 Scaled deviance

For an exponential dispersion family with a common dispersion parameter $\varphi$, scaled deviance compares a fitted model with the saturated statistical model at the same dispersion:For a normal distribution with variance ${\sigma }^2$, unscaled deviance is the residual sum of squares and scaled deviance is that sum divided by ${\sigma }^2$. For the binomial distribution, $\varphi =1$ and the two coincide. Unknown Gaussian dispersion requires variance estimation; raw deviance differences should not be treated as chi-squared statistics without the scale.