A SIMPLE BIBD DESIGN - YOUR NAME 13:05 Thursday, January 24, 2008 1 Here n=k=4, s=p=3, and la=2 in the definition of BIBD Treatments are rows and Blocks are columns From Montgomery "Design and Analysis of Experiments" 1st edn - p166 THE DATA AS SAS SEES IT Obs Catalyst Block Yield 1 1 1 73 2 1 2 74 3 1 4 71 4 2 2 75 5 2 3 67 6 2 4 72 7 3 1 73 8 3 2 75 9 3 3 68 10 4 1 75 11 4 3 72 12 4 4 75 A SIMPLE BIBD DESIGN - YOUR NAME 13:05 Thursday, January 24, 2008 2 Here n=k=4, s=p=3, and la=2 in the definition of BIBD MEANS FOR EACH LEVEL OF CATALYST and BLOCK This also checks the number of observations for each The MEANS Procedure Analysis Variable : Yield N Catalyst Obs Mean Std Dev ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ 1 3 72.67 1.53 2 3 71.33 4.04 3 3 72.00 3.61 4 3 74.00 1.73 ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ A SIMPLE BIBD DESIGN - YOUR NAME 13:05 Thursday, January 24, 2008 3 Here n=k=4, s=p=3, and la=2 in the definition of BIBD MEANS FOR EACH LEVEL OF CATALYST and BLOCK This also checks the number of observations for each The MEANS Procedure Analysis Variable : Yield N Block Obs Mean Std Dev ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ 1 3 73.67 1.15 2 3 74.67 0.58 3 3 69.00 2.65 4 3 72.67 2.08 ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ A SIMPLE BIBD DESIGN - YOUR NAME 13:05 Thursday, January 24, 2008 4 TEST CATALYST, AFTER ALLOWING FOR BLOCKS Catalyst has a moderately significant effect (P=0.0107) The GLM Procedure Class Level Information Class Levels Values Catalyst 4 1 2 3 4 Block 4 1 2 3 4 Number of Observations Read 12 Number of Observations Used 12 A SIMPLE BIBD DESIGN - YOUR NAME 13:05 Thursday, January 24, 2008 5 TEST CATALYST, AFTER ALLOWING FOR BLOCKS Catalyst has a moderately significant effect (P=0.0107) The GLM Procedure Dependent Variable: Yield Sum of Source DF Squares Mean Square F Value Pr > F Model 6 77.75000000 12.95833333 19.94 0.0024 Error 5 3.25000000 0.65000000 Corrected Total 11 81.00000000 R-Square Coeff Var Root MSE Yield Mean 0.959877 1.112036 0.806226 72.50000 Source DF Type I SS Mean Square F Value Pr > F Block 3 55.00000000 18.33333333 28.21 0.0015 Catalyst 3 22.75000000 7.58333333 11.67 0.0107 Source DF Type III SS Mean Square F Value Pr > F Block 3 66.08333333 22.02777778 33.89 0.0010 Catalyst 3 22.75000000 7.58333333 11.67 0.0107 A SIMPLE BIBD DESIGN - YOUR NAME 13:05 Thursday, January 24, 2008 6 TEST BLOCKS, AFTER ALLOWING FOR CATALYST Block has a highly significant effect (P=0.0010) The GLM Procedure Class Level Information Class Levels Values Catalyst 4 1 2 3 4 Block 4 1 2 3 4 Number of Observations Read 12 Number of Observations Used 12 A SIMPLE BIBD DESIGN - YOUR NAME 13:05 Thursday, January 24, 2008 7 TEST BLOCKS, AFTER ALLOWING FOR CATALYST Block has a highly significant effect (P=0.0010) The GLM Procedure Dependent Variable: Yield Sum of Source DF Squares Mean Square F Value Pr > F Model 6 77.75000000 12.95833333 19.94 0.0024 Error 5 3.25000000 0.65000000 Corrected Total 11 81.00000000 R-Square Coeff Var Root MSE Yield Mean 0.959877 1.112036 0.806226 72.50000 Source DF Type I SS Mean Square F Value Pr > F Catalyst 3 