Calculating Confidence Intervals of Cohen's d and Eta-squared:A Practical Primer

Abstract

The recent replication crisis in psychology has motivated many researchers to reform the methods they used in research, reporting effect sizes (ES) and their confidence intervals (CIs) becomes a new standard in mainstream journals. However, a practical tutorial for calculating CIs is still lacking. In this primer, we introduced theoretical basis of CIs of the two most widely-used effect size, Cohen’s d and η2, in plain language. The CIs of both Cohen’s d and η2 are calculated under the condition that the alternative hypothesis (H1) is true, and both rely on the estimation of non-centrality parameters of non-central distributions by using iterative approximations. More specifically, non-central t-distribution for Cohen’s d and non-central F-distribution for η2. Then, we illustrated how to calculate them in R and JASP with real data. This practical primer may help Chinese psychological researchers understand the CIs better and report CIs in their own research.