MTB > read 'smsg.dat' c1-c4 43 ROWS READ ROW C1 C2 C3 C4 1 1 2.750 1 1.625 2 1 7.400 1 3.950 3 1 4.280 1 4.200 4 1 5.875 1 4.417 . . . MTB > describe c2 c4; SUBC> by c3. C3 N MEAN MEDIAN TRMEAN STDEV SEMEAN C2 0 22 17.79 18.29 17.94 5.02 1.07 1 21 11.95 10.70 11.68 6.03 1.32 C4 0 22 7.708 7.220 7.704 2.968 0.633 1 21 7.004 6.071 6.854 3.288 0.717 C3 MIN MAX Q1 Q3 C2 0 7.00 25.70 13.88 22.51 1 2.75 26.18 8.81 12.66 C4 0 3.462 12.050 5.371 11.031 1 1.625 15.227 4.993 7.766 MTB > copy c2 c4 into c10 c11; SUBC> use c3=1. MTB > copy c2 c4 into c20 c21; SUBC> use c3=0. MTB > mplot c10 versus c11, c20 vs c21 - A - B A - 2 - B B B 21.0+ B A - B B B - B B A B - B - B B 14.0+ B B - B A 2 - B AAA A A - A A A - B A A 7.0+ B A - A - A - A - ----+---------+---------+---------+---------+---------+-- 2.5 5.0 7.5 10.0 12.5 15.0 A = C10 vs. C11 B = C20 vs. C21 MTB > let c5 = c3*c4 MTB > print c5 C5 1.625 3.950 4.200 4.417 4.607 5.379 5.444 5.538 5.800 6.000 6.071 6.517 6.788 7.222 7.529 7.533 8.000 9.538 11.647 14.048 15.227 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 MTB > regress c2 3 c3 c4 c5 The regression equation is C2 = 7.68 - 7.81 C3 + 1.31 C4 + 0.412 C5 Predictor Coef Stdev t-ratio Constant 7.682 1.668 4.61 C3 -7.806 2.206 -3.54 C4 1.3118 0.2025 6.48 C5 0.4118 0.2759 1.49 s = 2.755 R-sq = 81.8% R-sq(adj) = 80.4% Analysis of Variance SOURCE DF SS MS Regression 3 1327.88 442.63 Error 39 295.96 7.59 Total 42 1623.84 SOURCE DF SEQ SS C3 1 367.18 C4 1 943.79 C5 1 16.91 Unusual Observations Obs. C3 C2 Fit Stdev.Fit Residual St.Resid 19 1.00 26.176 19.950 1.057 6.226 2.45R 21 1.00 25.091 26.121 1.654 -1.030 -0.47 X 22 0.00 7.000 12.223 1.041 -5.223 -2.05R 32 0.00 22.500 16.787 0.608 5.713 2.13R 41 0.00 15.855 22.666 0.954 -6.811 -2.64R R denotes an obs. with a large st. resid. X denotes an obs. whose X value gives it large influence. MTB > regress c2 2 c3 c4 The regression equation is C2 = 5.97 - 4.77 C3 + 1.53 C4 Predictor Coef Stdev t-ratio Constant 5.971 1.230 4.85 C3 -4.7655 0.8589 -5.55 C4 1.5337 0.1396 10.98 s = 2.797 R-sq = 80.7% R-sq(adj) = 79.8% Analysis of Variance SOURCE DF SS MS Regression 2 1310.98 655.49 Error 40 312.86 7.82 Total 42 1623.84 SOURCE DF SEQ SS C3 1 367.18 C4 1 943.79 Unusual Observations Obs. C3 C2 Fit Stdev.Fit Residual St.Resid 19 1.00 26.176 19.069 0.890 7.107 2.68R 21 1.00 25.091 24.559 1.300 0.532 0.21 X 32 0.00 22.500 16.617 0.606 5.883 2.15R 41 0.00 15.855 23.491 0.790 -7.636 -2.85R R denotes an obs. with a large st. resid. X denotes an obs. whose X value gives it large influence. MTB > regress c2 1 c4 The regression equation is C2 = 2.99 + 1.62 C4 Predictor Coef Stdev t-ratio Constant 2.991 1.454 2.06 C4 1.6224 0.1822 8.90 s = 3.675 R-sq = 65.9% R-sq(adj) = 65.1% Analysis of Variance SOURCE DF SS MS Regression 1 1070.2 1070.2 Error 41 553.7 13.5 Total 42 1623.8 Unusual Observations Obs. C4 C2 Fit Stdev.Fit Residual St.Resid 21 15.2 25.091 27.695 1.539 -2.604 -0.78 X 26 5.4 19.120 11.687 0.669 7.433 2.06R 32 6.9 22.500 14.252 0.566 8.248 2.27R **************WITHIN-GROUP REGRESSIONS*************** MTB > regress c10 1 c11 The regression equation is C10 = - 0.12 + 1.72 C11 Predictor Coef Stdev t-ratio Constant -0.124 1.115 -0.11 C11 