/*These data are the same as Assignment #4*/
data oneway;
input group y1 y2 y3;
cards;
1 19.6 5.15 9.5
1 15.4 5.75 9.1
1 22.3 4.35 3.3
1 24.3 7.55 5.0
1 22.5 8.50 6.0
1 20.5 10.25 5.0
1 14.1 5.95 18.8
1 13.0 6.30 16.5
1 14.1 5.45 8.9
1 16.7 3.75 6.0
1 16.8 5.10 7.4
2 17.1 9.00 7.5
2 15.7 5.30 8.5
2 14.9 9.85 6.0
2 19.7 3.60 2.9
2 17.2 4.05 0.2
2 16.0 4.40 2.6
2 12.8 7.15 7.0
2 13.6 7.25 3.2
2 14.2 5.30 6.2
2 13.1 3.10 5.5
2 16.5 2.40 6.6
3 16.0 4.55 2.9
3 12.5 2.65 0.7
3 18.5 6.50 5.3
3 19.2 4.85 8.3
3 12.0 8.75 9.0
3 13.0 5.20 10.3
3 11.9 4.75 8.5
3 12.0 5.85 9.5
3 19.8 2.85 2.3
3 16.5 6.55 3.3
3 17.4 6.60 1.9
;
proc glm; class group;
model y1 y2 y3 = group;
manova h = group;
contrast '1vs2' group 1 -1 0;
contrast '1vs3' group 1 0 -1;
contrast '2vs3' group 0 1 -1;
run;
---------------------------------------------------------------------------------
The SAS System
General Linear Models Procedure
Class Level Information
Class Levels Values
GROUP 3 1 2 3
Number of observations in data set = 33
Dependent Variable: Y1
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 2 52.9242424 26.4621212 2.70 0.0835
Error 30 293.9654545 9.7988485
Corrected Total 32 346.8896970
R-Square C.V. Root MSE Y1 Mean
0.152568 19.16873 3.13031 16.3303
Dependent Variable: Y1
Source DF Type I SS Mean Square F Value Pr > F
GROUP 2 52.9242424 26.4621212 2.70 0.0835
Source DF Type III SS Mean Square F Value Pr > F
GROUP 2 52.9242424 26.4621212 2.70 0.0835
---------------------------------------------------------------------------------
Dependent Variable: Y2
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 2 3.97515152 1.98757576 0.47 0.6282
Error 30 126.28727273 4.20957576
Corrected Total 32 130.26242424
R-Square C.V. Root MSE Y2 Mean
0.030516 35.89975 2.05173 5.71515
Dependent Variable: Y2
Source DF Type I SS Mean Square F Value Pr > F
GROUP 2 3.97515152 1.98757576 0.47 0.6282
Source DF Type III SS Mean Square F Value Pr > F
GROUP 2 3.97515152 1.98757576 0.47 0.6282
---------------------------------------------------------------------------------
Dependent Variable: Y3
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 2 81.8296970 40.9148485 2.88 0.0718
Error 30 426.3709091 14.2123636
Corrected Total 32 508.2006061
R-Square C.V. Root MSE Y3 Mean
0.161018 58.21603 3.76993 6.47576
Dependent Variable: Y3
Source DF Type I SS Mean Square F Value Pr > F
GROUP 2 81.8296970 40.9148485 2.88 0.0718
Source DF Type III SS Mean Square F Value Pr > F
GROUP 2 81.8296970 40.9148485 2.88 0.0718
---------------------------------------------------------------------------------
General Linear Models Procedure
Multivariate Analysis of Variance
Characteristic Roots and Vectors of: E Inverse * H, where
H = Type III SS&CP Matrix for GROUP E = Error SS&CP Matrix
Characteristic Percent Characteristic Vector V'EV=1
Root
Y1 Y2 Y3
0.89198797 99.42 0.06410227 -0.00186162 0.05375070
0.00524207 0.58 0.01442654 0.06888879 -0.02620577
0.00000000 0.00 -0.03149580 0.05943386 0.01270798
---------------------------------------------------------------------------------
General Linear Models Procedure
Multivariate Analysis of Variance
Manova Test Criteria and F Approximations for
the Hypothesis of no Overall GROUP Effect
H = Type III SS&CP Matrix for GROUP E = Error SS&CP Matrix
S=2 M=0 N=13
Statistic Value F Num DF Den DF Pr > F
Wilks' Lambda 0.52578837 3.5382 6 56 0.0049
Pillai's Trace 0.47667015 3.0248 6 58 0.0122
Hotelling-Lawley Trace 0.89723004 4.0375 6 54 0.0021
Roy's Greatest Root 0.89198797 8.6226 3 29 0.0003
NOTE: F Statistic for Roy's Greatest Root is an upper bound.
NOTE: F Statistic for Wilks' Lambda is exact.
---------------------------------------------------------------------------------
General Linear Models Procedure
Dependent Variable: Y1
Contrast DF Contrast SS Mean Square F Value Pr > F
1vs2 1 36.9204545 36.9204545 3.77 0.0617
1vs3 1 42.2840909 42.2840909 4.32 0.0464
2vs3 1 0.1818182 0.1818182 0.02 0.8926
Dependent Variable: Y2
Contrast DF Contrast SS Mean Square F Value Pr > F
1vs2 1 2.04045455 2.04045455 0.48 0.4917
1vs3 1 3.68181818 3.68181818 0.87 0.3571
2vs3 1 0.24045455 0.24045455 0.06 0.8127
Dependent Variable: Y3
Contrast DF Contrast SS Mean Square F Value Pr > F
1vs2 1 70.2040909 70.2040909 4.94 0.0339
1vs3 1 51.0113636 51.0113636 3.59 0.0678
2vs3 1 1.5290909 1.5290909 0.11 0.7452
Group Centroids
Group 1 -> [18.12 6.19 8.68]
Group 2 -> [15.53 5.58 5.11]
Group 3 -> [15.35 5.37 5.64]
View plot of group centroids