|
|
|
||||
|
|
|||||
We need to create a variable to use as a constant and then run the manova with the noconstant option.input s y1 y2 y3 y4 1 3 4 4 3 2 2 4 4 5 3 2 3 3 6 4 3 3 3 5 5 1 2 4 7 6 3 3 6 6 7 4 4 5 10 8 6 5 5 8 end
generate con = 1
manova y1 y2 y3 y4 = con, noconstant
Number of obs = 8
W = Wilks' lambda L = Lawley-Hotelling trace
P = Pillai's trace R = Roy's largest root
Source | Statistic df F(df1, df2) = F Prob>F
-----------+--------------------------------------------------
con | W 0.0196 1 4.0 4.0 49.92 0.0011 e
| P 0.9804 4.0 4.0 49.92 0.0011 e
| L 49.9217 4.0 4.0 49.92 0.0011 e
| R 49.9217 4.0 4.0 49.92 0.0011 e
|--------------------------------------------------
Residual | 7
-----------+--------------------------------------------------
Total | 8
--------------------------------------------------------------
e = exact, a = approximate, u = upper bound on F
Next, we need to create contrasts among the dependent variables.
If there are k dependent variables than we will create k-1 contrasts. These contrasts are created
in a manner simmilar to that which is done with categorical predictors. We will create the
contrasts using an effect coding.
mat ycomp = (1,0,0,-1\0,1,0,-1\0,0,1,-1)
mat list ycomp
ycomp[3,4]
c1 c2 c3 c4
r1 1 0 0 -1
r2 0 1 0 -1
r3 0 0 1 -1
manovatest con, ytrans(ycomp)
Transformations of the dependent variables
(1) y1 - y4
(2) y2 - y4
(3) y3 - y4
W = Wilks' lambda L = Lawley-Hotelling trace
P = Pillai's trace R = Roy's largest root
Source | Statistic df F(df1, df2) = F Prob>F
-----------+--------------------------------------------------
con | W 0.2458 1 3.0 5.0 5.11 0.0554 e
| P 0.7542 3.0 5.0 5.11 0.0554 e
| L 3.0682 3.0 5.0 5.11 0.0554 e
| R 3.0682 3.0 5.0 5.11 0.0554 e
|--------------------------------------------------
Residual | 7
---------------------------------------------------------
The F-test of 5.11 is the multivariate test of the
within-subjects treatment. The result is not significant
at the .05 level.The first manova is a test of the between-subjects factor.input s a y1 y2 y3 y4 1 1 3 4 7 7 2 1 6 5 8 8 3 1 3 4 7 9 4 1 3 3 6 8 5 2 1 2 5 10 6 2 2 3 6 10 7 2 2 4 5 9 8 2 2 3 6 11 end
manova y1 y2 y3 y4 = a
Number of obs = 8
W = Wilks' lambda L = Lawley-Hotelling trace
P = Pillai's trace R = Roy's largest root
Source | Statistic df F(df1, df2) = F Prob>F
-----------+--------------------------------------------------
a | W 0.1374 1 4.0 3.0 4.71 0.1169 e
| P 0.8626 4.0 3.0 4.71 0.1169 e
| L 6.2764 4.0 3.0 4.71 0.1169 e
| R 6.2764 4.0 3.0 4.71 0.1169 e
|--------------------------------------------------
Residual | 6
-----------+--------------------------------------------------
Total | 7
--------------------------------------------------------------
e = exact, a = approximate, u = upper bound on
The between-subjects factor is not significant. Next, we code the
contrasts among the
dependent variables and test for the a*y interaction (between-subject*within-subjects)
interaction.
mat ymat = (1,0,0,-1\0,1,0,-1\0,0,1,-1)
mat list ymat
ymat[3,4]
c1 c2 c3 c4
r1 1 0 0 -1
r2 0 1 0 -1
r3 0 0 1 -1
/* test of the a*y interaction */
manovatest a, ytransform(ymat)
Transformations of the dependent variables
(1) y1 - y4
(2) y2 - y4
(3) y3 - y4
W = Wilks' lambda L = Lawley-Hotelling trace
P = Pillai's trace R = Roy's largest root
Source | Statistic df F(df1, df2) = F Prob>F
-----------+--------------------------------------------------
a | W 0.1443 1 3.0 4.0 7.91 0.0371 e
| P 0.8557 3.0 4.0 7.91 0.0371 e
| L 5.9296 3.0 4.0 7.91 0.0371 e
| R 5.9296 3.0 4.0 7.91 0.0371 e
|--------------------------------------------------
Residual | 6
--------------------------------------------------------------
e = exact, a = approximate, u = upper bound on F
Even though the interaction is significant, we will go ahead
and test the effect
of the within-subjects variable. To do this we will create a contrast for the
predictor variables, such that, the levels of each variable sums to one.
/* test of y */
mat xmat = (1, .5, .5)
mat list xmat
xmat[1,3]
c1 c2 c3
r1 1 .5 .5
manovatest, test(xmat) ytransform(ymat)
Transformations of the dependent variables
(1) y1 - y4
(2) y2 - y4
(3) y3 - y4
Test constraint
(1) _cons + .5 a[1] + .5 a[2] = 0
W = Wilks' lambda L = Lawley-Hotelling trace
P = Pillai's trace R = Roy's largest root
Source | Statistic df F(df1, df2) = F Prob>F
-----------+--------------------------------------------------
manovatest | W 0.0275 1 3.0 4.0 47.19 0.0014 e
| P 0.9725 3.0 4.0 47.19 0.0014 e
| L 35.3944 3.0 4.0 47.19 0.0014 e
| R 35.3944 3.0 4.0 47.19 0.0014 e
|--------------------------------------------------
Residual | 6
-------------------------------------------------------------
The test of the within-subjects factor is also significant,
although care must be
taken in interpreting this result due to the significant interaction effect.
UCLA Researchers are invited to our Statistical Consulting Services
We recommend others to our list of Other Resources for Statistical Computing Help
These pages are Copyrighted (c) by UCLA Academic Technology Services