11.66666667 3.88888889 5.98 0.0415 Block 3 66.08333333 22.02777778 33.89 0.0010 Source DF Type III SS Mean Square F Value Pr > F Catalyst 3 22.75000000 7.58333333 11.67 0.0107 Block 3 66.08333333 22.02777778 33.89 0.0010 A SECOND BIBD DESIGN (ALSO A YOUDEN SQUARE) - YOUR NAME 8 Here n=k=7, s=p=4, and la=2 in the definition of BIBD A second Blocking variable is indicated by Greek letters From text (Box-Hunter-Hunter) Table 4.15 p165 THE DATA AS SAS SEES IT 13:05 Thursday, January 24, 2008 Obs Cycle Column Yy Treat Position 1 C1 1 627 B al 2 C1 2 248 D be 3 C1 3 563 F ga 4 C1 4 252 G de 5 C2 1 344 A al 6 C2 2 233 C be 7 C2 3 442 F de 8 C2 4 226 G ga 9 C3 1 251 C al 10 C3 2 211 D ga 11 C3 3 160 E de 12 C3 4 297 G be 13 C4 1 337 A be 14 C4 2 537 B de 15 C4 3 195 E ga 16 C4 4 300 G al 17 C5 1 520 B ga 18 C5 2 278 C de 19 C5 3 199 E be 20 C5 4 595 F al 21 C6 1 369 A ga 22 C6 2 196 D de 23 C6 3 185 E al 24 C6 4 606 F be 25 C7 1 396 A de 26 C7 2 602 B be 27 C7 3 240 C ga 28 C7 4 273 D al A SECOND BIBD DESIGN (ALSO A YOUDEN SQUARE) - YOUR NAME 9 Here n=k=7, s=p=4, and la=2 in the definition of BIBD MEANS FOR EACH LEVEL OF TREAT, CYCLE, and POSITION This also checks the number of observations for each 13:05 Thursday, January 24, 2008 The MEANS Procedure Analysis Variable : Yy N Treat Obs Mean Std Dev ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ A 4 361.50 26.79 B 4 571.50 51.16 C 4 250.50 19.77 D 4 232.00 35.00 E 4 184.75 17.52 F 4 551.50 75.24 G 4 268.75 35.98 ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ A SECOND BIBD DESIGN (ALSO A YOUDEN SQUARE) - YOUR NAME 10 Here n=k=7, s=p=4, and la=2 in the definition of BIBD MEANS FOR EACH LEVEL OF TREAT, CYCLE, and POSITION This also checks the number of observations for each 13:05 Thursday, January 24, 2008 The MEANS Procedure Analysis Variable : Yy N Cycle Obs Mean Std Dev ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ C1 4 422.50 200.90 C2 4 311.25 102.57 C3 4 229.75 58.28 C4 4 342.25 143.09 C5 4 398.00 189.47 C6 4 339.00 196.94 C7 4 377.75 163.88 ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ A SECOND BIBD DESIGN (ALSO A YOUDEN SQUARE) - YOUR NAME 11 Here n=k=7, s=p=4, and la=2 in the definition of BIBD MEANS FOR EACH LEVEL OF TREAT, CYCLE, and POSITION This also checks the number of observations for each 13:05 Thursday, January 24, 2008 The MEANS Procedure Analysis Variable : Yy N Position Obs Mean Std Dev ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ al 7 367.86 173.21 be 7 360.29 172.32 de 7 323.00 138.47 ga 7 332.00 154.48 ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ A SECOND BIBD DESIGN (ALSO A YOUDEN SQUARE) - YOUR NAME 12 Here n=k=7, s=p=4, and la=2 in the definition of BIBD ANOVA ANALYSIS AS A BIBD FOR CYCLE AND TREATMENT 13:05 Thursday, January 24, 2008 The GLM Procedure Class Level Information Class Levels Values Cycle 7 C1 C2 C3 C4 C5 C6 C7 Treat 7 A B C D E F G Number of Observations Read 28 Number of Observations Used 28 A SECOND BIBD DESIGN (ALSO A YOUDEN SQUARE) - YOUR NAME 13 Here n=k=7, s=p=4, and la=2 in the definition of BIBD ANOVA ANALYSIS AS A BIBD FOR CYCLE AND TREATMENT 13:05 Thursday, January 24, 2008 The GLM