On the Multivariate Analysis of Interaction for Nominal Variables |
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analysis asymptotically independent Bartlett's chi-square statistics classifications Column and Layer Column by Layer Column cross-classification Column independence Column relationship Column variable complete mutual independence component hypotheses conditional cross-classifications Conditional Independence conditional Row Contingency Tables cross products cubic equation CXRL defining condition definition degrees of freedom dependent variable elements example expected values families of tests H₁ H₂ implied hypothesis independence of Layers independence of Rows independent of Columns L₂ Lancaster Layer variable Layers by Rows level of significance LXRC M. S. Bartlett marginal table necessary and sufficient null hypothesis P.jk pairwise independence population R₁ relation Row by Column Row by Layer Row variable Rows and Columns Royal Statistical Society RXCL RXCXL S. N. Roy second order interaction sufficient conditions test statistics test variable Theorem 3 Theorem three factor interaction three nominal variables three variables types of independence zero first order zero second order