* ch27ta08.sas, 2-factors, repeated measures on one; options ls=80 nodate; ; data bloodflw; input y R E B; lines; 4 1 1 1 3 1 1 2 5 1 1 3 5 1 1 4 4 1 1 5 1 2 1 1 3 2 1 2 6 2 1 3 3 2 1 4 8 2 1 5 3 3 1 1 1 3 1 2 4 3 1 3 4 3 1 4 7 3 1 5 1 4 1 1 4 4 1 2 3 4 1 3 2 4 1 4 7 4 1 5 3 1 2 1 6 1 2 2 12 1 2 3 22 1 2 4 11 1 2 5 3 2 2 1 5 2 2 2 8 2 2 3 18 2 2 4 12 2 2 5 4 3 2 1 7 3 2 2 10 3 2 3 20 3 2 4 14 3 2 5 2 4 2 1 4 4 2 2 7 4 2 3 16 4 2 4 8 4 2 5 ; proc glm; class R E B; model y = E | B | R(E); random R(E) R*B(E); means E B E*B; test h=E e=R(E); test h=B E*B e=R*B(E); ; proc mixed CL CovTest; class R E B; model y = E | B; random R(E); * R*B(E) removed from model since no replication; lsmeans B / adjust=Tukey CL; lsmeans E / CL; lsmeans E*B / adjust=Bon CL; The SAS System 1 The GLM Procedure Class Level Information Class Levels Values R 4 1 2 3 4 E 2 1 2 B 5 1 2 3 4 5 Number of Observations Read 40 Number of Observations Used 40 The SAS System 2 The GLM Procedure Dependent Variable: y Sum of Source DF Squares Mean Square F Value Pr > F Model 39 1067.500000 27.371795 . . Error 0 0.000000 . Corrected Total 39 1067.500000 Source DF Type III SS Mean Square F Value Pr > F E 1 324.9000000 324.9000000 . . B 4 389.5000000 97.3750000 . . E*B 4 262.1000000 65.5250000 . . R(E) 6 44.2000000 7.3666667 . . R*B(E) 24 46.8000000 1.9500000 . . The SAS System 3 The GLM Procedure Source Type III Expected Mean Square E Var(Error) + Var(R*B(E)) + 5 Var(R(E)) + Q(E,E*B) B Var(Error) + Var(R*B(E)) + Q(B,E*B) E*B Var(Error) + Var(R*B(E)) + Q(E*B) R(E) Var(Error) + Var(R*B(E)) + 5 Var(R(E)) R*B(E) Var(Error) + Var(R*B(E)) The SAS System 4 The GLM Procedure Level of --------------y-------------- E N Mean Std Dev 1 20 3.90000000 1.99736669 2 20 9.60000000 5.92408110 Level of --------------y-------------- B N Mean Std Dev 1 8 2.6250000 1.18773494 2 8 4.1250000 1.88509189 3 8 6.8750000 3.04431555 4 8 11.2500000 8.49789890 5 8 8.8750000 3.22656385 Level of Level of --------------y-------------- E B N Mean Std Dev 1 1 4 2.2500000 1.50000000 1 2 4 2.7500000 1.25830574 1 3 4 4.5000000 1.29099445 1 4 4 3.5000000 1.29099445 1 5 4 6.5000000 1.73205081 2 1 4 3.0000000 0.81649658 2 2 4 5.5000000 1.29099445 2 3 4 9.2500000 2.21735578 2 4 4 19.0000000 2.58198890 2 5 4 11.2500000 2.50000000 The SAS System 5 The GLM Procedure Dependent