The SAS System 1 11:57 Tuesday, March 20, 2018 The MEANS Procedure Analysis Variable : score N bowler Obs Mean Std Dev --------------------------------------------------- 1 56 209.6607143 31.9592222 2 56 198.8750000 25.7074892 3 56 212.9464286 23.4586054 4 56 216.1785714 26.0733979 5 56 208.1964286 24.1799463 6 56 198.6250000 27.1451067 7 56 209.5357143 29.6941771 8 56 208.4285714 25.8652854 9 56 198.9642857 23.7279768 10 56 209.3035714 28.9261880 11 56 202.4285714 20.6836406 12 56 194.7500000 26.5304285 13 56 202.7321429 25.4669062 14 56 211.5892857 23.5733106 15 56 205.7142857 21.8538237 --------------------------------------------------- The SAS System 2 11:57 Tuesday, March 20, 2018 The MEANS Procedure Analysis Variable : score N pattern Obs Mean Std Dev --------------------------------------------------- 1 210 210.0904762 28.8131483 2 210 204.5714286 24.4571130 3 210 201.3952381 24.3291027 4 210 207.3904762 26.6856574 --------------------------------------------------- The SAS System 3 11:57 Tuesday, March 20, 2018 The MEANS Procedure Analysis Variable : score N bowler pattern Obs Mean Std Dev ------------------------------------------------------------------- 1 1 14 223.2857143 42.4362482 2 14 208.7857143 22.9821957 3 14 195.5714286 27.2670957 4 14 211.0000000 28.8497434 2 1 14 211.7857143 28.7727932 2 14 195.7142857 27.0567170 3 14 196.4285714 24.3080053 4 14 191.5714286 19.7745535 3 1 14 218.1428571 24.5070073 2 14 208.5000000 26.2348858 3 14 209.6428571 27.7782625 4 14 215.5000000 14.0917324 4 1 14 219.4285714 18.7153343 2 14 216.6428571 21.7418672 3 14 212.4285714 27.5198230 4 14 216.2142857 35.6244915 5 1 14 210.5714286 20.7724458 2 14 198.4285714 18.8014496 3 14 204.7142857 28.6958281 4 14 219.0714286 24.8176869 6 1 14 211.0000000 30.9092966 2 14 203.2857143 16.8998342 ------------------------------------------------------------------- The SAS System 4 11:57 Tuesday, March 20, 2018 The MEANS Procedure Analysis Variable : score N bowler pattern Obs Mean Std Dev ------------------------------------------------------------------- 6 3 14 193.0714286 23.7242631 4 14 187.1428571 30.8242091 7 1 14 223.3571429 34.2583109 2 14 199.2857143 30.2869065 3 14 194.4285714 20.2435718 4 14 221.0714286 22.8421482 8 1 14 209.5714286 25.1662603 2 14 214.2142857 31.6353711 3 14 208.6428571 20.7609365 4 14 201.2857143 25.9390664 9 1 14 199.5714286 27.9827262 2 14 198.5714286 21.6678219 3 14 193.2857143 18.5697379 4 14 204.4285714 26.7803438 10 1 14 205.8571429 33.0171451 2 14 213.7142857 20.7306112 3 14 198.3571429 31.2252539 4 14 219.2857143 27.8386244 11 1 14 202.5000000 26.8807910 2 14 205.2857143 14.4883432 3 14 194.3571429 21.3995224 4 14 207.5714286 17.6666321 ------------------------------------------------------------------- The SAS System 5 11:57 Tuesday, March 20, 2018 The MEANS Procedure Analysis Variable : score N bowler pattern Obs Mean Std Dev ------------------------------------------------------------------- 12 1 14 206.2142857 31.9835981 2 14 182.6428571 25.7998424 3 14 196.1428571 16.7325438 4 14 194.0000000 26.5938107 13 1 14 198.5000000 15.5055821 2 14 207.8571429 22.3876929 3 14 210.7142857 25.8796878 4 14 193.8571429 33.6380214 14 1 14 212.0000000 30.0281919 2 14 205.8571429 25.4856133 3 14 208.2857143 22.4308461 4 