Sampling distribution

The sampling distribution of a statistic is its probability distribution under repeated samples from a specified data-generating model.

Sampling variability is the variation of a statistic over random samples generated by a specified sampling design or model. It concerns the statistic before the sample is realized, even when the observed dataset is later treated as fixed.

For independent identically distributed observations with variance ${\sigma }^2$, the sample mean has variance ${\sigma }^2/n$ and standard error $\sigma /\sqrt{n}$. Thus increasing $n$ from 100 to 400 halves that standard error under the same model. A sampling distribution describes this variation; the bias of an estimator describes a displacement of the estimator's expectation from its target. Correlated observations or an informative selection mechanism can invalidate the simple independent-sample formula.