Variable: y Tests of Hypotheses Using the Type III MS for R(E) as an Error Term Source DF Type III SS Mean Square F Value Pr > F E 1 324.9000000 324.9000000 44.10 0.0006 Tests of Hypotheses Using the Type III MS for R*B(E) as an Error Term Source DF Type III SS Mean Square F Value Pr > F B 4 389.5000000 97.3750000 49.94 <.0001 E*B 4 262.1000000 65.5250000 33.60 <.0001 The SAS System 6 The Mixed Procedure Model Information Data Set WORK.BLOODFLW Dependent Variable y Covariance Structure Variance Components Estimation Method REML Residual Variance Method Profile Fixed Effects SE Method Model-Based Degrees of Freedom Method Containment Class Level Information Class Levels Values R 4 1 2 3 4 E 2 1 2 B 5 1 2 3 4 5 Dimensions Covariance Parameters 2 Columns in X 18 Columns in Z 8 Subjects 1 Max Obs Per Subject 40 Number of Observations Number of Observations Read 40 Number of Observations Used 40 Number of Observations Not Used 0 Iteration History Iteration Evaluations -2 Res Log Like Criterion 0 1 132.28911935 1 1 127.00895246 0.00000000 Convergence criteria met. Covariance Parameter Estimates Standard Z Cov Parm Estimate Error Value Pr Z Alpha Lower Upper R(E) 1.0833 0.8580 1.26 0.1034 0.05 0.3562 13.3223 Residual 1.9500 0.5629 3.46 0.0003 0.05 1.1889 3.7738 The SAS System 7 The Mixed Procedure Fit Statistics -2 Res Log Likelihood 127.0 AIC (smaller is better) 131.0 AICC (smaller is better) 131.5 BIC (smaller is better) 131.2 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F E 1 6 44.10 0.0006 B 4 24 49.94 <.0001 E*B 4 24 33.60 <.0001 Least Squares Means Standard Effect E B Estimate Error DF t Value Pr > |t| Alpha B 1 2.6250 0.6158 24 4.26 0.0003 0.05 B 2 4.1250 0.6158 24 6.70 <.0001 0.05 B 3 6.8750 0.6158 24 11.16 <.0001 0.05 B 4 11.2500 0.6158 24 18.27 <.0001 0.05 B 5 8.8750 0.6158 24 14.41 <.0001 0.05 E 1 3.9000 0.6069 6 6.43 0.0007 0.05 E 2 9.6000 0.6069 6 15.82 <.0001 0.05 E*B 1 1 2.2500 0.8708 24 2.58 0.0163 0.05 E*B 1 2 2.7500 0.8708 24 3.16 0.0043 0.05 E*B 1 3 4.5000 0.8708 24 5.17 <.0001 0.05 E*B 1 4 3.5000 0.8708 24 4.02 0.0005 0.05 E*B 1 5 6.5000 0.8708 24 7.46 <.0001 0.05 E*B 2 1 3.0000 0.8708 24 3.45 0.0021 0.05 Least Squares Means Effect E B Lower Upper B 1 1.3541 3.8959 B 2 2.8541 5.3959 B 3 5.6041 8.1459 B 4 9.9791 12.5209 B 5 7.6041 10.1459 E 1 2.4150 5.3850 E 2 8.1150 11.0850 