Danta -

I'll take a guess at what you might need here. 

First, sample sizes are driven by obtaining an acceptable standard error - assuming bias is not problematic.  For a stratified random sample, the objective is to obtain good overall inference, but if results are needed for each stratum, that is not really a case of stratified random sampling, because each stratum is then not really a stratum, but actually a separate subpopulation for which you want good results.  It seems as if you might be looking at five subpopulations here, if I'm guessing correctly.  I am guessing that you want to compare these five areas, and thus need adequate sample sizes in each. 

Further, it seems here that what you are actually considering is somewhat more than just sampling from populations.  It appears that you are looking at logistic regressions in each subpopulation, as you want to predict "yes" or "no" with regard to "likely predictors of screening uptake."  Logistic regression is not an area for me, but if you can get the square roots of estimated variances of prediction errors, you might see when you have an adequate sample size for your needs in each area.  If you have software that will do this, be sure that you understand exactly what is being predicted.  Also, if you have test data, I think you might want to compare performances of models using various predictors and combinations of predictors. 

Oh ... you also mentioned barriers. Well, I don't know if you want to look at them separately or together, but you will need to consider that.

Just some thoughts. 

Cheers - Jim

Stratified random sampling is a method of sampling that involves the division of a population into smaller groups known as strata. And the formula is N(N-n)/n

Thank you James R Knaub and Mohamed Jama Mohamed, what do all the N/ns stand for? James, your first guess was right. I am doing the survey across all the areas just to have an overall view of the problem, but it will be just one population. The results will be presented for the whole study population, and not for each subpopulation. Another reason why I wanted to have participants from all the zones was to determine if living area could be a predictor of screening uptake too. The barriers part will be addressed in a qualitative component of the study. It is a mixed method design. After the quantitative part, I will have to interview only the women who have not used the screening services to identify the barriers. So, basically, the quantitative component will be to define the population for my qualitative component and to determine the predictors of screening uptake among those who have been screened. Any additional thought will be helpful. Thank you guys.

Stratified random sampling is covered well in textbooks such as W.G. Cochran(1977), Sampling Techniques, 3rd edition, Wiley, and you could even use yes/no data to look at proportions and get sample size info, but that would not help you with the study of predictors that you want.

You might do a pilot study using logistic regression for each area separately, and a combined one, and adjust the mix as to where you randomly select, to see what mix seems optimal overall (in the combined data case). You might then iteratively add respondents from each area according to the mix that seems best, until you obtain adequate results in terms of estimated variances of prediction errors, or perhaps just until the results stabilize (do not change much when new data are introduced) to your satisfaction. In that case, you will only be able to project your sample size needs once you have already collected a substantial part of your sample.

As I said, logistic regression is not an area of expertise for me, but I think it might be useful for you and therefore you might want to look into it.

I agree with u