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A MODEL OP THE POSSIBLE RELATIONSHIPS
HI TESTS OF SIGNIFICANCE FOR HYPOTHESES OF INDEPENDENCE
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analysis asymptotically independent Bartlett's cell frequencies chi-square distribution classifications 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 implied hypothesis independence of Layers independence of Rows independent of Columns Journal Lancaster Layer variable Layers by Rows level of significance LXRC M. S. Bartlett marginal table Measures of Association Mitra necessary and sufficient null hypothesis pairwise associations pairwise independence plll population Row by Column Row by Layer Row variable Rows and Columns Royal Statistical Society RXC n RXL RXCL RXCXL S. N. Roy second order interaction Statistical Association sufficient conditions test statistics test variable third variable three factor interaction three nominal variables three variables types of independence zero first order zero second order