E*B 1 1 0.4527 4.0473 E*B 1 2 0.9527 4.5473 E*B 1 3 2.7027 6.2973 E*B 1 4 1.7027 5.2973 E*B 1 5 4.7027 8.2973 E*B 2 1 1.2027 4.7973 The SAS System 8 The Mixed Procedure Least Squares Means Standard Effect E B Estimate Error DF t Value Pr > |t| Alpha E*B 2 2 5.5000 0.8708 24 6.32 <.0001 0.05 E*B 2 3 9.2500 0.8708 24 10.62 <.0001 0.05 E*B 2 4 19.0000 0.8708 24 21.82 <.0001 0.05 E*B 2 5 11.2500 0.8708 24 12.92 <.0001 0.05 Least Squares Means Effect E B Lower Upper E*B 2 2 3.7027 7.2973 E*B 2 3 7.4527 11.0473 E*B 2 4 17.2027 20.7973 E*B 2 5 9.4527 13.0473 Differences of Least Squares Means Standard Effect E B _E _B Estimate Error DF t Value Pr > |t| Adjustment B 1 2 -1.5000 0.6982 24 -2.15 0.0420 Tukey-Kramer B 1 3 -4.2500 0.6982 24 -6.09 <.0001 Tukey-Kramer B 1 4 -8.6250 0.6982 24 -12.35 <.0001 Tukey-Kramer B 1 5 -6.2500 0.6982 24 -8.95 <.0001 Tukey-Kramer B 2 3 -2.7500 0.6982 24 -3.94 0.0006 Tukey-Kramer B 2 4 -7.1250 0.6982 24 -10.20 <.0001 Tukey-Kramer B 2 5 -4.7500 0.6982 24 -6.80 <.0001 Tukey-Kramer B 3 4 -4.3750 0.6982 24 -6.27 <.0001 Tukey-Kramer B 3 5 -2.0000 0.6982 24 -2.86 0.0085 Tukey-Kramer B 4 5 2.3750 0.6982 24 3.40 0.0023 Tukey-Kramer E*B 1 1 1 2 -0.5000 0.9874 24 -0.51 0.6172 Bonferroni Differences of Least Squares Means Adj Adj Effect E B _E _B Adj P Alpha Lower Upper Lower Upper B 1 2 0.2332 0.05 -2.9410 -0.05896 -3.5570 0.5570 B 1 3 <.0001 0.05 -5.6910 -2.8090 -6.3070 -2.1930 B 1 4 <.0001 0.05 -10.0660 -7.1840 -10.6820 -6.5680 B 1 5 <.0001 0.05 -7.6910 -4.8090 -8.3070 -4.1930 B 2 3 0.0051 0.05 -4.1910 -1.3090 -4.8070 -0.6930 B 2 4 <.0001 0.05 -8.5660 -5.6840 -9.1820 -5.0680 B 2 5 <.0001 0.05 -6.1910 -3.3090 -6.8070 -2.6930 B 3 4 <.0001 0.05 -5.8160 -2.9340 -6.4320 -2.3180 B 3 5 0.0595 0.05 -3.4410 -0.5590 -4.0570 0.05695 B 4 5 0.0181 0.05 0.9340 3.8160 0.3180 4.4320 E*B 1 1 1 2 1.0000 0.05 -2.5379 1.5379 -4.1567 3.1567 The SAS System 9 The Mixed Procedure Differences of Least Squares Means Standard Effect E B _E _B Estimate Error DF t Value Pr > |t| Adjustment E*B 1 1 1 3 -2.2500 0.9874 24 -2.28 0.0319 Bonferroni E*B 1 1 1 4 -1.2500 0.9874 24 -1.27 0.2177 Bonferroni E*B 1 1 1 5 -4.2500 0.9874 24 -4.30 0.0002 Bonferroni E*B 1 1 2 1 -0.7500 1.2315 24 -0.61 0.5482 Bonferroni E*B 1 1 2 2 -3.2500 1.2315 24 -2.64 0.0144 Bonferroni E*B 1 1 2 3 -7.0000 1.2315 24 -5.68 <.0001 