# What is the difference between sample variance and sampling variance?

What is the difference between sample variance and sampling variance? They seem same. Aren't they?

Sample variance refers to variation of observations (the data points) in a single sample. Sampling variance refers to variation of a particular statistic (e.g. the mean) calculated in sample, if to repeat the study (sample-creation/data-collection/statistic-calculation) many times. Due to central limit theorem, though, for some statistics you don't have to repeat the study many times in reality, but can deduce sampling variance from a single sample if the sample is representative (this is asymptotic approach). Or you could simulate repetition of the study by a single sample (this is bootstrapping approach).

An additional note on "sample variance". Two may be mixed in one term:

• Estimate of population variance based on this sample. This is what we usually use, it has denominator (degrees of freedom) n-1.

• Variance of this sample. It has denominator n.

The sample variance, $s^2$, is the variance of the sample, an estimate of the variance of the population from which the sample was drawn.

"Sampling variance" I would interpret as "the variance that is due to sampling", for example of an estimator (like the mean). And so I would consider these two terms to be quite different.

But "sampling variance" is a bit vague, and I would need to see some context to be sure. And I'd prefer to say "sampling variation" for the general idea.

[Many people (particularly in quantitative genetics) use the term "variance" in place of "variation", whereas I would reserve "variance" solely for the particular measure of variation.]