Goodness-of-fit tests check how well the model fits the data. Small p-values indicate the model is inadequate. Goodness-of-fit tests are also known as lack-of-fit tests and discrepancy-of-fit tests. Minitab displays 2 goodness-of-fit tests.

The Deviance Test compares the log-likelihood of the model to the maximum log-likelihood. The Deviance Test is additive for nested models that use maximum likelihood estimates for the parameters. This additivity makes the test useful when you compare two models where the smaller model is a subset of the larger model. You can see the change in the deviance as you add and remove terms from the model.

The Pearson Test compares the observed counts in the data to the fitted counts for the model. The Pearson Test has a more practical interpretation because you can look at the residuals to see where the observed counts and the fitted counts differ the most.

With large samples, small discrepancies can appear statistically significant. Consider the practical importance of the lack-of-fit through an examination of the difference between the observed counts and the fitted counts.

For the resin defect data, the p-values for the goodness-of-fit tests are 0.486 and 0.503. Neither test is significant at the α-level of 0.05. From the perspective of the goodness-of-fit tests, this model is adequate.