Bonferroni E*B 1 1 2 4 -16.7500 1.2315 24 -13.60 <.0001 Bonferroni E*B 1 1 2 5 -9.0000 1.2315 24 -7.31 <.0001 Bonferroni E*B 1 2 1 3 -1.7500 0.9874 24 -1.77 0.0890 Bonferroni E*B 1 2 1 4 -0.7500 0.9874 24 -0.76 0.4549 Bonferroni E*B 1 2 1 5 -3.7500 0.9874 24 -3.80 0.0009 Bonferroni E*B 1 2 2 1 -0.2500 1.2315 24 -0.20 0.8408 Bonferroni E*B 1 2 2 2 -2.7500 1.2315 24 -2.23 0.0351 Bonferroni E*B 1 2 2 3 -6.5000 1.2315 24 -5.28 <.0001 Bonferroni E*B 1 2 2 4 -16.2500 1.2315 24 -13.19 <.0001 Bonferroni E*B 1 2 2 5 -8.5000 1.2315 24 -6.90 <.0001 Bonferroni E*B 1 3 1 4 1.0000 0.9874 24 1.01 0.3213 Bonferroni E*B 1 3 1 5 -2.0000 0.9874 24 -2.03 0.0541 Bonferroni E*B 1 3 2 1 1.5000 1.2315 24 1.22 0.2351 Bonferroni E*B 1 3 2 2 -1.0000 1.2315 24 -0.81 0.4248 Bonferroni E*B 1 3 2 3 -4.7500 1.2315 24 -3.86 0.0008 Bonferroni E*B 1 3 2 4 -14.5000 1.2315 24 -11.77 <.0001 Bonferroni E*B 1 3 2 5 -6.7500 1.2315 24 -5.48 <.0001 Bonferroni E*B 1 4 1 5 -3.0000 0.9874 24 -3.04 0.0057 Bonferroni E*B 1 4 2 1 0.5000 1.2315 24 0.41 0.6883 Bonferroni E*B 1 4 2 2 -2.0000 1.2315 24 -1.62 0.1174 Bonferroni E*B 1 4 2 3 -5.7500 1.2315 24 -4.67 <.0001 Bonferroni E*B 1 4 2 4 -15.5000 1.2315 24 -12.59 <.0001 Bonferroni E*B 1 4 2 5 -7.7500 1.2315 24 -6.29 <.0001 Bonferroni E*B 1 5 2 1 3.5000 1.2315 24 2.84 0.0090 Bonferroni E*B 1 5 2 2 1.0000 1.2315 24 0.81 0.4248 Bonferroni E*B 1 5 2 3 -2.7500 1.2315 24 -2.23 0.0351 Bonferroni E*B 1 5 2 4 -12.5000 1.2315 24 -10.15 <.0001 Bonferroni E*B 1 5 2 5 -4.7500 1.2315 24 -3.86 0.0008 Bonferroni E*B 2 1 2 2 -2.5000 0.9874 24 -2.53 0.0183 Bonferroni E*B 2 1 2 3 -6.2500 0.9874 24 -6.33 <.0001 Bonferroni E*B 2 1 2 4 -16.0000 0.9874 24 -16.20 <.0001 Bonferroni E*B 2 1 2 5 -8.2500 0.9874 24 -8.36 <.0001 Bonferroni E*B 2 2 2 3 -3.7500 0.9874 24 -3.80 0.0009 Bonferroni E*B 2 2 2 4 -13.5000 0.9874 24 -13.67 <.0001 Bonferroni E*B 2 2 2 5 -5.7500 0.9874 24 -5.82 <.0001 Bonferroni E*B 2 3 2 4 -9.7500 0.9874 24 -9.87 <.0001 Bonferroni E*B 2 3 2 5 -2.0000 0.9874 24 -2.03 0.0541 Bonferroni E*B 2 4 2 5 7.7500 0.9874 24 7.85 <.0001 Bonferroni The SAS System 10 The Mixed Procedure Differences of Least Squares Means Adj Adj Effect E B _E _B Adj P Alpha Lower Upper Lower Upper E*B 1 1 1 3 1.0000 0.05 -4.2879 -0.2121 -5.9067 1.4067 E*B 1 1 1 4 1.0000 0.05 -3.2879 0.7879 -4.9067 2.4067 E*B 1 1 1 5 0.0110 0.05 -6.2879 -2.2121 -7.9067 -0.5933 E*B 1 1 2 1 1.0000 0.05 -3.2918 1.7918 -5.3107 3.8107 E*B 1 1 2 2 0.6469 0.05 -5.7918 -0.7082 -7.8107 1.3107 E*B 1 1 2 3 0.0003 0.05 -9.5418 -4.4582 -11.5607 -2.4393 E*B 1 1 2 4 <.0001 0.05 -19.2918 -14.2082 -21.3107 -12.1893 E*B 1 1 2 5 <.0001 0.05 -11.5418 -6.4582 -13.5607 -4.4393 E*B 1 2 1 3 1.0000 0.05 -3.7879 0.2879 -5.4067 1.9067 E*B 1 2 1 4 1.0000 0.05 -2.7879 1.2879 -4.4067 2.9067 E*B 1 2 1 5 0.0395 0.05 -5.7879 -1.7121 -7.4067 -0.09329 E*B 1 2 2 1 1.0000 0.05 -2.7918 2.2918 -4.8107 4.3107 E*B 1 2 2 2 1.0000 0.05 -5.2918 -0.2082 -7.3107 1.8107 E*B 1 2 2 3 0.0009 0.05 -9.0418 -3.9582 -11.0607 -1.9393 E*B 1 2 2 4 <.0001 0.05 -18.7918 -13.7082 -20.8107 -11.6893 E*B 1 2 2 5 <.0001 0.05 -11.0418 -5.9582 -13.0607 -3.9393 E*B 1 3 1 4 1.0000 0.05 -1.0379 3.0379 -2.6567 4.6567 E*B 1 3 1 5 1.0000 0.05 -4.0379 0.03794 -5.6567 1.6567 E*B 1 3 2 1 1.0000 0.05 -1.0418 4.0418 -3.0607 6.0607 E*B 1 3 2 2 1.0000 0.05 -3.5418 1.5418 -5.5607 3.5607 E*B 1 3 2 3 0.0340 0.05 -7.2918 -2.2082 -9.3107 -0.1893 E*B 1 3 2 4 <.0001 0.05 -17.0418 -11.9582 -19.0607 -9.9393 E*B 1 3 2 5 0.0006 0.05 -9.2918 -4.2082 -11.3107 -2.1893 E*B 1 4 1 5 0.2550 0.05 -5.0379 -0.9621 -6.6567 0.6567 E*B 1 4 2 1 1.0000 0.05 -2.0418 3.0418 -4.0607 5.0607 E*B 1 4 2 2 1.0000 0.05 -4.5418 0.5418 -6.5607 2.5607 E*B 1 4 2 3 0.0043 0.05 -8.2918 -3.2082 -10.3107 -1.1893 E*B 1 4 2 4 <.0001 0.05 -18.0418 -12.9582 -20.0607 -10.9393 E*B 1 4 2 5 <.0001 0.05 -10.2918 -5.2082 -12.3107 -3.1893 E*B 1 5 2 1 0.4052 0.05 0.9582 6.0418 -1.0607 8.0607 E*B 1 5 2 2 1.0000 0.05 -1.5418 3.5418 -3.5607 5.5607 E*B 1 5 2 3 1.0000 0.05 -5.2918 -0.2082 -7.3107 1.8107 E*B 1 5 2 4 <.0001 0.05 -15.0418 -9.9582 -17.0607 -7.9393 E*B 1 5 2 5 0.0340 0.05 -7.2918 -2.2082 -9.3107 -0.1893 E*B 2 1 2 2 0.8238 0.05 -4.5379 -0.4621 -6.1567 1.1567 E*B 2 1 2 3 <.0001 0.05 -8.2879 -4.2121 -9.9067 -2.5933 E*B 2 1 2 4 <.0001 0.05 -18.0379 -13.9621 -19.6567 -12.3433 E*B 2 1 2 5 <.0001 0.05 -10.2879 -6.2121 -11.9067 -4.5933 E*B 2 2 2 3 0.0395 0.05 -5.7879 -1.7121 -7.4067 -0.09329 E*B 2 2 2 4 <.0001 0.05 -15.5379 -11.4621 -17.1567 -9.8433 E*B 2 2 2 5 0.0002 0.05 -7.7879 -3.7121 -9.4067 -2.0933 E*B 2 3 2 4 <.0001 0.05 -11.7879 -7.7121 -13.4067 -6.0933 E*B 2 3 2 5 1.0000 0.05 -4.0379 0.03794 -5.6567 1.6567 E*B 2 4 2 5 <.0001 0.05 5.7121 9.7879 4.0933 11.4067