This document discusses two-way ANOVA and repeated measures ANOVA using PROC GLM in SAS. It provides an example of a balanced 2-way ANOVA with blocks to analyze stem length data from different plant types. It also demonstrates how to specify the MODEL statement and use CONTRAST and TEST statements to analyze main effects and interactions. Repeated measures ANOVA is explained as measuring the same subjects under different conditions. An example 2-way repeated measures ANOVA is presented along with the appropriate MODEL statement syntax for PROC GLM. Dummy and effect coding schemes for categorical variables are also overviewed.

1. SAS tutorial : GLM
two-way anova
&
repeated measure
游如淇

2. PROC GLM (複習)
PROC GLM 選項串 ;
CLASS 變相名稱串;
MODEL 依變項=實驗效果串/選項串 ;
MEANS 實驗效果串/選項串;
CONTRAST “標題” 效果名稱串 各組效果係數/選項串
TEST H=效果項 E=殘差項
RUN;
• 還有ESTIMATE、RANDOM、LSMEAN…等其他
statement，跟 PROC ANOVA 差不多
Nominal or ordinal scale

3. Some statements (複習)
• CONTRAST：作對比分析
– CONTRAST “標題” 效果名稱串 各組效果係數/選項串;
• “標題”： 20字內，不能有“;”
• 效果名稱： 要在model中出現過，界定所要比較的效果
• 係數：總合為0 以空格隔開
– E.g. CONTRAST „A1B1 vs A2B2‟ A*B 1 0 0 -1;
– E.g. CONTRAST „b at a1‟ a*b 3 3 -2 -2 -2 0 0 0 0 0;
• 選項串：e, ss3……
• TEST：指定效果項與殘差項作F檢定
– TEST H=效果項 E=殘差項;
– E.g. TEST h=A*B e=S*A*B;
• CONTRAST必須擺在MODEL之後，TEST、
MANOVA、REPEATED、RANDOM之前
• CLASS需擺在MODEL之前

4. 2-way ANOVA

5. Example 39.1
title ‟Balanced Data from Randomized Complete Block‟;
data plants;
input Type $ @;
do Block = 1 to 3;
input StemLength @;
output;
end;
datalines;
Clarion 32.7 32.3 31.5
Clinton 32.1 29.7 29.1
Knox 35.7 35.9 33.1
O‟Neill 36.0 34.2 31.2
Compost 31.8 28.0 29.2
Wabash 38.2 37.8 31.9
Webster 32.5 31.1 29.7
;

6. Example 39.1
proc glm;
class Block Type;
model StemLength = Block Type;
run;
proc glm order=data;
class Block Type;
model StemLength = Block Type / solution;
/*----------------------------------clrn-cltn-knox-onel-cpst-wbsh-wstr */
contrast 'Compost vs. others' Type -1 -1 -1 -1 6 -1 -1;
contrast 'River soils vs. non' Type -1 -1 -1 -1 0 5 -1,
Type -1 4 -1 -1 0 0 -1;
contrast 'Glacial vs. drift' Type -1 0 1 1 0 0 -1;
contrast 'Clarion vs. Webster' Type -1 0 0 0 0 0 1;
contrast 'Knox vs. O‟Neill' Type 0 0 1 -1 0 0 0;
run;
means Type / waller regwq;
run;

7. Result-1

8. Result-2

9. Result-3

10. Result-4

11. Repeated measure

12. Repeated measures
• 如果每個參與者都作了某些作業／回答某
些題目。
• 那麼這些題目／作業便稱為重複量數
（repeated measures）。
– 或受試者內（within subject）設計。
• 可以去除來自個體差異的variance。

13. Example:
2-way repeated ANOVA
Source SS df MS F
A A / (S*A)
B B / (S*B)
A*B A*B / (S*A*B)
S
S*A
S*B
S*A*B
Error

14. data aaa;
do S= 1 to 3;
do A=1 to 2;
do B=1 to 2;
input x @@;
output;
end;
end;
end;
datalines;
5 10 20 10
6 11 22 13
4 12 24 9
;
GLM for repeated measures

15. GLM for repeated measures:
code
Between
proc glm data=AAA;
class A B S;
model x=A|B|S;
test h=A e=A*S;
test h=B e=B*S;
test h=A*B e=A*B*S;
mean A B A*B/tukey alpha=.5
run;
要考慮的變項
(分子)
要比較的值
要知道的變項
(分母)
error

16. Result (between) :
Interaction plot

17. Result (between)

18. Result (within)
DF 被model用完了，
沒有error可以除？

19. Result
Between

20. Dummy coding
data k;
input factor ncases @@;
x0=1;x1=0;x2=0;x3=0;x4=0;
if factor=1 then x1=1;
if factor=2 then x2=1;
if factor=3 then x3=1;
if factor=4 then x4=1;
cards;
1 12 1 18 2 14 2 12 2 13 3 19 3
17 3 21 4 24 4 30
;
proc print;
var factor ncases x0 x1 x2 x3 x4;
proc glm;
class factor;
model ncases=factor;
run;
proc reg;
model ncases=x1 x2 x3 x4;
run;
proc reg;
model ncases=x1 x2 x3;
run;

21. Dummy coding

22. Dummy coding

23. Dummy coding – proc reg

24. Dummy coding – proc reg

25. Effect coding
data k;
input factor ncases @@;
x1=0;x2=0;x3=0;
if factor=1 then x1=1;
if factor=2 then x2=1;
if factor=3 then x3=1;
if factor=4 then do;
x1=-1;x2=-1;x3=-1;
end
cards;
1 12 1 18 2 14 2 12 2 13 3 19 3
17 3 21 4 24 4 30
;
proc glm;
class factor;
model ncases=factor;
run;
proc reg;
model ncases=x1 x2 x3 x4;
run;
proc reg;
model ncases=x1 x2 x3;
run;

26. 2-way effect coding
data k;
input area ses ncases @@;
x1=0;y1=0;y2=0;
if area=1 then x1=1;
if area=2 then do; x1=-1; end;
if ses=1 then y1=1;
if ses=2 then y2=1;
If ses=3 then do; y1=-1;y2=-1;
end;
x1y1=x1*y1
x1y2=x1*y2
cards;
………………………………
;
proc print;
proc reg;
model ncases = x1 y1 y2
x1y1 x1y2;
run;