In the field of statistics, a sampling bias occurs when the selection of the sample used is not appropriately representative of the population as a whole.

Example: Fox News runs a poll on their website which finds that the Republican candidate is certain to win. Unfortunately, it is unlikely that they managed to engage a random sample of the American voting public, so these results should be suspected of being biased.

A sampling bias does not necessarily invalidate a study, it simply limits the conclusions that can be drawn from a study. It is not surprising that most Fox News viewers plan on voting republican, but this poll should raise our confidence that this supposition is correct. While the terms are not entirely formalized, a sampling error that does invalidate a study because it does not measure any population accurately may be termed a selection bias.

Example: A researcher sets up a study to test the effects of a drug on iron absorption. They recruit their subjects from a local university (students are cheap), resulting in test subjects that are mostly the same age, comparatively wealthy, and share approximately the same diet. This introduces a sampling bias, and will limit their confidence that their results will apply, for example, to older populations.

The researcher then tests 100 students, and selects the 10 with the lowest blood iron level to complete the drug trial. This almost guarantees that there will be regression to the mean, and without a control group, invalidates the study: it introduces selection bias.

Sampling bias can be very subtle, as in Berkson's fallacy, in which samples drawn from hospitals ignore the unusually high base rate of illness in samples; survivorship bias, in which the dead are ignored; or the astronomical Malmquist bias, in which bright celestial objects are sampled more easily than dim ones. However, we often see less subtle forms of it in everyday life -- as in the news poll, where participants self-select, or when a politician talks about "what Americans want", having sampled only their party members.

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