Pseudo-bivariate structure of 2 x 2 contingency table - preliminary analysis

Abstract

The paper by R. C. Geary on the comparative sensitivity of tests of significance to sample size contains the interesting suggestion that any 2 x 2 contingency table might be thought of as a sample realisation of a bivariate Normal distribution. Such an approach, if workable, might permit reduced sample size to establish significant correlation between the inherent x and y variates in question. These variates are the pair whose joint probability volume is supposedly estimated over four quadrants of the (x, y) plane by the four entries in the 2 x 2 table. An important outcome would be the finding of significant correlation in cases where the usual x2 test failed to find significant relationship through inadequate size of sample.