Sampling bias is a systematic distortion arising when the sampling mechanism makes the observed sample unrepresentative of the target statistical population for the estimand of interest. It is distinct from random sampling variability and from other causes of the bias of an estimator.
Suppose a population has equal-sized groups with values zero and ten, so its mean is five. If independent sampling with replacement chooses the first group with probability , the sample mean has expectation one and converges to one as the sample grows. More data reduce its random variation without removing the selection bias. Known selection probabilities can support a design-based correction, but a group never sampled cannot be recovered merely by assigning larger weights to observed units.
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