 for layer k = 2, g k = __ -~ --+ - x: [lo].…”

On Simultaneous Confidence Intervals for Multinomial Proportions

“…In situations where relative differences (or ratios) among multinomial parameters are of interest, the relative differences between the corresponding ratios in two (or more) multinomial populations can be analyzed by methods that are closely related to, but different in detail from, the methods presented in Section 6 above (see Goodman, 1964a). In addition, two (or more) sets of two binomial populations can be compared in situations where differences between the parameters are of interest using the generalization of the Stouffer method given by the author in (1963b), and two (or more ) sets of J multinomial populations can be compared in situations where ratios of the parameters are of interest using the various methods that have been developed for the analysis of three-factor interaction in a three-way contingency table (see, e.g., Goodman, 196413 and the literature cited there).…”