Using Cohen's Tables to Determine the Proper n

Dear Ammar,

You asked me how to use Cohen's tables to determine the proper sample size to use in a study comparing two group means. I don't have the table in front of me, but I'll help you as much as I can going on memory.

In using Cohen's tables to help determine the "proper" sample size, the first 2 things the researcher should think about are (1) the level of significance and (2) the one-tailed vs. two-tailed option. Those 2 things dictate which of the many tables should be used. (Most researchers, I suspect, would choose a table that's labeled "a2 = .05" (meaning two-tailed at the .05 level of significance.)

Next, the researcher decides what level of power he/she wants, and that determines which row of the table will be used. You're right in remembering that Cohen (and others) argue that .80 is the minimum power one should have in doing inferential tests.

So, at this point, the researcher is in (we hope) the right row of the right table. Now, the only thing left to do is determine the proper column to use. Knowing which column to use involves specifying the study's "effect size." Once we have that column, the intersection of it and the proper row contains the "n" needed to carry out the study.

To determine the proper column, the researcher can do one of two things, both of which involve specifying the "effect size." The very best way to do this is to do it in an "unstandardized" manner. This requires that the researcher (1) know the population SD and (2) be able to indicate how far apart two means need to be, in raw score units, in order for the mean difference to worth talking about (i.e., noteworthy) rather than so small that the word "trivial" aptly describes the mean difference. The unstandardized effect size is simply the second of these things divided by the first.

For example, in an IQ study, I might say that the mean difference between an experimental group (which gets training on taking IQ tests) and a control group needs to be 5 IQ points of more in order for the impact of the experimental treatment to be worth talking about. Since IQ scores in the general population have a SD of about 15, my effect size would be 5 divided by 15, or .33. This value (.33) would indicate which column of Cohen's chart is used.

In many cases, researchers do not know the population SD. To help them design their studies (and compute the "proper n") even though they can't use the procedure outlined in the previous two paragraphs, Cohen suggests they use a "standardized" effect size, .2 ("small") or .5 ("medium") or .8 ("large"). The researcher simply selects one of these figures and then uses the chart to figure out how large the "n" should be.

I hope this explanation helps.

Sky Huck

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Schuyler W. Huck
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