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Please note that in Stata 11 the _cons is the last element in the design matrix. Stata 10 has the _cons as the first element. This will make a difference in xm matrix below.input id y1 y2 y3 grp 1 19 20 18 1 2 20 21 19 1 3 19 22 22 1 4 18 19 21 1 5 16 18 20 1 6 17 22 19 1 7 20 19 20 1 8 15 19 19 1 9 12 14 12 2 10 15 15 17 2 11 15 17 15 2 12 13 14 14 2 13 14 16 13 2 14 15 14 17 3 15 13 14 15 3 16 12 15 15 3 17 12 13 13 3 18 8 9 10 4 19 10 10 12 4 20 11 10 10 4 21 11 7 12 4 end tabstat y1 y2 y3, by(grp) Summary statistics: mean by categories of: grp grp | y1 y2 y3 ---------+------------------------------ 1 | 18 20 19.75 2 | 13.8 15.2 14.2 3 | 13 14 15 4 | 10 9 11 ---------+------------------------------ Total | 14.52381 15.61905 15.85714 ---------------------------------------- /* preliminary one-way manova */ manova y1 y2 y3 = grp Number of obs = 21 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 -----------+-------------------------------------------------- grp | W 0.0479 3 9.0 36.7 10.12 0.0000 a | P 1.1609 9.0 51.0 3.58 0.0016 a | L 15.6417 9.0 41.0 23.75 0.0000 a | R 15.3753 3.0 17.0 87.13 0.0000 u |-------------------------------------------------- Residual | 17 -----------+-------------------------------------------------- Total | 20 -------------------------------------------------------------- e = exact, a = approximate, u = upper bound on F manovatest, showorder Order of columns in the design matrix 1: (grp==1) 2: (grp==2) 3: (grp==3) 4: (grp==4) 5: _cons
/* test of parallelism */
matrix c1 = (1,-1,0\0,1,-1)
manovatest grp, ytrans(c1)
Transformations of the dependent variables
(1) y1 - y2
(2) y2 - y3
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
-----------+--------------------------------------------------
grp | W 0.5633 3 6.0 32.0 1.77 0.1364 e
| P 0.4873 6.0 34.0 1.83 0.1234 a
| L 0.6853 6.0 30.0 1.71 0.1522 a
| R 0.5088 3.0 17.0 2.88 0.0662 u
|--------------------------------------------------
Residual | 17
--------------------------------------------------------------
e = exact, a = approximate, u = upper bound on F
/* test of levels (group differencs) */
mat c2 = (1,1,1)
manovatest grp, ytrans(c2)
Transformation of the dependent variables
(1) y1 + y2 + y3
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
-----------+--------------------------------------------------
grp | W 0.0740 3 3.0 17.0 70.93 0.0000 e
| P 0.9260 3.0 17.0 70.93 0.0000 e
| L 12.5165 3.0 17.0 70.93 0.0000 e
| R 12.5165 3.0 17.0 70.93 0.0000 e
|--------------------------------------------------
Residual | 17
--------------------------------------------------------------
e = exact, a = approximate, u = upper bound on
/* test of flatness */
matrix xm = (0,0,0,0,1)
/* the xm matrix used to select the constant */
/* Stata 11: matrix xm = (0,0,0,0,1) */
/* Stata 10: matrix xm = (1,0,0,0,0) */
manovatest, test(xm) ytrans(c1)
Transformations of the dependent variables
(1) y1 - y2
(2) y2 - y3
Test constraint
(1) _cons = 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 0.5365 1 2.0 16.0 6.91 0.0069 e
| P 0.4635 2.0 16.0 6.91 0.0069 e
| L 0.8639 2.0 16.0 6.91 0.0069 e
| R 0.8639 2.0 16.0 6.91 0.0069 e
|--------------------------------------------------
Residual | 17
--------------------------------------------------------------
e = exact, a = approximate, u = upper bound on FUCLA Researchers are invited to our Statistical Consulting Services
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