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Program
8

OPTIONS LS=80 NODATE PAGENO=1;
TITLE 'Latin-Square designs, Y603';
DATA ls;
INPUT wheel car rubber repeat score;
LABEL wheel='the first nuisance variable--a fixed factor'
car ='the second nuisance variable--a random factor'
rubber='the treatment factor--fixed'
repeat='repetition of the test'
score ='thickness of tread remaining after 10,000 miles of driving';
CARDS;
1 1 1 1 3
1 1 1 2 1
2 1 2 1 4
2 1 2 2 2
3 1 3 1 7
3 1 3 2 5
4 1 4 1 7
4 1 4 2 10
1 2 2 1 5
1 2 2 2 3
2 2 3 1 8
2 2 3 2 6
3 2 4 1 8
3 2 4 2 10
4 2 1 1 6
4 2 1 2 2
1 3 3 1 7
1 3 3 2 5
2 3 4 1 9
2 3 4 2 9
3 3 1 1 3
3 3 1 2 2
4 3 2 1 4
4 3 2 2 4
1 4 4 1 8
1 4 4 2 11
2 4 1 1 3
2 4 1 2 2
3 4 2 1 3
3 4 2 2 3
4 4 3 1 6
4 4 3 2 6
;
PROC PRINT;
PROC GLM;
CLASS car wheel rubber;
MODEL score=car wheel rubber car*wheel*rubber;
TITLE2 'This is the analysis result based on Example 9 in the handout';
PROC GLM;
CLASS repeat car wheel rubber;
MODEL score=repeat car wheel rubber repeat*car repeat*wheel repeat*rubber;
TITLE2 'This is the analysis result based on Example 9b in the handout';
RUN;
Latin-Square designs, Y603 1
OBS WHEEL CAR RUBBER REPEAT SCORE
1 1 1 1 1 3
2 1 1 1 2 1
3 2 1 2 1 4
4 2 1 2 2 2
5 3 1 3 1 7
6 3 1 3 2 5
7 4 1 4 1 7
8 4 1 4 2 10
9 1 2 2 1 5
10 1 2 2 2 3
11 2 2 3 1 8
12 2 2 3 2 6
13 3 2 4 1 8
14 3 2 4 2 10
15 4 2 1 1 6
16 4 2 1 2 2
17 1 3 3 1 7
18 1 3 3 2 5
19 2 3 4 1 9
20 2 3 4 2 9
21 3 3 1 1 3
22 3 3 1 2 2
23 4 3 2 1 4
24 4 3 2 2 4
25 1 4 4 1 8
26 1 4 4 2 11
27 2 4 1 1 3
28 2 4 1 2 2
29 3 4 2 1 3
30 3 4 2 2 3
31 4 4 3 1 6
32 4 4 3 2 6
Latin-Square designs, Y603 2
This is the analysis result based on Example 9 in the handout
General Linear Models Procedure
Class Level Information
Class Levels Values
CAR 4 1 2 3 4
WHEEL 4 1 2 3 4
RUBBER 4 1 2 3 4
Number of observations in data set = 32
Latin-Square designs, Y603 3
This is the analysis result based on Example 9 in the handout
General Linear Models Procedure
Dependent Variable: SCORE thickness of tread remaining after 10,00
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 15 203.50000000 13.56666667 6.78 0.0002
Error 16 32.00000000 2.00000000
Corrected Total 31 235.50000000
R-Square C.V. Root MSE SCORE Mean
0.864119 26.31095 1.4142136 5.3750000
Source DF Type I SS Mean Square F Value Pr > F
CAR 3 5.25000000 1.75000000 0.88 0.4746
WHEEL 3 1.00000000 0.33333333 0.17 0.9173
RUBBER 3 194.50000000 64.83333333 32.42 0.0001
CAR*WHEEL*RUBBER 6 2.75000000 0.45833333 0.23 0.9610
Source DF Type III SS Mean Square F Value Pr > F
CAR 3 5.25000000 1.75000000 0.88 0.4746
WHEEL 3 1.00000000 0.33333333 0.17 0.9173
RUBBER 3 194.50000000 64.83333333 32.42 0.0001
CAR*WHEEL*RUBBER 6 2.75000000 0.45833333 0.23 0.9610
Latin-Square designs, Y603 4
This is the analysis result based on Example 9b in the handout
General Linear Models Procedure
Class Level Information
Class Levels Values
REPEAT 2 1 2
CAR 4 1 2 3 4
WHEEL 4 1 2 3 4
RUBBER 4 1 2 3 4
Number of observations in data set = 32
Latin-Square designs, Y603 5
This is the analysis result based on Example 9b in the handout
General Linear Models Procedure
Dependent Variable: SCORE thickness of tread remaining after 10,00
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 19 228.75000000 12.03947368 21.40 0.0001
Error 12 6.75000000 0.56250000
Corrected Total 31 235.50000000
R-Square C.V. Root MSE SCORE Mean
0.971338 13.95349 0.7500000 5.3750000
Source DF Type I SS Mean Square F Value Pr > F
REPEAT 1 3.12500000 3.12500000 5.56 0.0362
CAR 3 5.25000000 1.75000000 3.11 0.0667
WHEEL 3 1.00000000 0.33333333 0.59 0.6317
RUBBER 3 194.50000000 64.83333333 115.26 0.0001
REPEAT*CAR 3 4.12500000 1.37500000 2.44 0.1144
REPEAT*WHEEL 3 1.37500000 0.45833333 0.81 0.5100
REPEAT*RUBBER 3 19.37500000 6.45833333 11.48 0.0008
Source DF Type III SS Mean Square F Value Pr > F
REPEAT 1 3.12500000 3.12500000 5.56 0.0362
CAR 3 5.25000000 1.75000000 3.11 0.0667
WHEEL 3 1.00000000 0.33333333 0.59 0.6317
RUBBER 3 194.50000000 64.83333333 115.26 0.0001
REPEAT*CAR 3 4.12500000 1.37500000 2.44 0.1144
REPEAT*WHEEL 3 1.37500000 0.45833333 0.81 0.5100
REPEAT*RUBBER 3 19.37500000 6.45833333 11.48 0.0008

Comments: peng@indiana.edu
Dr. Peng's Home Page: Dr.
Chao-Ying Joanne Peng
Copyright
1999, The Trustees of Indiana
University
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