Pearson's chi-squared test - Wikipedia

To compute a chi-square test statistic, I first standardized the verbalscores data by subtracting the sample mean and dividing by the sample standarddeviation.

what null-hypothesis do you want your "goodness of fit test" to test?

GLM models have a defined relationship between the expected variance and the mean. This relationship can be used to evaluate the model's goodness of fit to the data. The deviance can be used for this goodness of fit check. Under asymptotic conditions the deviance is expected to be distributed. Pearson's can also be used for this measure of goodness of fit, though it is the deviance which is minimized when fitting a GLM model.

Statistical hypothesis testing - Wikipedia

We can check the goodness of fit of this model. We will use the deviance of the residuals for this test.

The p-value is approximately .001. This deviance is not likely to have occurred by chance, under the null hypothesis of the deviances being . Therefore we have evidence of overdispersion. The presence of overdispersion suggested the use of the F-test for nested models. We will test if the squared term can be dropped from the model.