Estimated standard error

New Member
Why is it ok to estimate the population variance with the sample variance formula (i.e. the unbiased estimate of the variance). I understand how we can build a confidence interval using the central limit theorem and the following formula . But, the unbiased estimate of the variance means that the estimate corresponds to the population variance in the long run (and the sd is biased, but nearly correct). Replacing s with σ in the formula above is just that, not the value of s squared in the long run. So, why is it ok to use it?

Dason

Ambassador to the humans
Describe the situation in which you think it's ok to do that.

katxt

Active Member
There are two formulas for SD. You need to use the n-1 version which gives an unbiased estimate of population sigma. These are still uncertainties with smaller samples because the sigma estimate, while unbiased, won;t be exactly the real sigma. The t distribution is designed to take care of that.