# Statistical deviance

Statistical deviance is a quantity whose expected values can be used for statistical hypothesis testing.

It is defined as:

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

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

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