= Sampling variability
= Sampling variation
{synonym}
<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.
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