An effect size estimates the magnitude of the difference of proportions or the association between two categorical variables.
The effect size that best describes a 2 x 2 contingency table depends on the study design that produced the data:
- When both variables are random variables, the odds ratio provides the best measure of association between the variables.
- When one variable is an explanatory variable (a fixed variable) and the other a response variable (a random variable), the effect size between the two groups of the response variable can be expressed as the odds ratio, the difference between proportions, or ratio of proportions.
- When the variables are matched-pairs or repeated measurements, the odds ratio or the difference between proportions are appropriate. The ratio of proportions is meaningless in this scenario.
A point estimate is a single value that is the best estimate of the true unknown parameter; a confidence interval is a range of values and indicates the uncertainty of the estimate.
For tables larger than 2 x 2, you must partition the contingency table into a series of 2 x 2 sub-tables to estimate the effect size.