The Four Types of Estimable Functions


Many regression and analysis of variance procedures in SAS/STAT label tests for various effects in the model as Type I, Type II, Type III, or Type IV. These four types of hypotheses might not always be sufficient for a statistician to perform all desired inferences, but they should suffice for the vast majority of analyses. This chapter explains the hypotheses involved in each of the four test types. For additional discussion, see Freund, Littell, and Spector (1991) or Milliken and Johnson (1984).

The primary context of the discussion is testing linear hypotheses in least squares regression and analysis of variance, such as with PROC GLM. In this context, tests correspond to hypotheses about linear functions of the true parameters and are evaluated using sums of squares of the estimated parameters. Thus, there will be frequent references to Type I, II, III, and IV (estimable) functions and corresponding Type I, II, III, and IV sums of squares, or simply SS.