So I have population A and population B. The demographics are similar (assumes that the true expected value is the same in both populations). Population B, however, is twice the size of population A, which has 500,000 subjects. The sampling size for a survey was 1,000. What sample size should I choose for population B to maintain the same accuracy/standard error in my estimates?
2026-03-30 12:35:14.1774874114
Equivalent standard error for different populations
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We assume that we want to estimate the population mean. Each of A and B is large enough that sampling with or without replacement are essentially equivalent. We assume the populations are enough alike that the standard deviations are the same.
The standard deviation of a sample meandepends only on the population standard deviation and the sample size. So for population B we use the same sample size of $1000$ as for population A to get equivalent accuracy.