Deviance (statistics)

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In statistics, deviance is a quantity whose expected values can be used for statistical hypothesis testing.

It is defined as

$D(y,\theta) = -2 \log[p(y|\theta)].\,$

As a function of θ with y treated as fixed, it is −2 times the log-likelihood. In the framework of the generalized linear model, if θ is the true parameter, D(y, θ) follows a chi-squared distribution.