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13
TITLE '1-WAY ANCOVA, Ex 12, Y603';
OPTIONS LS=75 NODATE PAGENO=1;
DATA ANCOVA;
INPUT TREAT $ X Y;
LABEL TREAT='methods of teaching Y603'
X='motivation'
Y='dependent score';
CARDS;
1 1 1
1 2 1.5
1 4 2
1 3 1.8
2 4.5 2.6
2 2 2
2 3 2.3
2 4 2.5
3 3 4.8
3 2 4
3 4 5.3
3 5 6
;
PROC PRINT;
PROC REG;
MODEL y=x;
PLOT y*x;
BY treat;
TITLE2 'Regression of y on x';
RUN;
PROC GLM;
CLASS treat;
MODEL y=x treat/SOLUTION;
LSMEANS treat/E STDERR PDIFF;
TITLE2 'ANCOVA analysis through TYPE I SS';
RUN;
PROC GLM;
CLASS treat;
MODEL y=x treat x*treat;
TITLE2 'test of the equal slope assumption';
RUN;
PROC GLM;
CLASS treat;
MODEL y=treat;
TITLE2 'This is an CR-p analysis of the same data';
RUN;
1-WAY ANCOVA, Ex 12, Y603 1
OBS TREAT X Y
1 1 1.0 1.0
2 1 2.0 1.5
3 1 4.0 2.0
4 1 3.0 1.8
5 2 4.5 2.6
6 2 2.0 2.0
7 2 3.0 2.3
8 2 4.0 2.5
9 3 3.0 4.8
10 3 2.0 4.0
11 3 4.0 5.3
12 3 5.0 6.0
1-WAY ANCOVA, Ex 12, Y603 2
Regression of y on x
----------------------- methods of teaching Y603=1 ------------------------
Model: MODEL1
Dependent Variable: Y dependent score
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 1 0.54450 0.54450 47.348 0.0205
Error 2 0.02300 0.01150
C Total 3 0.56750
Root MSE 0.10724 R-square 0.9595
Dep Mean 1.57500 Adj R-sq 0.9392
C.V. 6.80877
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 0.750000 0.13133926 5.710 0.0293
X 1 0.330000 0.04795832 6.881 0.0205
Variable
Variable DF Label
INTERCEP 1 Intercept
X 1 motivation
1-WAY ANCOVA, Ex 12, Y603 3
Regression of y on x
----------------------- methods of teaching Y603=1 ------------------------
|---|----|----|----|----|----|----|----|----|----|----|----|----|----|
Y | |
| |
| |
| |
| |
| |
2.0 + 1 +
| |
| |
| |
| |
| |
1.8 + 1 +
d | |
e | |
p | |
e | |
n | |
d 1.6 + +
e | |
n | |
t | 1 |
| |
s | |
c 1.4 + +
o | |
r | |
e | |
| |
| |
1.2 + +
| |
| |
| |
| |
| |
1.0 + 1 +
| |
| |
| |
| |
| |
|---|----|----|----|----|----|----|----|----|----|----|----|----|----|
1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00
motivation X
1-WAY ANCOVA, Ex 12, Y603 4
Regression of y on x
----------------------- methods of teaching Y603=2 ------------------------
Model: MODEL1
Dependent Variable: Y dependent score
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 1 0.20763 0.20763 175.000 0.0057
Error 2 0.00237 0.00119
C Total 3 0.21000
Root MSE 0.03444 R-square 0.9887
Dep Mean 2.35000 Adj R-sq 0.9831
C.V. 1.46573
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 1.549153 0.06294049 24.613 0.0016
X 1 0.237288 0.01793730 13.229 0.0057
Variable
Variable DF Label
INTERCEP 1 Intercept
X 1 motivation
1-WAY ANCOVA, Ex 12, Y603 5
Regression of y on x
----------------------- methods of teaching Y603=2 ------------------------
|---|----|----|----|----|----|----|----|----|----|----|----|----|----|
Y | |
| |
| |
2.6 + 1 +
| |
| |
| |
| |
| |
2.5 + 1 +
| |
| |
| |
d | |
e | |
p 2.4 + +
e | |
n | |
d | |
e | |
n | |
t 2.3 + 1 +
| |
s | |
c | |
o | |
r | |
e 2.2 + +
| |
| |
| |
| |
| |
2.1 + +
| |
| |
| |
| |
| |
2.0 +1 +
| |
| |
|---|----|----|----|----|----|----|----|----|----|----|----|----|----|
2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6
motivation X
1-WAY ANCOVA, Ex 12, Y603 6
Regression of y on x
----------------------- methods of teaching Y603=3 ------------------------
Model: MODEL1
Dependent Variable: Y dependent score
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Prob>F
Model 1 2.11250 2.11250 281.667 0.0035
Error 2 0.01500 0.00750
C Total 3 2.12750
Root MSE 0.08660 R-square 0.9929
Dep Mean 5.02500 Adj R-sq 0.9894
C.V. 1.72343
Parameter Estimates
Parameter Standard T for H0:
Variable DF Estimate Error Parameter=0 Prob > |T|
INTERCEP 1 2.750000 0.14230249 19.325 0.0027
X 1 0.650000 0.03872983 16.783 0.0035
Variable
Variable DF Label
INTERCEP 1 Intercept
X 1 motivation
1-WAY ANCOVA, Ex 12, Y603 7
Regression of y on x
----------------------- methods of teaching Y603=3 ------------------------
