# Finite population correction for the variance

Just when I thought I was starting to understand Bessel's correction, I noticed that it is not valid when the sample size equals the population size and so likely not valid for sample sizes close to the population size.

I know that Bessel's correction is for small samples, but my question is: What can we do if we sample, say, 20% of the population or 50%?

Is there an alternative to Bessel's correction that takes into account the size of the sample relative to the population, analogous to the FPC?

• Which formula are you using? The ones I am familiar with work even for the entire population and they do account for the size of the sample relative to the population.
– whuber
Commented Feb 3, 2023 at 14:26
• I'm talking about multiplying the variance by a factor of $n/(n-1)$. I'm not aware of any other formula for Bessel's correction.
– Zaz
Commented Feb 4, 2023 at 0:45
• There are very many. The ones for finite population use different factors than that. So do formulas for regression models.
– whuber
Commented Feb 4, 2023 at 15:46