On pearson's chi-squared for coitingency tables and zero bivariate binomial correlation

Abstract

Abstract Each of the marginal multinomials of an rxc contingency table is dichotomized in all possible ways, and the resulting different bivariate binomial distributions are considered. K. Pearson's usual chi-squared criterion for testing independence between the two marginal variables is then viewed as a test for zero correlation in all the resulting bivariate binomial distributions. An alternative test criterion for zero bivariate binomial correlation is considered and compared with Pearson's chi-squared criterion. Keywords: chi-squaredcontingency tablebivariate binomialtest for zero correlation