The SAS System 1 10:21 Wednesday, March 25, 2015 The GLM Procedure Class Level Information Class Levels Values oil 5 1 2 3 4 5 bowler 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 tourney_oil 3 1 2 3 Number of Observations Read 1110 Number of Observations Used 1110 The SAS System 2 10:21 Wednesday, March 25, 2015 The GLM Procedure Dependent Variable: score Sum of Source DF Squares Mean Square F Value Pr > F Model 554 969.531302 1.750057 3.28 <.0001 Error 555 296.264800 0.533810 Corrected Total 1109 1265.796102 R-Square Coeff Var Root MSE score Mean 0.765946 4.755385 0.730623 15.36413 Source DF Type I SS Mean Square F Value Pr > F oil 4 337.0658852 84.2664713 157.86 <.0001 tourney_oil(oil) 10 97.6500495 9.7650050 18.29 <.0001 bowler 36 84.4443423 2.3456762 4.39 <.0001 oil*bowler 144 129.3209414 0.8980621 1.68 <.0001 bowler*tourney_(oil) 360 321.0500838 0.8918058 1.67 <.0001 Source DF Type III SS Mean Square F Value Pr > F oil 4 337.0658852 84.2664713 157.86 <.0001 tourney_oil(oil) 10 97.6500495 9.7650050 18.29 <.0001 bowler 36 84.4443423 2.3456762 4.39 <.0001 oil*bowler 144 129.3209414 0.8980621 1.68 <.0001 bowler*tourney_(oil) 360 321.0500838 0.8918058 1.67 <.0001 The SAS System 3 10:21 Wednesday, March 25, 2015 The GLM Procedure Source Type III Expected Mean Square oil Var(Error) + 2 Var(bowler*tourney_(oil)) + 6 Var(oil*bowler) + 74 Var(tourney_oil(oil)) + Q(oil) tourney_oil(oil) Var(Error) + 2 Var(bowler*tourney_(oil)) + 74 Var(tourney_oil(oil)) bowler Var(Error) + 2 Var(bowler*tourney_(oil)) + 6 Var(oil*bowler) + 30 Var(bowler) oil*bowler Var(Error) + 2 Var(bowler*tourney_(oil)) + 6 Var(oil*bowler) bowler*tourney_(oil) Var(Error) + 2 Var(bowler*tourney_(oil)) The SAS System 4 10:21 Wednesday, March 25, 2015 The GLM Procedure Tests of Hypotheses for Mixed Model Analysis of Variance Dependent Variable: score Source DF Type III SS Mean Square F Value Pr > F oil 4 337.065885 84.266471 8.62 0.0028 Error 10.005 97.757791 9.771261 Error: MS(tourney_oil(oil)) + MS(oil*bowler) - MS(bowler*tourney_(oil)) - 46E-15*MS(Error) Source DF Type III SS Mean Square F Value Pr > F tourney_oil(oil) 10 97.650050 9.765005 10.95 <.0001 oil*bowler 144 129.320941 0.898062 1.01 0.4721 Error 360 321.050084 0.891806 Error: MS(bowler*tourney_(oil)) Source DF Type III SS Mean Square F Value Pr > F bowler 36 84.444342 2.345676 2.61 <.0001 Error 144 129.320941 0.898062 Error: MS(oil*bowler) Source DF Type III SS Mean Square F Value Pr > F bowler*tourney_(oil) 360 321.050084 0.891806 1.67 <.0001 Error: MS(Error) 555 296.264800 0.533810 The SAS System 5 10:21 Wednesday, March 25, 2015 Bonferroni (Dunn) t Tests for score NOTE: This test controls the Type I experimentwise error rate, but it generally has a higher Type II error rate than REGWQ. Alpha 0.05 Error Degrees of Freedom 555 Error Mean Square 0.53381 Critical Value of t 2.81830 Minimum Significant Difference 0.1954 Means with the same letter are not significantly different. Bon Grouping Mean N oil A 15.90450 222 2 A A 15.80703 222 3 B 15.43563 222 1 B B 15.32086 222 5 C 14.35261 222 4 The SAS System 6 10:21 Wednesday, March 25, 2015 The Mixed Procedure Model Information Data Set WORK.PBAHASSE Dependent Variable score Covariance Structure Variance Components Estimation Method REML Residual Variance Method Profile Fixed Effects SE Method Model-Based Degrees of Freedom Method Satterthwaite Class Level Information Class Levels Values oil 5 1 2 3 4 5 bowler 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 tourney_oil 3 1 2 3 Dimensions Covariance Parameters 5 Columns in X 6 Columns in Z 792 Subjects 1 Max Obs per Subject 1110 Number of Observations Number of Observations Read 1110 Number of Observations Used 1110 Number of Observations Not Used 0 Iteration History Iteration Evaluations -2 Res Log Like Criterion 0 1 2970.83808314 1 1 2811.26192531 0.00000000 The SAS System 7 10:21 Wednesday, March 25, 2015 The Mixed Procedure Convergence criteria met. Covariance Parameter Estimates Cov Parm Estimate Alpha Lower Upper tourney_oil(oil) 0.1199 0.05 0.05525 0.4285 bowler 0.04825 0.05 0.02548 0.1240 oil*bowler 0.001043 0.05 . . bowler*tourney_(oil) 0.1790 0.05 0.1241 0.2807 Residual 0.5338 0.05 0.4762 0.6026 Fit Statistics -2 Res Log Likelihood 2811.3 AIC (Smaller is Better) 2821.3 AICC (Smaller is Better) 2821.3 BIC (Smaller is Better) 2824.8 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F oil 4 10 8.62 0.0028 Least Squares Means Standard Effect oil Estimate Error DF t Value Pr > |t| oil 1 15.4356 0.2129 10.6 72.51 <.0001 oil 2 15.9045 0.2129 10.6 74.71 <.0001 oil 3 15.8070 0.2129 10.6 74.25 <.0001 oil 4 14.3526 0.2129 10.6 67.42 <.0001 oil 5 15.3209 0.2129 10.6 71.97 <.0001 Differences of Least Squares Means Standard Effect oil _oil Estimate Error DF t Value Pr > |t| Adjustment oil 1 2 -0.4689 0.2967 10 -1.58 0.1451 Bonferroni oil 1 3 -0.3714 0.2967 10 -1.25 0.2391 Bonferroni The SAS System 8 10:21 Wednesday, March 25, 2015 The Mixed Procedure Differences of Least Squares Means Standard Effect oil _oil Estimate Error DF t Value Pr > |t| Adjustment oil 1 4 1.0830 0.2967 10 3.65 0.0045 Bonferroni oil 1 5 0.1148 0.2967 10 0.39 0.7070 Bonferroni oil 2 3 0.09748 0.2967 10 0.33 0.7493 Bonferroni oil 2 4 1.5519 0.2967 10 5.23 0.0004 Bonferroni oil 2 5 0.5836 0.2967 10 1.97 0.0775 Bonferroni oil 3 4 1.4544 0.2967 10 4.90 0.0006 Bonferroni oil 3 5 0.4862 0.2967 10 1.64 0.1323 Bonferroni oil 4 5 -0.9682 0.2967 10 -3.26 0.0085 Bonferroni Differences of Least Squares Means Effect oil _oil Adj P oil 1 2 1.0000 oil 1 3 1.0000 oil 1 4 0.0446 oil 1 5 1.0000 oil 2 3 1.0000 oil 2 4 0.0038 oil 2 5 0.7750 oil 3 4 0.0062 oil 3 5 1.0000 oil 4 5 0.0852 The SAS System 9 10:21 Wednesday, March 25, 2015 The Mixed Procedure Model Information Data Set WORK.PBAHASSE Dependent Variable score Covariance Structure Variance Components Estimation Method REML Residual Variance Method Profile Fixed Effects SE Method Kenward-Roger Degrees of Freedom Method Kenward-Roger Class Level Information Class Levels Values oil 5 1 2 3 4 5 bowler 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 tourney_oil 3 1 2 3 Dimensions Covariance Parameters 5 Columns in X 6 Columns in Z 792 Subjects 1 Max Obs per Subject 1110 Number of Observations Number of Observations Read 1110 Number of Observations Used 1110 Number of Observations Not Used 0 Iteration History Iteration Evaluations -2 Res Log Like Criterion 0 1 2970.83808314 1 1 2811.26192531 0.00000000 The SAS System 10 10:21 Wednesday, March 25, 2015 The Mixed Procedure Convergence criteria met. Covariance Parameter Estimates Cov Parm Estimate Alpha Lower Upper tourney_oil(oil) 0.1199 0.05 0.05525 0.4285 bowler 0.04825 0.05 0.02548 0.1240 oil*bowler 0.001043 0.05 . . bowler*tourney_(oil) 0.1790 0.05 0.1241 0.2807 Residual 0.5338 0.05 0.4762 0.6026 Fit Statistics -2 Res Log Likelihood 2811.3 AIC (Smaller is Better) 2821.3 AICC (Smaller is Better) 2821.3 BIC (Smaller is Better) 2824.8 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F oil 4 10 8.62 0.0028 Least Squares Means Standard Effect oil Estimate Error DF t Value Pr > |t| oil 1 15.4356 0.2129 10.6 72.51 <.0001 oil 2 15.9045 0.2129 10.6 74.71 <.0001 oil 3 15.8070 0.2129 10.6 74.25 <.0001 oil 4 14.3526 0.2129 10.6 67.42 <.0001 oil 5 15.3209 0.2129 10.6 71.97 <.0001 Differences of Least Squares Means Standard Effect oil _oil Estimate Error DF t Value Pr > |t| Adjustment oil 1 2 -0.4689 0.2967 10 -1.58 0.1451 Bonferroni oil 1 3 -0.3714 0.2967 10 -1.25 0.2391 Bonferroni The SAS System 11 10:21 Wednesday, March 25, 2015 The Mixed Procedure Differences of Least Squares Means Standard Effect oil _oil Estimate Error DF t Value Pr > |t| Adjustment oil 1 4 1.0830 0.2967 10 3.65 0.0045 Bonferroni oil 1 5 0.1148 0.2967 10 0.39 0.7070 Bonferroni oil 2 3 0.09748 0.2967 10 0.33 0.7493 Bonferroni oil 2 4 1.5519 0.2967 10 5.23 0.0004 Bonferroni oil 2 5 0.5836 0.2967 10 1.97 0.0775 Bonferroni oil 3 4 1.4544 0.2967 10 4.90 0.0006 Bonferroni oil 3 5 0.4862 0.2967 10 1.64 0.1323 Bonferroni oil 4 5 -0.9682 0.2967 10 -3.26 0.0085 Bonferroni Differences of Least Squares Means Effect oil _oil Adj P oil 1 2 1.0000 oil 1 3 1.0000 oil 1 4 0.0446 oil 1 5 1.0000 oil 2 3 1.0000 oil 2 4 0.0038 oil 2 5 0.7750 oil 3 4 0.0062 oil 3 5 1.0000 oil 4 5 0.0852