"Elmaache, Hamani" <Hamani.Elmaache@ccra-adrc.gc.ca>, against my express wishes, wrote to me personally instead of to the list:

> I think that this problem is equvalent to: > Estimate the sample size n necessary ( for Dichotomic Outcomes: 0 or 1) in order > to test if the proportion (=P) is equal to p=0.02 given: > 1) power(=1-BETA=0.8) > 2) the specified ALPHA (=0.05) > and > 3)EFFECT SIZE (0.005)

I am beginning to suspect that you are having this problem because you are confusing the *difference*in*proportion* you wish to detect with the *effect*size* . These are not at all the same. Detecting a difference of 0.005 is a rational goal. Detecting an effect size of 0.005 is *not*. Cohen considers something 40 times larger to be a 'small' effect size.

> PS. > I know and I have the article of Cohen, but I don't know how does he do to > calcul (or estimate the n). > I tried to use SAS to estimate n, but SAS ask me to give it the data.(I Used > interactive windows of SAS: Solutions/Analysis/Analyst) without succes.

That's because SAS Analyst tool does not have a sample-size calculator for a test of proportions. And Cohen focuses on tests on continuous variables. In particular, for normally-distributed data, the sample mean is statistically independent of the sample variance. For binomial data, the sample proportion is *used* to compute the sample variance. So defining the effect size is not the same problem.

Furthermore, you have only said that you wish to sample from 'a population'. How is this sample going to be achieved? Is this longitudinal data, or a target population from which you will design a sampling regimen? Will this be a simple random sample, or will there be sampling design effects? Is the population finite, or conceptually infinite? Your choices on the sampling design will determine whether the classical sample-size formulas are even relevant. If you end up using, for example, a stratified sample, then the sample sizes needed for the individual strata may not be the same, and the total sample size may be very different than that for a simple random sample [in fact, it may be noticeably smaller if your sample is designed well].

Perhap you could write to the list and give us some more details, so that we might try to give you some more guidance. I'm not sure that you are as yet asking the right questions.

Hoping I didn't sound too abrupt, David -- David Cassell, CSC Cassell.David@epa.gov Senior computing specialist mathematical statistician