1.7236 0.1447 11.91 s = 2.128 R-sq = 88.2% R-sq(adj) = 87.6% Analysis of Variance SOURCE DF SS MS Regression 1 642.30 642.30 Error 19 86.06 4.53 Total 20 728.37 Unusual Observations Obs. C11 C10 Fit Stdev.Fit Residual St.Resid 19 11.6 26.176 19.950 0.817 6.226 3.17R 21 15.2 25.091 26.121 1.278 -1.030 -0.61 X R denotes an obs. with a large st. resid. X denotes an obs. whose X value gives it large influence. MTB > regress c20 1 c21 The regression equation is C20 = 7.68 + 1.31 C21 Predictor Coef Stdev t-ratio Constant 7.682 1.961 3.92 C21 1.3118 0.2382 5.51 s = 3.240 R-sq = 60.3% R-sq(adj) = 58.3% Analysis of Variance SOURCE DF SS MS Regression 1 318.40 318.40 Error 20 209.90 10.49 Total 21 528.29 Unusual Observations Obs. C21 C20 Fit Stdev.Fit Residual St.Resid 20 11.4 15.855 22.666 1.122 -6.811 -2.24R R denotes an obs. with a large st. resid. MTB > twot 95 c2, c3 TWOSAMPLE T FOR C2 C3 N MEAN STDEV SE MEAN 1 21 11.95 6.03 1.3 0 22 17.79 5.02 1.1 95 PCT CI FOR MU 1 - MU 0: (-9.3, -2.4) TTEST MU 1 = MU 0 (VS NE): T=-3.45 P=0.0014 DF=38.9 ================================================================ MTB > read 'a:\ed257\smsg.dat' c1-c4 43 ROWS READ ROW C1 C2 C3 C4 1 1 2.750 1 1.625 2 1 7.400 1 3.950 3 1 4.280 1 4.200 4 1 5.875 1 4.417 MTB > ancova c2 =c3; SUBC> covariates c4; SUBC> means c3. * NOTE * Unequal cell counts (Make sure your design is orthogonal) Factor Levels Values C3 2 0 1 Analysis of Covariance for C2 Source DF ADJ SS MS F P Covariates 1 943.79 943.79 120.66 0.000 C3 1 240.80 240.80 30.79 0.000 Error 40 312.86 7.82 Total 42 1623.84 Covariate Coeff Stdev t-value P C4 1.534 0.140 10.98 0.000 ADJUSTED MEANS C3 N C2 0 22 17.266 1 21 12.500 ========================================================== Comparison of ANCOVA output and GLM using covariates You get the same thing in slighty different form MTB > read 'smsg.dat' c1-c4 43 ROWS READ ROW C1 C2 C3 C4 1 1 2.750 1 1.625 2 1 7.400 1 3.950 3 1 4.280 1 4.200 4 1 5.875 1 4.417 . . . MTB > ancova c2 = c3; SUBC> covariate c4. * NOTE * Unequal cell counts (Make sure your design is orthogonal) DRR note-- but you can see for one-way design, this doesn't matter Factor Levels Values C3 2 0 1 Analysis of Covariance for C2 Source DF ADJ SS MS F P Covariates 1 943.79 943.79 120.66 0.000 1 240.80 240.80 30.79 0.000 Error 40 312.86 7.82 Total 42 1623.84 Covariate Coeff Stdev t-value P C4 1.534 0.140 10.98 0.000 -------------------------------------------------- Now do this via GLM ---------------------------- MTB > glm c2 = c3 c4; SUBC> covariate c4. Factor Levels Values C3 2 0 1 Analysis of Variance for C2 Source DF Seq SS Adj SS Adj MS F P C3 1 367.18 240.80 240.80 30.79 0.000 C4 1 943.79 943.79 943.79 120.66 0.000 Error 40 312.86 312.86 7.82 Total 42 1623.84 Term Coeff Stdev t-value P Constant 3.588 1.112 3.23 0.002 C4 1.5337 0.1396 10.98 0.000 Unusual Observations for C2 Obs. C2 Fit Stdev.Fit Residual St.Resid 19 26.1760 19.0687 0.8904 7.1073 2.68R 21 25.0910 24.5594 1.3003 0.5316 0.21 X 32 22.5000 16.6166 0.6058 5.8834 2.15R 41 15.8550 23.4907 0.7903 -7.6357 -2.85R R denotes an obs. with a large st. resid. X denotes an obs. whose X value gives it large influence. ============================== END OF FILE (I believe)