14 220.2142857 13.0099286 15 1 14 199.5714286 27.9827262 2 14 209.7857143 23.9331716 3 14 204.8571429 20.2669004 4 14 208.6428571 13.6190316 ------------------------------------------------------------------- The SAS System 6 11:57 Tuesday, March 20, 2018 The Mixed Procedure Model Information Data Set WORK.WPBA2009 Dependent Variable score 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 bowler 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 pattern 4 1 2 3 4 Dimensions Covariance Parameters 3 Columns in X 5 Columns in Z 75 Subjects 1 Max Obs per Subject 840 Number of Observations Number of Observations Read 840 Number of Observations Used 840 Number of Observations Not Used 0 Iteration History Iteration Evaluations -2 Res Log Like Criterion 0 1 7850.11885111 1 1 7834.53042538 0.00000000 Convergence criteria met. The SAS System 7 11:57 Tuesday, March 20, 2018 The Mixed Procedure Covariance Parameter Estimates Standard Z Cov Parm Estimate Error Value Pr > Z Alpha Lower bowler 23.5846 14.7947 1.59 0.0555 0.05 9.2431 bowler*pattern 12.1437 12.9894 0.93 0.1749 0.05 3.1052 Residual 649.59 32.8932 19.75 <.0001 0.05 589.65 Covariance Parameter Estimates Cov Parm Upper bowler 138.95 bowler*pattern 757.62 Residual 719.20 Fit Statistics -2 Res Log Likelihood 7834.5 AIC (Smaller is Better) 7840.5 AICC (Smaller is Better) 7840.6 BIC (Smaller is Better) 7842.7 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F pattern 3 42 3.57 0.0217 Least Squares Means Standard Effect pattern Estimate Error DF t Value Pr > |t| pattern 1 210.09 2.3399 42 89.79 <.0001 pattern 2 204.57 2.3399 42 87.43 <.0001 pattern 3 201.40 2.3399 42 86.07 <.0001 pattern 4 207.39 2.3399 42 88.63 <.0001 The SAS System 8 11:57 Tuesday, March 20, 2018 The Mixed Procedure Differences of Least Squares Means Standard Effect pattern _pattern Estimate Error DF t Value Pr > |t| pattern 1 2 5.5190 2.7939 42 1.98 0.0548 pattern 1 3 8.6952 2.7939 42 3.11 0.0033 pattern 1 4 2.7000 2.7939 42 0.97 0.3394 pattern 2 3 3.1762 2.7939 42 1.14 0.2620 pattern 2 4 -2.8190 2.7939 42 -1.01 0.3187 pattern 3 4 -5.9952 2.7939 42 -2.15 0.0377 The SAS System 9 11:57 Tuesday, March 20, 2018 The GLM Procedure Class Level Information Class Levels Values bowler 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 pattern 4 1 2 3 4 Number of Observations Read 840 Number of Observations Used 840 The SAS System 10 11:57 Tuesday, March 20, 2018 The GLM Procedure Dependent Variable: score Sum of Source DF Squares Mean Square F Value Pr > F Model 59 73172.9810 1240.2200 1.91 <.0001 Error 780 506679.0000 649.5885 Corrected Total 839 579851.9810 R-Square Coeff Var Root MSE score Mean 0.126193 12.38064 25.48703 205.8619 Source DF Type I SS Mean Square F Value Pr > F pattern 3 8785.09524 2928.36508 4.51 0.0038 bowler 14 29964.69524 2140.33537 3.29 <.0001 bowler*pattern 42 34423.19048 819.59977 1.26 0.1271 Source DF Type III SS Mean Square F Value Pr > F pattern 3 8785.09524 2928.36508 4.51 0.0038 bowler 14 29964.69524 2140.33537 3.29 <.0001 bowler*pattern 42 34423.19048 819.59977 1.26 0.1271 Tests of Hypotheses Using the Type III MS for bowler*pattern as an Error Term Source DF Type III SS Mean Square F Value Pr > F pattern 3 8785.09524 2928.36508 3.57 0.0217 bowler 14 29964.69524 2140.33537 2.61 0.0082