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In this paper

Cumming, G. (2014). The new statistics: Why and how. Psychological science, 25(1), 7-29.

one can read this about Cohens' d:

For two independent groups, if we assume homogeneity of variance, the pooled standard deviation within groups, $s_p$, is our standardizer, just as we use for the independent-groups t test. If we suspect the treatment notably affects variability, we might prefer the control population’s standard deviation, estimated by $s_C$ (the control group’s standard deviation), as the standardizer.

I was wondering why one should prefer the standard deviation of the control group when the treatment affects variability and whether they are references that justify this point.

danilinares
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2 Answers2

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The logic of Cohen's $d$ is to standardize the effect in terms of the natural variation on that outcome, that is, variation without the influence of the treatment. This is the basis of the preference for the control standard deviation and not the treatment standard deviation. However, Hedges' did some work in the early/mid 1980s that showed that the pooled standard deviation provides a better estimate of the population standard deviation (this is what we really want) than the control group standard deviation unless the treatment has a rather large effect on outcome variability.

dbwilson
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According to wikipedia, the effect size is called Glass' $\Delta$

and the reason to use it proposed by Glass is that

if several treatments were compared to the control group it would be better to use just the standard deviation computed from the control group, so that effect sizes would not differ under equal means and different variances.

danilinares
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