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

It is defined as:

D(y,θ) = - 2logp(θ | y)

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.