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This is quite a basic question but I could not find a clear answer elsewhere.

If we wish to draw a simple random sample to determine the estimated proportion of an attribute in the population, given a desired level of precision and confidence level, the Cochran's formula is often used: enter image description here

This formula says that a sample of N= 384 is needed to estimate the prevalence at 95% CI and 5 pp Margin of Error (assuming null p = 0.5).

However, Stata has no direct command for a Cochran's formula sampling. Instead, one can use the Wald test comparing a proportion to a reference value as below: Code:

power oneproportion 0.5 0.55, test(wald) continuity

The above command gives an N of 797, for the same level of precision and Margin of Error.

Clearly, I am misunderstanding something here. Could you please help? Thanks!

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You can find the equations used by Stata at https://www.stata.com/manuals/pss.pdf (page 710). The difference with Cochran formula is that Stata uses 2*z(1-a/2) for two-sided CI's and z(1-a) for one-sided CI's. Now, if anyone could give references supporting Stata's variation over Cochran formula, I would be truly grateful.

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