Procedure Dependent Variable: Yy Sum of Source DF Squares Mean Square F Value Pr > F Model 12 604193.2857 50349.4405 34.22 <.0001 Error 15 22071.4286 1471.4286 Corrected Total 27 626264.7143 R-Square Coeff Var Root MSE Yy Mean 0.964757 11.09335 38.35920 345.7857 Source DF Type I SS Mean Square F Value Pr > F Cycle 6 97394.7143 16232.4524 11.03 <.0001 Treat 6 506798.5714 84466.4286 57.40 <.0001 Source DF Type III SS Mean Square F Value Pr > F Cycle 6 14570.0714 2428.3452 1.65 0.2015 Treat 6 506798.5714 84466.4286 57.40 <.0001 A SECOND BIBD DESIGN (ALSO A YOUDEN SQUARE) - YOUR NAME 14 Here n=k=7, s=p=4, and la=2 in the definition of BIBD ANOVA ANALYSIS AS A YOUDEN SQUARE FOR CYCLE, POSITION, and TREATMENT 13:05 Thursday, January 24, 2008 The GLM Procedure Class Level Information Class Levels Values Cycle 7 C1 C2 C3 C4 C5 C6 C7 Position 4 al be de ga Treat 7 A B C D E F G Number of Observations Read 28 Number of Observations Used 28 A SECOND BIBD DESIGN (ALSO A YOUDEN SQUARE) - YOUR NAME 15 Here n=k=7, s=p=4, and la=2 in the definition of BIBD ANOVA ANALYSIS AS A YOUDEN SQUARE FOR CYCLE, POSITION, and TREATMENT 13:05 Thursday, January 24, 2008 The GLM Procedure Dependent Variable: Yy Sum of Source DF Squares Mean Square F Value Pr > F Model 15 614039.7143 40935.9810 40.18 <.0001 Error 12 12225.0000 1018.7500 Corrected Total 27 626264.7143 R-Square Coeff Var Root MSE Yy Mean 0.980480 9.230533 31.91786 345.7857 Source DF Type I SS Mean Square F Value Pr > F Cycle 6 97394.7143 16232.4524 15.93 <.0001 Position 3 9846.4286 3282.1429 3.22 0.0612 Treat 6 506798.5714 84466.4286 82.91 <.0001 Source DF Type III SS Mean Square F Value Pr > F Cycle 6 14570.0714 2428.3452 2.38 0.0944 Position 3 9846.4286 3282.1429 3.22 0.0612 Treat 6 506798.5714 84466.4286 82.91 <.0001 A SECOND BIBD DESIGN (ALSO A YOUDEN SQUARE) - YOUR NAME 16 Here n=k=7, s=p=4, and la=2 in the definition of BIBD ANOVA ANALYSIS AS A YOUDEN SQUARE FOR CYCLE, TREATMENT, and POSITION Note that the F-stats and P-values for Treat and Posn are unchanged 13:05 Thursday, January 24, 2008 The GLM Procedure Class Level Information Class Levels Values Cycle 7 C1 C2 C3 C4 C5 C6 C7 Treat 7 A B C D E F G Position 4 al be de ga Number of Observations Read 28 Number of Observations Used 28 A SECOND BIBD DESIGN (ALSO A YOUDEN SQUARE) - YOUR NAME 17 Here n=k=7, s=p=4, and la=2 in the definition of BIBD ANOVA ANALYSIS AS A YOUDEN SQUARE FOR CYCLE, TREATMENT, and POSITION Note that the F-stats and P-values for Treat and Posn are unchanged 13:05 Thursday, January 24, 2008 The GLM Procedure Dependent Variable: Yy Sum of Source DF Squares Mean Square F Value Pr > F Model 15 614039.7143 40935.9810 40.18 <.0001 Error 12 12225.0000 1018.7500 Corrected Total 27 626264.7143 R-Square Coeff Var Root MSE Yy Mean 0.980480 9.230533 31.91786 345.7857 Source DF Type I SS Mean Square F Value Pr > F Cycle 6 97394.7143 16232.4524 15.93 <.0001 Treat 6 506798.5714 84466.4286 82.91 <.0001 Position 3 9846.4286 3282.1429 3.22 0.0612 Source DF Type III SS Mean Square F Value Pr > F Cycle 6 14570.0714 2428.3452 2.38 0.0944 Treat 6 506798.5714 84466.4286 82.91 <.0001 Position 3 9846.4286 3282.1429 3.22 0.0612