## Type III Tests

The **Type III Tests** table is a further
breakdown of the variation due to **MODEL**.
The **Sum of Squares** and **DF** for **Model** are
broken down into terms corresponding to the main
effect for **DRUG**, the main effect for **DISEASE**,
and the interaction effect for **DRUG*DISEASE**.
The sum of squares for each term represents the variation
among the means for the different levels of the factors.
The **Type III Tests** table presents the Type III
sums of squares associated with the effects in the model.
The Type III sum of squares for a particular effect is
the amount of variation in the response due to that
effect after correcting for all other terms in the model.
Type III sums of squares, therefore, do not depend on the
order in which the effects are specified in the model.
Refer to the chapter on "The Four Types of Estimable Functions," in
the *SAS/STAT User's Guide*
for a complete discussion of Type I -IV sums of squares.

*F* tests are formed from this table in the
same fashion that was explained previously in
the section "Analysis of Variance."
In this case, there are three null hypotheses being tested:
class means are all the same for the main effect **DRUG**, the
main effect **DISEASE**, and the interaction effect **DRUG*DISEASE**.
Begin by examining the test for the interaction effect
since a strong interaction makes the interpretation
of main effects difficult if not impossible.
The computed *F* statistic is **1.7406** with a *p*-value of
**0.1271**.
This gives little evidence for an interaction effect.
Now examine the main effects.
The computed *F* statistic for **DRUG** is **15.8053**
with a *p*-value less than or equal to 0.0001.
The computed *F* statistic for **DISEASE** is
**4.2220** with a *p*-value of 0.0193.
While both effects are significant,
the **DRUG** effect appears to be stronger.
Now you have more information about which
means are significantly different.
The results of the *F* test in the **Analysis of Variance**
table indicated
only that *at least one* of the class
means is different from the others.
Now you know that the difference in means can be
associated with the different levels of
the main effects, **DRUG** and **DISEASE**.

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.