Simple Effects

The GLM Procedure

Simple Effects

Suppose you use the following statements to fit a full factorial model to a two-way design:

   data twoway;
      input A B Y @@;
      datalines;
   1 1 10.6   1 1 11.0   1 1 10.6   1 1 11.3
   1 2 -0.2   1 2  1.3   1 2 -0.2   1 2  0.2
   1 3  0.1   1 3  0.4   1 3 -0.4   1 3  1.0
   2 1 19.7   2 1 19.3   2 1 18.5   2 1 20.4
   2 2 -0.2   2 2  0.5   2 2  0.8   2 2 -0.4
   2 3 -0.9   2 3 -0.1   2 3 -0.2   2 3 -1.7
   3 1 29.7   3 1 29.6   3 1 29.0   3 1 30.2
   3 2  1.5   3 2  0.2   3 2 -1.5   3 2  1.3
   3 3  0.2   3 3  0.4   3 3 -0.4   3 3 -2.2
   ;
   proc glm data=twoway;
      class A B;
      model Y = A B A*B;
   run;

Partial results for the analysis of variance are shown in Figure 30.17. The Type I and Type III results are the same because this is a balanced design.

The GLM Procedure

Dependent Variable: Y

Source	DF	Type I SS	Mean Square	F Value	Pr > F
A	2	219.905000	109.952500	165.11	<.0001
B	2	3206.101667	1603.050833	2407.25	<.0001
*AB**	4	487.103333	121.775833	182.87	<.0001

Source	DF	Type III SS	Mean Square	F Value	Pr > F
A	2	219.905000	109.952500	165.11	<.0001
B	2	3206.101667	1603.050833	2407.25	<.0001
*AB**	4	487.103333	121.775833	182.87	<.0001

Figure 30.17: Two-way Design with Significant Interaction

The interaction A*B is significant, indicating that the effect of A depends on the level of B. In some cases, you may be interested in looking at the differences between predicted values across A for different levels of B. Winer (1971) calls this the simple effects of A. You can compute simple effects with the LSMEAN statement by specifying the SLICE= option. In this case, since the GLM procedure is interactive, you can compute the simple effects of A by submitting the following statements after the preceding statements.

   lsmeans A*B / slice=B;
   run;

The results are shown Figure 30.18. Note that A has a significant effect for B=1 but not for B=2 and B=3.

The GLM Procedure

Least Squares Means

A	B	Y LSMEAN
1	1	10.8750000
1	2	0.2750000
1	3	0.2750000
2	1	19.4750000
2	2	0.1750000
2	3	-0.7250000
3	1	29.6250000
3	2	0.3750000
3	3	-0.5000000

The GLM Procedure

Least Squares Means

*AB Effect Sliced by B for Y**
B	DF	Sum of Squares	Mean Square	F Value	Pr > F
1	2	704.726667	352.363333	529.13	<.0001
2	2	0.080000	0.040000	0.06	0.9418
3	2	2.201667	1.100833	1.65	0.2103

Figure 30.18: Interaction LS-means and Simple Effects

Chapter Contents
Previous
Next
Top