Berkson's paradox

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Berkson's paradox, also known as Berkson's bias, collider bias, endogenous selection bias or Berkson's fallacy, is a result in conditional probability and statistics which is often found to be counterintuitive, and hence a veridical paradox. It is a complicating factor arising in statistical tests of proportions. Specifically, it arises when there is a sampling bias inherent in a study design. The effect is related to the explaining away phenomenon in Bayesian networks, and conditioning on a collider in graphical models. This paradox is often illustrated using scenarios from the fields of medical statistics or biostatistics, as in the original description of the problem by Joseph Berkson. The most common example of Berkson's paradox is a false observation of a negative correlation between two desirable traits, i.e., that members of a population which have some desirable traits tend to lack a second. Berkson's paradox occurs when this observation appears true when in reality the two properties...

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