Cohen’s d – Interpretation in Non-Significant T-Test Results

cohens-dinterpretationt-test

I did several independend t-tests. Some of them are significant, some of them are not.

Next, I computed Cohens $d$ for effect size.

For significant results, Cohens $d$ feels intuitively reasonable (How "large" is the found effect between both samples?). But how do I properly interpret Cohens $d$ in non-significant results?

Best Answer

Cohen's d can help to explain non-significant results: if your study has a small sample size, the chances of finding a statistically significant difference between the groups is unlikely, unless the effect size is large.

It's probably a good idea to include a confidence interval for your Cohen's d since the effect size based on your sample is still an estimate of the 'true' effect size.

This can be done easily in R using the tes() function in the compute.es package:

library(compute.es) 
tes(t=??, n.1=??, n.2=??)

Here is a useful short article on effect size thresholds: thresholds for interpreting effect sizes2.

And here is one on combining effect sizes with significance test interpretations (see especially sections 4 and 5): It's the Effect Size, Stupid: What effect size is and why it is important.

Here is a related post on how to interpret the confidence interval of Cohen's d in case you choose to find that: Why is the p-value for Cohen's $d$ not equal to the p-value of a t-test?.

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