Printout of Factorial Data 1 09:57 Tuesday, October 28, 2003 Obs a b rep yield 1 0 0 1 12 2 0 0 2 15 3 0 0 3 14 4 0 0 4 13 5 0 1 1 19 6 0 1 2 22 7 0 1 3 23 8 0 1 4 21 9 1 0 1 29 10 1 0 2 27 11 1 0 3 33 12 1 0 4 30 13 1 1 1 32 14 1 1 2 35 15 1 1 3 38 16 1 1 4 37 ANOVA assuming A and B are fixed effects 2 09:57 Tuesday, October 28, 2003 The ANOVA Procedure Class Level Information Class Levels Values rep 4 1 2 3 4 a 2 0 1 b 2 0 1 Number of observations 16 ANOVA assuming A and B are fixed effects 3 09:57 Tuesday, October 28, 2003 The ANOVA Procedure Dependent Variable: yield Sum of Source DF Squares Mean Square F Value Pr > F Model 6 1149.000000 191.500000 82.07 <.0001 Error 9 21.000000 2.333333 Corrected Total 15 1170.000000 R-Square Coeff Var Root MSE yield Mean 0.982051 6.110101 1.527525 25.00000 Source DF Anova SS Mean Square F Value Pr > F rep 3 32.5000000 10.8333333 4.64 0.0317 a 1 930.2500000 930.2500000 398.68 <.0001 b 1 182.2500000 182.2500000 78.11 <.0001 a*b 1 4.0000000 4.0000000 1.71 0.2229 ANOVA assuming A and B are fixed effects 4 09:57 Tuesday, October 28, 2003 The ANOVA Procedure t Tests (LSD) for yield NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 9 Error Mean Square 2.333333 Critical Value of t 2.26216 Least Significant Difference 1.7278 Means with the same letter are not significantly different. t Grouping Mean N a A 32.6250 8 1 B 17.3750 8 0 ANOVA assuming A and B are fixed effects 5 09:57 Tuesday, October 28, 2003 The ANOVA Procedure t Tests (LSD) for yield NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 9 Error Mean Square 2.333333 Critical Value of t 2.26216 Least Significant Difference 1.7278 Means with the same letter are not significantly different. t Grouping Mean N b A 28.3750 8 1 B 21.6250 8 0 ANOVA assuming A and B are fixed effects 6 09:57 Tuesday, October 28, 2003 The ANOVA Procedure Level of Level of ------------yield------------ a b N Mean Std Dev 0 0 4 13.5000000 1.29099445 0 1 4 21.2500000 1.70782513 1 0 4 29.7500000 2.50000000 1 1 4 35.5000000 2.64575131 ANOVA assuming A and B are random effects 7 09:57 Tuesday, October 28, 2003 The ANOVA Procedure Class Level Information Class Levels Values rep 4 1 2 3 4 a 2 0 1 b 2 0 1 Number of observations 16 ANOVA assuming A and B are random effects 8 09:57 Tuesday, October 28, 2003 The ANOVA Procedure Dependent Variable: yield Sum of Source DF Squares Mean Square F Value Pr > F Model 6 1149.000000 191.500000 82.07 <.0001 Error 9 21.000000 2.333333 Corrected Total 15 1170.000000 R-Square Coeff Var Root MSE yield Mean 0.982051 6.110101 1.527525 25.00000 Source DF Anova SS Mean Square F Value Pr > F rep 3 32.5000000 10.8333333 4.64 0.0317 a 1 930.2500000 930.2500000 398.68 <.0001 b 1 182.2500000 182.2500000 78.11 <.0001 a*b 1 4.0000000 4.0000000 1.71 0.2229 Tests of Hypotheses Using the Anova MS for a*b as an Error Term Source DF Anova SS Mean Square F Value Pr > F a 1 930.2500000 930.2500000 232.56 0.0417 b 1 182.2500000 182.2500000 45.56 0.0936 ANOVA assuming A and B are random effects 9 09:57 Tuesday, October 28, 2003 The ANOVA Procedure t Tests (LSD) for yield NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 1 Error Mean Square 4 Critical Value of t 12.70620 Least Significant Difference 12.706 Means with the same letter are not significantly different. t Grouping Mean N a A 32.625 8 1 B 17.375 8 0 ANOVA assuming A and B are random effects 10 09:57 Tuesday, October 28, 2003 The ANOVA Procedure t Tests (LSD) for yield NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 1 Error Mean Square 4 Critical Value of t 12.70620 Least Significant Difference 12.706 Means with the same letter are not significantly different. t Grouping Mean N b A 28.375 8 1 A A 21.625 8 0 ANOVA assuming A and B are random effects 11 09:57 Tuesday, October 28, 2003 The ANOVA Procedure Level of Level of ------------yield------------ a b N Mean Std Dev 0 0 4 13.5000000 1.29099445 0 1 4 21.2500000 1.70782513 1 0 4 29.7500000 2.50000000 1 1 4 35.5000000 2.64575131