Variants of chi-square for 2 × 2 contingency tables

Richardson, John T. E. (1990). Variants of chi-square for 2 × 2 contingency tables. British Journal of Mathematical and Statistical Psychology, 43(2) pp. 309–326.

DOI: https://doi.org/10.1111/j.2044-8317.1990.tb00943.x

Abstract

Four variants of the chi-square statistic are evaluated in terms of their adequacy as tests of association in 2 × 2 contingency tables. When both sets of marginal totals are fixed in advance, none of these variants is wholly satisfactory, even with moderately large samples. When one set of marginal totals is fixed in advance while the other is free to vary, or when neither set of marginal totals is fixed in advance, a variant of chi-square proposed by Upton (1982) is to be preferred both theoretically and in practice. The variant proposed by Yates (1934) which incorporates a correction for continuity and which is often recommended in statistics textbooks is theoretically unsound, shows an extremely conservative bias, and lacks sufficient power.