Effect size estimation: methods and examples

While the p-value will tell the reader a study's results are statistically significant, it does not provide any information about the practical or clinical importance of the findings. Furthermore, p-values are influenced by sample size. They are more likely to be significant when sample size is large and less likely if the sample is small. Effect size estimates, on the other hand, are not sensitive to sample size and provide information about the direction and strength of the relationship between variables (e.g., a treatment and an outcome). In addition to providing valuable clinical information about study findings, effect size estimates can provide a common metric to compare results across studies. Despite their usefulness, effect size estimates are often not reported as part of the research results. Consequently, effect sizes often have to be calculated based on summary and test statistics reported in research articles.

This article provides the formulas utilized to directly calculate common effective size estimates using summary statistics reported in research studies, as well as methods to more indirectly estimate these effect sizes when basis summary statistics are not reported. In addition we present formulas to compute the corresponding confidence interval for each effect size.