This page is currently being updated from the earlier version of my website. Sorry that it is not yet fully available.

*Hello, I am looking at your page on sample size
calculation, and
I'm curious as to where you got the equation shown there:*

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*I can't seem to find that exact form in Cohen's book, not does it
appear anywhere else that I've looked. Would you happen to know its
original source?*

I'm away from all my books for the time being, so I can only speculate. If you let the two standard deviations be equal, then the formula simplifies somewhat.

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I can't say for sure what Cohen's formula is, but I suspect that it assumes both variances are equal.

Some formulas will place the common standard deviation in the denominator of this equation, which yields

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The quantity

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is sometimes called the effect size, and is often called Cohen's d (notice the change from upper case to lower case).

Some formulas will substitute a t distribution for the z distribution although this requires iteration, as the degrees of freedom are dependent on the sample size. This is a slightly better approximation, but the best answer will come from the non-central t-distribution. You would have to rely on tables or software for any power or sample size calculation involving the non-central t-distribution..

As far as a source, I suspect you would find this formula in many textbooks. Perhaps Rosner would be a good source.

- Fundamentals of Biostatistics. Bernard Rosner (1990) Belmont, California: Duxbury Press. ISBN: 0-534-91973-1. Description: Bernard Rosner provides a good solid introduction to Statistics with nice examples of sample size calculations. This book is good for someone looking for an introduction to statistics.

If there's a different formula from a definitive source, I would not be at all offended if you used it instead.

You can find an earlier version of this page on my original website.