6.2 Cohen’s d
This might be starting to sound a little familiar by now, but here are some effect sizes for t-tests. Note that they’re different to the Cramer’s V we saw in the chi-square test of independence last week - this is because it is a) conceptually different and b) interpreted differently too.
6.2.1 What is Cohen’s d?
Cohen’s d is a measure of effect size that is used when comparing between two means (i.e. in a t-test). It essentially is a measure of the distance between the two means. See below for three pairs of means:
If two groups aren’t all that different (e.g. panel A), then any effect of group will be small or negligible. If the two groups are further apart, however (like panel C), there is a more obvious effect of group - and so the size of the effect itself will be larger. Cohen’s d essentially is a measure of this ‘distance’.
The basic formula for calculating Cohen’s d is: \[ d = \frac{M_1 - M_2}{\sigma_{pooled}} \]
In other words, Cohen’s d is calculated by taking the difference between the two group means and dividing that by the pooled standard deviation across both groups. Pooled SD is essentially an aggregate SD across both groups in the sample, and not something we’ll concern ourselves with this week (because like the maths for the t-statistic, the calculation of the pooled SD depends on the test and is hard).