MANOVA CRF-32 Example
Same data as Assignment 8
data crf32;
input a b y1 y2;
cards;
1 1 10 21
1 1 12 22
1 1 9 19
1 1 10 21
1 1 14 23
1 2 9 14
1 2 8 15
1 2 11 16
1 2 9 17
1 2 9 17
2 1 11 23
2 1 14 27
2 1 13 24
2 1 15 26
2 1 14 24
2 2 11 15
2 2 12 18
2 2 10 16
2 2 9 17
2 2 9 18
3 1 8 17
3 1 7 15
3 1 10 18
3 1 8 17
3 1 7 19
3 2 9 22
3 2 8 18
3 2 10 17
3 2 9 19
3 2 8 19
;
proc glm; classes a b;
model y1 y2 = a b a*b;
manova h=a b a*b m=(1 -1);
run;
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General Linear Models Procedure
Class Level Information
Class Levels Values
A 3 1 2 3
B 2 1 2
Number of observations in data set = 30
Dependent Variable: Y1
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 5 93.1000000 18.6200000 9.80 0.0001
Error 24 45.6000000 1.9000000
Corrected Total 29 138.7000000
R-Square C.V. Root MSE Y1 Mean
0.671233 13.64757 1.37840 10.1000
Dependent Variable: Y1
Source DF Type I SS Mean Square F Value Pr > F
A 2 57.8000000 28.9000000 15.21 0.0001
B 1 14.7000000 14.7000000 7.74 0.0104
A*B 2 20.6000000 10.3000000 5.42 0.0114
Source DF Type III SS Mean Square F Value Pr > F
A 2 57.8000000 28.9000000 15.21 0.0001
B 1 14.7000000 14.7000000 7.74 0.0104
A*B 2 20.6000000 10.3000000 5.42 0.0114
Dependent Variable: Y2
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 5 283.466667 56.693333 24.30 0.0001
Error 24 56.000000 2.333333
Corrected Total 29 339.466667
R-Square C.V. Root MSE Y2 Mean
0.835035 7.983581 1.52753 19.1333
Dependent Variable: Y2
Source DF Type I SS Mean Square F Value Pr > F
A 2 42.466667 21.233333 9.10 0.0011
B 1 112.133333 112.133333 48.06 0.0001
A*B 2 128.866667 64.433333 27.61 0.0001
Source DF Type III SS Mean Square F Value Pr > F
A 2 42.466667 21.233333 9.10 0.0011
B 1 112.133333 112.133333 48.06 0.0001
A*B 2 128.866667 64.433333 27.61 0.0001
General Linear Models Procedure
Multivariate Analysis of Variance
M Matrix Describing Transformed Variables
Y1 Y2
MVAR1 1 -1
Characteristic Roots and Vectors of: E Inverse * H, where
H = Type III SS&CP Matrix for A E = Error SS&CP Matrix
Variables have been transformed by the M Matrix
Characteristic Percent Characteristic Vector V'EV=1
Root
MVAR1
0.13655914 100.00 0.12700013
Manova Test Criteria and Exact F Statistics for
the Hypothesis of no Overall A Effect
on the variables defined by the M Matrix Transformation
H = Type III SS&CP Matrix for A E = Error SS&CP Matrix
S=1 M=0 N=11
Statistic Value F Num DF Den DF Pr > F
Wilks' Lambda 0.87984863 1.6387 2 24 0.2152
Pillai's Trace 0.12015137 1.6387 2 24 0.2152
Hotelling-Lawley Trace 0.13655914 1.6387 2 24 0.2152
Roy's Greatest Root 0.13655914 1.6387 2 24 0.2152
Characteristic Roots and Vectors of: E Inverse * H, where
H = Type III SS&CP Matrix for B E = Error SS&CP Matrix
Variables have been transformed by the M Matrix
Characteristic Percent Characteristic Vector V'EV=1
Root
MVAR1
0.73602151 100.00 0.12700013
Manova Test Criteria and Exact F Statistics for
the Hypothesis of no Overall B Effect
on the variables defined by the M Matrix Transformation
H = Type III SS&CP Matrix for B E = Error SS&CP Matrix
S=1 M=-0.5 N=11
Statistic Value F Num DF Den DF Pr > F
Wilks' Lambda 0.57602973 17.6645 1 24 0.0003
Pillai's Trace 0.42397027 17.6645 1 24 0.0003
Hotelling-Lawley Trace 0.73602151 17.6645 1 24 0.0003
Roy's Greatest Root 0.73602151 17.6645 1 24 0.0003
Characteristic Roots and Vectors of: E Inverse * H, where
H = Type III SS&CP Matrix for A*B E = Error SS&CP Matrix
Variables have been transformed by the M Matrix
Characteristic Percent Characteristic Vector V'EV=1
Root
MVAR1
0.75591398 100.00 0.12700013
Manova Test Criteria and Exact F Statistics for
the Hypothesis of no Overall A*B Effect
on the variables defined by the M Matrix Transformation
H = Type III SS&CP Matrix for A*B E = Error SS&CP Matrix
S=1 M=0 N=11
Statistic Value F Num DF Den DF Pr > F
Wilks' Lambda 0.56950398 9.0710 2 24 0.0012
Pillai's Trace 0.43049602 9.0710 2 24 0.0012
Hotelling-Lawley Trace 0.75591398 9.0710 2 24 0.0012
Roy's Greatest Root 0.75591398 9.0710 2 24 0.0012