extra-binomial variation

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Greater variability in repeat estimates of a population proportion than would be expected if the population had a binomial distribution. For example, suppose that n observations are taken on independent Bernoulli variables that take the value 1 with probability p, and the value 0 with probability 1−p. The mean of the total of the observations will be np and the variance will be np(1−p). However, if the probability varies from variable to variable, with overall mean p as before, then the variance of the total will now be>np(1−p). In the context of plant and animal populations, extra-binomial variation may be termed overdispersion. See also index of dispersion.

Subjects: Probability and Statistics.

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