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Berkson's paradox, also known as Berkson's bias, collider 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.
Given two events A and B from the sigma-field of a probability space, with the unconditional probability of B being greater than zero (i.e., P(B) > 0), the conditional probability of A given B (()) is the probability of A occurring if B has or is assumed to have happened. [5]
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations , probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms .
Given two jointly distributed random variables and , the conditional probability distribution of given is the probability distribution of when is known to be a particular value; in some cases the conditional probabilities may be expressed as functions containing the unspecified value of as a parameter.
In this sense, "the concept of a conditional probability with regard to an isolated hypothesis whose probability equals 0 is inadmissible. " ( Kolmogorov [ 6 ] ) The additional input may be (a) a symmetry (invariance group); (b) a sequence of events B n such that B n ↓ B , P ( B n ) > 0; (c) a partition containing the given event.
A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).
CCISD elementary and secondary students show off their science fair projects at Miller High School on Friday, Jan. 19, 2024, in Corpus Christi, Texas.
In the case of tossing a fair coin, frequentists say that the probability of getting a heads is 1/2, not because there are two equally likely outcomes but because repeated series of large numbers of trials demonstrate that the empirical frequency converges to the limit 1/2 as the number of trials goes to infinity.