. * do-file for extra lecture 2, May 2018 . * note: interpretation of output after each command . version 15 /* works also with versions 13-14 */ . set more off . cd "r:\data" r:\data . . import delimited orthwide.csv, clear (7 vars, 27 obs) . manova dist08-dist14 = sex Number of obs = 27 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 -----------+------------------------------------------------------- sex |W 0.6023 1 4.0 22.0 3.63 0.0203 e |P 0.3977 4.0 22.0 3.63 0.0203 e |L 0.6603 4.0 22.0 3.63 0.0203 e |R 0.6603 4.0 22.0 3.63 0.0203 e |------------------------------------------------------- Residual | 25 -----------+------------------------------------------------------- Total | 26 ------------------------------------------------------------------- e = exact, a = approximate, u = upper bound on F . * test of equality between groups (no parallelism) . mvreg Equation Obs Parms RMSE "R-sq" F P -------------------------------------------------------------------------- dist08 27 2 2.327113 0.1213 3.450811 0.0750 dist10 27 2 2.045672 0.1354 3.914354 0.0590 dist12 27 2 2.540815 0.2181 6.972702 0.0141 dist14 27 2 2.232877 0.3737 14.91756 0.0007 ------------------------------------------------------------------------------ | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- dist08 | 1.sex | -1.693182 .9114713 -1.86 0.075 -3.570392 .1840285 _cons | 22.875 .5817782 39.32 0.000 21.67681 24.07319 -------------+---------------------------------------------------------------- dist10 | 1.sex | -1.585227 .8012379 -1.98 0.059 -3.235408 .0649531 _cons | 23.8125 .5114179 46.56 0.000 22.75922 24.86578 -------------+---------------------------------------------------------------- dist12 | 1.sex | -2.627841 .9951728 -2.64 0.014 -4.677438 -.5782441 _cons | 25.71875 .6352036 40.49 0.000 24.41052 27.02698 -------------+---------------------------------------------------------------- dist14 | 1.sex | -3.377841 .8745614 -3.86 0.001 -5.179034 -1.576648 _cons | 27.46875 .5582192 49.21 0.000 26.31908 28.61842 ------------------------------------------------------------------------------ . manova dist08-dist14 = ibn.sex, nocons Number of obs = 27 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 -----------+------------------------------------------------------- sex |W 0.0046 2 8.0 44.0 76.02 0.0000 e |P 1.1932 8.0 46.0 8.50 0.0000 a |L 175.2362 8.0 42.0 459.99 0.0000 a |R 174.9879 4.0 23.0 1006.18 0.0000 u |------------------------------------------------------- Residual | 25 -----------+------------------------------------------------------- Total | 27 ------------------------------------------------------------------- e = exact, a = approximate, u = upper bound on F . mvreg Equation Obs Parms RMSE "R-sq" F P -------------------------------------------------------------------------- dist08 27 2 2.327113 0.9899 1228.67 0.0000 dist10 27 2 2.045672 0.9928 1733.324 0.0000 dist12 27 2 2.540815 0.9903 1273.933 0.0000 dist14 27 2 2.232877 0.9933 1850.94 0.0000 ------------------------------------------------------------------------------ | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- dist08 | sex | 0 | 22.875 .5817782 39.32 0.000 21.67681 24.07319 1 | 21.18182 .7016509 30.19 0.000 19.73674 22.6269 -------------+---------------------------------------------------------------- dist10 | sex | 0 | 23.8125 .5114179 46.56 0.000 22.75922 24.86578 1 | 22.22727 .6167932 36.04 0.000 20.95696 23.49758 -------------+---------------------------------------------------------------- dist12 | sex | 0 | 25.71875 .6352036 40.49 0.000 24.41052 27.02698 1 | 23.09091 .7660844 30.14 0.000 21.51313 24.66869 -------------+---------------------------------------------------------------- dist14 | sex | 0 | 27.46875 .5582192 49.21 0.000 26.31908 28.61842 1 | 24.09091 .6732377 35.78 0.000 22.70435 25.47747 ------------------------------------------------------------------------------ . * means . matrix define error=e(E) . matrix cov=error/25 . matrix list cov symmetric cov[4,4] dist08 dist10 dist12 dist14 dist08 5.4154545 dist10 2.7168182 4.1847727 dist12 3.9102273 2.9271591 6.4557386 dist14 2.7102273 3.3171591 4.1307386 4.9857386 . * covariance matrix . . manova dist08-dist14 = sex Number of obs = 27 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 -----------+------------------------------------------------------- sex |W 0.6023 1 4.0 22.0 3.63 0.0203 e |P 0.3977 4.0 22.0 3.63 0.0203 e |L 0.6603 4.0 22.0 3.63 0.0203 e |R 0.6603 4.0 22.0 3.63 0.0203 e |------------------------------------------------------- Residual | 25 -----------+------------------------------------------------------- Total | 26 ------------------------------------------------------------------- e = exact, a = approximate, u = upper bound on F . mat timediff=(1,-1,0,0\1,0,-1,0\1,0,0,-1) . manovatest sex, ytransf(timediff) Transformations of the dependent variables (1) dist08 - dist10 (2) dist08 - dist12 (3) dist08 - dist14 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 -----------+------------------------------------------------------- sex |W 0.7399 1 3.0 23.0 2.70 0.0696 e |P 0.2601 3.0 23.0 2.70 0.0696 e |L 0.3516 3.0 23.0 2.70 0.0696 e |R 0.3516 3.0 23.0 2.70 0.0696 e |------------------------------------------------------- Residual | 25 ------------------------------------------------------------------- e = exact, a = approximate, u = upper bound on F . * test of parallelism . mat boygirl=(1,0,1\0,1,1) . manovatest , test(boygirl) ytransf(timediff) Transformations of the dependent variables (1) dist08 - dist10 (2) dist08 - dist12 (3) dist08 - dist14 Test constraints (1) 0.sex + _cons = 0 (2) 1.sex + _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 0.1606 2 6.0 46.0 11.46 0.0000 e |P 0.8622 6.0 48.0 6.06 0.0001 a |L 5.0844 6.0 44.0 18.64 0.0000 a |R 5.0563 3.0 24.0 40.45 0.0000 u |------------------------------------------------------- Residual | 25 ------------------------------------------------------------------- e = exact, a = approximate, u = upper bound on F . * test of no time differences . mat boy=(1,0,1) . mat girl=(0,1,1) . manovatest , test(boy) ytransf(timediff) Transformations of the dependent variables (1) dist08 - dist10 (2) dist08 - dist12 (3) dist08 - dist14 Test constraint (1) 0.sex + _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 0.1938 1 3.0 23.0 31.89 0.0000 e |P 0.8062 3.0 23.0 31.89 0.0000 e |L 4.1602 3.0 23.0 31.89 0.0000 e |R 4.1602 3.0 23.0 31.89 0.0000 e |------------------------------------------------------- Residual | 25 ------------------------------------------------------------------- e = exact, a = approximate, u = upper bound on F . manovatest , test(girl) ytransf(timediff) Transformations of the dependent variables (1) dist08 - dist10 (2) dist08 - dist12 (3) dist08 - dist14 Test constraint (1) 1.sex + _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 0.5197 1 3.0 23.0 7.09 0.0015 e |P 0.4803 3.0 23.0 7.09 0.0015 e |L 0.9242 3.0 23.0 7.09 0.0015 e |R 0.9242 3.0 23.0 7.09 0.0015 e |------------------------------------------------------- Residual | 25 ------------------------------------------------------------------- e = exact, a = approximate, u = upper bound on F . * separate tests of no time differences for boys and girls . lincom [dist08]0.sex-[dist08]1.sex+[dist10]0.sex-[dist10]1.sex+[dist12]0.sex-[dist12]1.sex+[dist14]0.sex > -[dist14]1.sex ( 1) [dist08]0b.sex - [dist08]1.sex + [dist10]0b.sex - [dist10]1.sex + [dist12]0b.sex - [dist12]1.sex + [dist14]0b.sex - [dist14]1.sex = 0 ------------------------------------------------------------------------------ | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- (1) | 9.284091 3.045667 3.05 0.005 3.011421 15.55676 ------------------------------------------------------------------------------ . * no group differences, assuming parallelism . mat boyvgirl=(0,1,0) . manovatest , test(boyvgirl) ytransf(timediff) Transformations of the dependent variables (1) dist08 - dist10 (2) dist08 - dist12 (3) dist08 - dist14 Test constraint (1) 1.sex = 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 0.7399 1 3.0 23.0 2.70 0.0696 e |P 0.2601 3.0 23.0 2.70 0.0696 e |L 0.3516 3.0 23.0 2.70 0.0696 e |R 0.3516 3.0 23.0 2.70 0.0696 e |------------------------------------------------------- Residual | 25 ------------------------------------------------------------------- e = exact, a = approximate, u = upper bound on F . * test of parallism (same as in manova command . tab sex sex | Freq. Percent Cum. ------------+----------------------------------- 0 | 16 59.26 59.26 1 | 11 40.74 100.00 ------------+----------------------------------- Total | 27 100.00 . manova dist08-dist14 = ibn.sex, nocons Number of obs = 27 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 -----------+------------------------------------------------------- sex |W 0.0046 2 8.0 44.0 76.02 0.0000 e |P 1.1932 8.0 46.0 8.50 0.0000 a |L 175.2362 8.0 42.0 459.99 0.0000 a |R 174.9879 4.0 23.0 1006.18 0.0000 u |------------------------------------------------------- Residual | 25 -----------+------------------------------------------------------- Total | 27 ------------------------------------------------------------------- e = exact, a = approximate, u = upper bound on F . mvreg Equation Obs Parms RMSE "R-sq" F P -------------------------------------------------------------------------- dist08 27 2 2.327113 0.9899 1228.67 0.0000 dist10 27 2 2.045672 0.9928 1733.324 0.0000 dist12 27 2 2.540815 0.9903 1273.933 0.0000 dist14 27 2 2.232877 0.9933 1850.94 0.0000 ------------------------------------------------------------------------------ | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- dist08 | sex | 0 | 22.875 .5817782 39.32 0.000 21.67681 24.07319 1 | 21.18182 .7016509 30.19 0.000 19.73674 22.6269 -------------+---------------------------------------------------------------- dist10 | sex | 0 | 23.8125 .5114179 46.56 0.000 22.75922 24.86578 1 | 22.22727 .6167932 36.04 0.000 20.95696 23.49758 -------------+---------------------------------------------------------------- dist12 | sex | 0 | 25.71875 .6352036 40.49 0.000 24.41052 27.02698 1 | 23.09091 .7660844 30.14 0.000 21.51313 24.66869 -------------+---------------------------------------------------------------- dist14 | sex | 0 | 27.46875 .5582192 49.21 0.000 26.31908 28.61842 1 | 24.09091 .6732377 35.78 0.000 22.70435 25.47747 ------------------------------------------------------------------------------ . mat paraltime=(.5926,.4074,-.5926,-.4074,0,0,0,0\.5926,.4074,0,0,-.5926,-.4074,0,0\.5926,.4074,0,0,0,0,- > .5926,-.4074) . test ,test(paraltime) ( 1) .5926*[dist08]0bn.sex + .4074*[dist08]1.sex - .5926*[dist10]0bn.sex - .4074*[dist10]1.sex = 0 ( 2) .5926*[dist08]0bn.sex + .4074*[dist08]1.sex - .5926*[dist12]0bn.sex - .4074*[dist12]1.sex = 0 ( 3) .5926*[dist08]0bn.sex + .4074*[dist08]1.sex - .5926*[dist14]0bn.sex - .4074*[dist14]1.sex = 0 F( 3, 25) = 39.44 Prob > F = 0.0000 . * test for no time differences, assuming parallism . * not quite the same as in lecture .