The difference between Type-I, Type-II, and Type-III tests

Although often not explicitly stated, there are several “types” of tests or methods of calculating sums of squares in statistics. The different types of tests test different hypotheses and thus it is important to know which type was used.

Type-I tests are sequential tests and test the effect of removing a term and all successive terms in the model. Type-I tests are order dependent and in some sense attempt to construct the model step-by-step. Type-I tests are the default in R but often test hypotheses that we do not career about in the brain and behavioral sciences.

Type-II and Type-III tests do not depend on the order of terms in the model and instead focus on the effect of removing individual terms.

Type-II tests are marginal tests and follow the principle of marginality when testing lower-order terms: a lower-order term, whose coefficient(s) is not significant, can nonetheless be significant when the combined effect with its interactions are.

Type-III tests, as made popular in commercial statistical software, are not marginal tests and do not follow the principle of marginality when testing lower-order terms: they test the effect of removing a term while leaving all of its higher-order interactions in place.