|---|----|----|----|----|----|----|----|----|----|----|----|----|----|
Y | |
6.00 + 1 +
| |
| |
| |
| |
5.75 + +
| |
| |
| |
| |
5.50 + +
| |
d | |
e | |
p | 1 |
e 5.25 + +
n | |
d | |
e | |
n | |
t 5.00 + +
| |
s | |
c | |
o | 1 |
r 4.75 + +
e | |
| |
| |
| |
4.50 + +
| |
| |
| |
| |
4.25 + +
| |
| |
| |
| |
4.00 + 1 +
|---|----|----|----|----|----|----|----|----|----|----|----|----|----|
2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00
motivation X
1-WAY ANCOVA, Ex 12, Y603 8
ANCOVA analysis through TYPE I SS
General Linear Models Procedure
Class Level Information
Class Levels Values
TREAT 3 1 2 3
Number of observations in data set = 12
1-WAY ANCOVA, Ex 12, Y603 9
ANCOVA analysis through TYPE I SS
Dependent Variable: Y dependent score
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 3 28.6482420 9.5494140 163.09 0.0001
Error 8 0.4684247 0.0585531
Corrected Total 11 29.1166667
R-Square C.V. Root MSE Y Mean
0.983912 8.110976 0.24198 2.98333
Source DF Type I SS Mean Square F Value Pr > F
X 1 8.5587938 8.5587938 146.17 0.0001
TREAT 2 20.0894482 10.0447241 171.55 0.0001
Source DF Type III SS Mean Square F Value Pr > F
X 1 2.4365753 2.4365753 41.61 0.0002
TREAT 2 20.0894482 10.0447241 171.55 0.0001
T for H0: Pr > |T| Std Error of
Parameter Estimate Parameter=0 Estimate
INTERCEPT 3.548287671 B 13.70 0.0001 0.25892459
X 0.421917808 6.45 0.0002 0.06540528
TREAT 1 -3.028082192 B -16.53 0.0001 0.18317858
2 -2.622260274 B -15.31 0.0001 0.17129910
3 0.000000000 B . . .
NOTE: The X'X matrix has been found to be singular and a generalized
inverse was used to solve the normal equations. Estimates followed
by the letter 'B' are biased, and are not unique estimators of the
parameters.
1-WAY ANCOVA, Ex 12, Y603 10
ANCOVA analysis through TYPE I SS
Coefficients for TREAT Least Square Means
TREAT 1 2 3
Effect Coefficients
INTERCEPT 1 1 1
X 3.125 3.125 3.125
TREAT 1 1 0 0
2 0 1 0
3 0 0 1
1-WAY ANCOVA, Ex 12, Y603 11
ANCOVA analysis through TYPE I SS
TREAT Y Std Err Pr > |T| LSMEAN
LSMEAN LSMEAN H0:LSMEAN=0 Number
1 1.83869863 0.12770789 0.0001 1
2 2.24452055 0.12208864 0.0001 2
3 4.86678082 0.12344976 0.0001 3
Pr > |T| H0: LSMEAN(i)=LSMEAN(j)
i/j 1 2 3
1 . 0.0546 0.0001
2 0.0546 . 0.0001
3 0.0001 0.0001 .
NOTE: To ensure overall protection level, only probabilities associated
with pre-planned comparisons should be used.
1-WAY ANCOVA, Ex 12, Y603 12
test of the equal slope assumption
Class Levels Values
TREAT 3 1 2 3
Number of observations in data set = 12
1-WAY ANCOVA, Ex 12, Y603 13
test of the equal slope assumption
Dependent Variable: Y dependent score
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 5 29.0762938 5.8152588 864.23 0.0001
Error 6 0.0403729 0.0067288
Corrected Total 11 29.1166667
R-Square C.V. Root MSE Y Mean
0.998613 2.749587 0.08203 2.98333
Source DF Type I SS Mean Square F Value Pr > F
X 1 8.5587938 8.5587938 1271.96 0.0001
TREAT 2 20.0894482 10.0447241 1492.79 0.0001
X*TREAT 2 0.4280518 0.2140259 31.81 0.0006
Source DF Type III SS Mean Square F Value Pr > F
X 1 2.20771803 2.20771803 328.10 0.0001
TREAT 2 0.95405465 0.47702733 70.89 0.0001
X*TREAT 2 0.42805178 0.21402589 31.81 0.0006
1-WAY ANCOVA, Ex 12, Y603 14
This is an CR-p analysis of the same data
Class Levels Values
TREAT 3 1 2 3
Number of observations in data set = 12
1-WAY ANCOVA, Ex 12, Y603 15
This is an CR-p analysis of the same data
Dependent Variable: Y dependent score
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 2 26.2116667 13.1058333 40.60 0.0001
Error 9 2.9050000 0.3227778
Corrected Total 11 29.1166667
R-Square C.V. Root MSE Y Mean
0.900229 19.04364 0.56814 2.98333
Source DF Type I SS Mean Square F Value Pr > F
TREAT 2 26.2116667 13.1058333 40.60 0.0001
Source DF Type III SS Mean Square F Value Pr > F
TREAT 2 26.2116667 13.1058333 40.60 0.0001
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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