This document discusses running a two-way ANOVA in SAS with an unbalanced design. It shows the SAS code to specify a class and model statement to analyze the effects of factors A and B and their interaction on the response variable y. It also provides code examples for generating contrasts and least squares means comparisons. Dummy variable coding is explained as a method for representing categorical variables in the model. Finally, alternative approaches for analyzing main effects and interactions are suggested if contrast analysis cannot be run directly.

1. SAS tutorial 0524

2. proc anova;
class A B S;
model y=S|A|B;
test h=A e= S*A;
run;
The same as glm （但是比較沒用...）

3. Example
title 'Unbalanced Two-Way 2 1 28 . 23 34 42 13
Analysis of Variance'; 2 2 . 34 33 31 . 36
data a; 2 3 3 26 28 32 4 16
input drug disease @; 3 1 . . 1 29 . 19
do i=1 to 6; 3 2 . 11 9 7 1 -6
input y @; 3 3 21 1 . 9 3 .
output; 4 1 24 . 9 22 -2 15
end; 4 2 27 12 12 -5 16 15
datalines; 4 3 22 7 25 5 12 .
1 1 42 44 36 13 19 22 ;
1 2 33 . 26 . 33 21
1 3 31 -3 . 25 25 24

4. 4x3 2-way

5. code
ods graphics on;
proc glm;
class drug disease;
model y=drug disease drug*disease /ss3;
contrast 'drug 1 vs 2' drug 1 -1 0 0;
contrast 'drug 1 vs 3' drug 1 0 -1 0;
contrast 'drug 1 vs 4' drug 1 0 0 -1;
lsmeans drug/ pdiff=all adjust=tukey;
run;
ods graphics off;

6. Result

7. Interaction plot

10. Dummy variable
• Category variable
• Set reference group
• Set N-1 d.variables:
– 1 if xij belongs to the group specified
– 0 if xij belongs to other groups
• E.g. variable drug in the example:
– 0 0 0 => drug=1
– 1 0 0 => drug=2
– 0 1 0 => drug=3
– 0 0 1 => drug=4

11. Data

12. Result (is the same)

13. Why use d.v. coding?
http://www.sas.com/offices/NA/canada/downloads/presen
tations/VancouverMay11/Variable.pdf

15. If you cannot run contrast
analysis──
• Check coefficients
• Separate main effects and interactions into
different models.
• e.g. 2-way ANOVA with interaction:
– model y = A B;
(contrasts for main effects)
– model y = A*B;
(contrasts for interaction)