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Statistics Resources

This guide contains all of the ASC's statistics resources. If you do not see a topic, suggest it through the suggestion box on the Statistics home page.

Cohen's d

Cohen's d

When you're comparing two groups, like in an independent samples t-test, the most common method for assessing the size of the effect is by using Cohen's d. In this instance, we are simply standardizing the difference between the groups.

Computing Cohen's d

Starting from the "old school" method, we can compute Cohen's d using a basic formula:

cohen's d formula where D equals the mean of group 1 minus the mean of group 2 all over the pooled standard deviation estimate

where:

  • M1 and M2 represent the sample means for the two groups being compared and
  • Sp represents the pooled estimated population standard deviation.

Most of the time the actual population standard deviation is not known, this is why we estimate it using a pooled standard deviation from our two groups. This means we have another formula:

formula for pooled standard deviation estimate

 Here N represents the mean for each group (as numbered) and S^2 represents the variance for each group. Thankfully, most students aren't asked to do these calculations manually. Instead, we can simply use technology to compute Cohen's d.

Cohen's using SPSS

If you're using SPSS version 27 or higher, you can use SPSS to include an effect size estimate with your output for your independent samples t-test. Simply check the box next to "Estimate effect sizes" in the Independent Samples T-Test dialogue window, as shown below.

picture of the Independent Samples T-test window in SPSS

This will prompt SPSS to include the following table in the output:

Here we look in the top row, where it says "Cohen's d" and we look at the Point Estimate value. We would report this in the text as d = 1.084.

Interpreting Cohen's d 

The general guidelines for interpreting the effect size are as follows:

  • 0.2 = small effect
  • 0.5 = moderate effect
  • 0.8 = large effect

You should refer to your course resources to verify this is the same guideline followed by your readings, as some sources use slightly different interpretation values.

**For additional assistance with computing and interpreting the effect size for your analysis, attend the SPSS: T-tests group session**