Deviance (Statistics)

In statistics, deviance is a goodness-of-fit statistic for a statistical model, used often in hypothesis testing, that generalizes the idea of the residual sum of squares to maximum likelihood estimation. For a fitted model it is calculated as twice the difference between the log-likelihood of a saturated model that fits the data perfectly and the log-likelihood of the model under evaluation. Under Wilks' theorem, the difference in deviance between two nested models approximately follows a chi-squared distribution with degrees of freedom equal to the difference in the number of parameters, which is what allows deviance to be used for formal hypothesis tests comparing models.