Estimated standard error

[Mada]

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]

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

 

[katxt]

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.