Cohen's d adjusted for base rates
McGrath and Meyer (2006) proposed corrections for Cohen's d based upon the prevalence of the two groups in the real world. They suggest using larger values to represent small, medium and large effects as the group sizes become more unequal. This could happen, for example, if one is interested in real world comparisons of schizophrenics (which occur in the general population less than 2% of the time) and controls. One can think of this, as the group sizes obtained by randomly sampling the general population, as opposed to artifically fixing the group sizes.
They produced a table of suggested magnitudes of Cohen's d. The columns in the table represent p1, the proportion of people in the larger of the two groups.
Standard |
p1=0.50 |
p1=0.75 |
p1=0.95 |
p1=0.99 |
|||
Large |
0.80 |
0.92 |
1.84 |
4.02 |
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Medium |
0.50 |
0.58 |
1.15 |
2.51 |
|||
Small |
0.20 |
0.23 |
0.46 |
1.01 |
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Table showing rules of thumb for Cohen's d adjusted for population base rates.
Reference
(pdf downloadable via sciencedirect for CBSUers)
McGrath RE, Meyer, GJ (2006) When effect sizes disagree: the case of r and d. Psychological Methods 11(4) 386-401.