What are some conventions for interpreting different effect sizes?

Say you’ve got an effect size equivalent to r = .25. What does it mean? How do you interpret this effect size? Ideally you will be able to contextualize this effect against some meaningful frame of reference. But if that’s not possible another approach is to refer to conventions such as those developed by Jacob Cohen.

In his authoritative Statistical Power Analysis for the Behavioral Sciences, Cohen (1988) outlined a number of criteria for gauging small, medium and large effect sizes in different metrics, as follows:

r effects: small ≥ .10, medium ≥ .30, large ≥ .50

d effects: small ≥ .20, medium ≥ .50, large ≥ .80

According to Cohen, an effect size equivalent to r = .25 would qualify as small in size because it’s bigger than the minimum threshold of .10, but smaller than the cut-off of .30 required for a medium sized effect. So what can we say about r = .25? It’s small, and that’s about it.

Cohen’s conventions are easy to use. You just compare your estimate with his thresholds and get a ready-made interpretation of your result. (For a fun illustration of this, check out the infamous Result Whacker.)

But Cohen’s conventions are somewhat arbitrary and it is not difficult to conceive of situations where a small effect observed in one setting might be considered more important than a large effect observed in another. As always, context matters when interpreting results.

This entry was posted on Sunday, May 30th, 2010 at 11:32 pm and is filed under effect size, interpreting results. You can follow any responses to this entry through the RSS 2.0 feed.
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2 Responses to What are some conventions for interpreting different effect sizes?

I think your classification of r=0.25 is small not correct. It must be medium. Because small = or less than 0.10 then the correct classification is medium which = 0.10 to 0.30

Although it may be possible to show that an r of, say, 0.5, is substantively significant, Cohen would say any r < .10 is smaller than small, ie: it is trivial in size. A small ES, according to Cohen's arbitrary classification, is one in the 0.10 – 0.30 range.

“The primary product of a research inquiry is one or more measures of effect size, not p values.”
~ Jacob Cohen

“Statistical significance is the least interesting thing about the results. You should describe the results in terms of measures of magnitude – not just, does a treatment affect people, but how much does it affect them.”
~ Gene Glass

I think your classification of r=0.25 is small not correct. It must be medium. Because small = or less than 0.10 then the correct classification is medium which = 0.10 to 0.30

Although it may be possible to show that an r of, say, 0.5, is substantively significant, Cohen would say any r < .10 is smaller than small, ie: it is trivial in size. A small ES, according to Cohen's arbitrary classification, is one in the 0.10 – 0.30 range.