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?

Answer

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.

Attribution
Source : Link , Question Author : ilhan , Answer Author : ttnphns

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