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  • Reconciling sample size calculations using Cochran's formula and Wald test

    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:

    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:
    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!