Which of the following statements regarding deviance is true?

The statement that the deviance can be used to test the significance of explanatory variables is true. In statistical modeling, especially in the context of generalized linear models, deviance provides a measure of how well the model fits the data compared to a saturated model, which predicts perfectly.

When assessing the contribution of explanatory variables, we can use changes in deviance when adding or removing these variables from the model. A significant reduction in deviance indicates that the explanatory variable contributes meaningfully to the model, allowing researchers to test hypotheses about the importance of different predictors. This process often involves comparing the deviance of the model with the explanatory variable included to that of a simpler model without it.

In contrast, while deviance does relate to model fit, it is not solely used for that purpose; it serves a broader function by enabling comparisons and hypothesis testing. Deviance in models concerning normal distributions does not equal the total sum of squares, as that concept applies differently in that context. Additionally, deviance can indeed be defined in terms of fitted models since it is a measure derived from comparing the likelihood of observed data to that predicted by the fitted model.