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

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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.

In Psychology:Techniques and Applications
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