I am doing a prevalence study on HIV/AIDS patients. But I need to know the sample size using the single(one)-sample formula. I used 0.5 for the unknown but true proportion of the population, while the prevalence of HIV in my country is 0.4. I personally feel that the prevalence and proportion of true population same according to the context. In this case, is it possible to use the prevalence score as the proportion value? If yes, I need a reference in this regard or a short briefing will be enough.
One more confusion is according to the formula, proportion score 0.4 and 0.6 produce same sample size result. I know the mathematical base, but what is the contextual logic?
see attached extract from IARC WHO 1999 Cancer Epidemiology: Principles and Methods (dos Santos Silva.
You could use 0.4 as population prevalence estimate.
the reason why 0.4 and 0.6 give same sample size is that the no. of diseased cases (a in above) is a function of p(1-p) which is a parabola and thus symmetric about its axis p=0.5.
I was struggling to differentiate the same issue with sample size determination. I could clear my understanding on this point based on Jung's article that I have attached here for your quick reading. It has complete calculation and logic for concluding to a certain result.
Article Stratified Fisher's Exact Test and its Sample Size Calculation
See this link. I think it will help you:
https://b-ok.cc/book/2324520/acf6e2
BTW if you only have 2 groups it does not matter which is called A. Thus you get the same sample size with p=.4(q=.6) or the other way way around. Best wishes:
D. Booth
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