# 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: 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!