Effect Sizes for Binary Data and Correlation Coefficients

This session introduces effect size measures for binary outcomes, commonly used when a study classifies participants into two categories, such as disease versus no disease or treatment success versus failure. Students will learn to organize data in a (2 x 2) contingency table and calculate three key effect measures: the risk ratio (RR), odds ratio (OR), and risk difference (RD). RR and OR describe relative effects, whereas RD measures the absolute difference in outcome risks between groups. The session also covers logarithmic transformations of RR and OR, which facilitate statistical analysis in meta-analysis, as well as the estimation of variance, standard error, and confidence intervals. The session will focus on interpreting relative and absolute effects, handling rare events, and addressing zero-cell problems that can complicate effect size calculations and statistical synthesis.

The second component focuses on effect sizes derived from correlation data, particularly the Pearson correlation coefficient, which measures the direction and strength of a linear relationship between two quantitative variables. Because correlation coefficients have a bounded scale and sampling distributions that may be unsuitable for direct statistical pooling, students will learn the Fisher (z) transformation and its role in meta-analysis. The session explains how to estimate the variance of Fisher (z), calculate a pooled correlation on the transformed scale, and convert the pooled estimate back to the original correlation scale for interpretation. These procedures help researchers combine correlation findings from multiple studies while accounting for sampling uncertainty and producing an overall estimate of the relationship between variables.

Finally, students will compare effect size measures for binary outcomes with those used for correlation data and learn how to interpret their results appropriately. They will examine how the magnitude and direction of an effect provide different information depending on whether the measure represents a relative risk, an absolute risk difference, an odds ratio, or a correlation coefficient. A key distinction is that correlation indicates an association between variables but does not, by itself, establish causality. By the end of this session, students should be able to identify suitable effect measures for binary and correlational outcomes, explain the mathematical principles underlying their transformations and uncertainty estimates, and recognize important methodological challenges when synthesizing these measures in a meta-analysis.