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In this example the test of parallism was not significant, i.e., the profiles are parallel. The test of levels (groups differences) was significant, showing separation of the group profiles. The test of flatness was not significant, showing that there were no differences across the means of the three variables.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 /* test of parallelism */ mat 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 */ mat xm = (1,0,0,0,0) /* used to select the constant only */ manovatest, test(xm) ytans(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 0.7927 1 2.0 16.0 2.09 0.1559 e | P 0.2073 2.0 16.0 2.09 0.1559 e | L 0.2615 2.0 16.0 2.09 0.1559 e | R 0.2615 2.0 16.0 2.09 0.1559 e |-------------------------------------------------- Residual | 17 -------------------------------------------------------------- e = exact, a = approximate, u = upper bound on F
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