Measures of association for contingency tables

Introduction Paper (PDF)

Often when we carry out research we wish to measure the degree to which one variable affects the value of another, setting aside the question as to whether this impact is sufficiently large as to be considered significant (i.e., significantly different from zero).

The most general term for this type of measure is size of effect. Effect sizes allow us to make descriptive statements about samples. Traditionally, experimentalists have referred to ‘large’, ‘medium’ and ‘small’ effects, which is rather imprecise. Nonetheless, it is possible to employ statistically sound methods for comparing different sizes of effect by estimating a Gaussian confidence interval (Bishop, Fienberg and Holland 1975) or by comparing pairs of contingency tables employing a “difference of differences” calculation (Wallis 2011).

In this paper we consider effect size measures for contingency tables of any size, generally referred to as “r × c tables”. This effect size is the “measure of association” or “measure of correlation” between the two variables. There are more measures applying to 2 × 2 tables than for larger tables. Continue reading