Example 17.3: Split Plot
In some experiments, treatments can be applied only to groups of
experimental observations rather than separately to each observation.
When there are two nested groupings of the observations on the basis
of treatment application, this is known as a split plot design.
For example, in integrated circuit fabrication it is of interest to
see how different manufacturing methods affect the characteristics of
individual chips. However, much of the manufacturing process is
applied to a relatively large wafer of material, from which many chips
are made. Additionally, a chip's position within a wafer may also
affect chip performance. These two groupings of chips by
wafer and by positionwithinwafer might form the whole
plots and the subplots, respectively, of a split plot design
for integrated circuits.
The following statements produce an analysis for a splitplot design.
The CLASS statement includes the variables Block,
A, and B, where B defines subplots within
BLOCK*A whole plots.
The MODEL statement includes the independent
effects Block, A, Block*A, B, and A*B.
The TEST statement asks for an F test of the A effect, using
the Block*A effect as the error term.
The following statements produce Output 17.3.1
and Output 17.3.2:
title 'Split Plot Design';
data Split;
input Block 1 A 2 B 3 Response;
datalines;
142 40.0
141 39.5
112 37.9
111 35.4
121 36.7
122 38.2
132 36.4
131 34.8
221 42.7
222 41.6
212 40.3
211 41.6
241 44.5
242 47.6
231 43.6
232 42.8
;
proc anova;
class Block A B;
model Response = Block A Block*A B A*B;
test h=A e=Block*A;
run;
Output 17.3.1: Class Level Information and ANOVA Table
Class Level Information 
Class 
Levels 
Values 
Block 
2 
1 2 
A 
4 
1 2 3 4 
B 
2 
1 2 
Number of observations 
16 

The ANOVA Procedure 
Dependent Variable: Response 
Source 
DF 
Sum of Squares 
Mean Square 
F Value 
Pr > F 
Model 
11 
182.0200000 
16.5472727 
7.85 
0.0306 
Error 
4 
8.4300000 
2.1075000 


Corrected Total 
15 
190.4500000 



RSquare 
Coeff Var 
Root MSE 
Response Mean 
0.955736 
3.609007 
1.451723 
40.22500 

First, notice that the overall F
test for the model is significant.
Output 17.3.2: Tests of Effects
The ANOVA Procedure 
Dependent Variable: Response 
Source 
DF 
Anova SS 
Mean Square 
F Value 
Pr > F 
Block 
1 
131.1025000 
131.1025000 
62.21 
0.0014 
A 
3 
40.1900000 
13.3966667 
6.36 
0.0530 
Block*A 
3 
6.9275000 
2.3091667 
1.10 
0.4476 
B 
1 
2.2500000 
2.2500000 
1.07 
0.3599 
A*B 
3 
1.5500000 
0.5166667 
0.25 
0.8612 
Tests of Hypotheses Using the Anova MS for Block*A as an Error Term 
Source 
DF 
Anova SS 
Mean Square 
F Value 
Pr > F 
A 
3 
40.19000000 
13.39666667 
5.80 
0.0914 

The effect of Block is significant.
The effect of A is not significant: look at the F test produced
by the TEST statement, not at the F test produced by default.
Neither the B nor A*B effects are significant.
The test for Block*A is irrelevant,
as this is simply the mainplot error.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.