Interpretation of the four types of analysis of variance tables in sas

Various computational methods exist for generating sums of squares in an analysis of variance table. When the ANOVA design is balanced, most of these computational methods will produce equivalent sums of squares for testing the significance of the ANOVA model parameters. However, when the design is unbalanced, as is frequently the case in practice, these sums of squares depend on the computational method used.- The basic reason for the difference in these sums of squares is that different hypotheses are being tested. The purpose of this paper is to describe these hypotheses in terms of population or cell means. A numerical example is given for the two factor model with interaction. The hypotheses that are tested by the four computational methods of the SAS general linear model procedure are specified.

Although the ultimate choice of hypotheses should be made by the researcher before conducting the experiment, this paper

PENDLETON,VON TRESS,AND BREMER

presents the following guidelines in selecting these hypotheses:

When the design is balanced, all of the SAS procedures will agree.

In unbalanced ANOVA designs when there are no missing cells. SAS Type III should be used. SAS Type III tests an unweighted hypothesis about cell means. SAS Types I and II test hypotheses that are functions of the ceil frequencies. These frequencies are often merely arti¬facts of the experimental process and not reflective of any underlying frequencies in the population.

When there are missing cells, i.e. no observations for some factor level combinations. Type IV should be used with caution. SAS Type IV tests hypotheses which depend