printout of data 12:34 Wednesday, October 22, 2003 1 Obs square row column trt yield 1 1 1 1 b 41 2 1 1 2 c 25 3 1 1 3 a 15 4 1 2 1 a 20 5 1 2 2 b 32 6 1 2 3 c 24 7 1 3 1 c 22 8 1 3 2 a 12 9 1 3 3 b 21 10 2 1 1 c 27 11 2 1 2 b 28 12 2 1 3 a 3 13 2 2 1 a 4 14 2 2 2 c 17 15 2 2 3 b 9 16 2 3 1 b 22 17 2 3 2 a 4 18 2 3 3 c 17 19 3 1 1 b 43 20 3 1 2 c 27 21 3 1 3 a 17 22 3 2 1 a 22 23 3 2 2 b 34 24 3 2 3 c 26 25 3 3 1 c 24 26 3 3 2 a 14 27 3 3 3 b 23 anova of each individual square 2 12:34 Wednesday, October 22, 2003 ------------------------------------------- square=1 ------------------------------------------- The ANOVA Procedure Class Level Information Class Levels Values row 3 1 2 3 column 3 1 2 3 trt 3 a b c Number of observations 9 anova of each individual square 3 12:34 Wednesday, October 22, 2003 ------------------------------------------- square=1 ------------------------------------------- The ANOVA Procedure Dependent Variable: yield Sum of Source DF Squares Mean Square F Value Pr > F Model 6 584.6666667 97.4444444 9.04 0.1029 Error 2 21.5555556 10.7777778 Corrected Total 8 606.2222222 R-Square Coeff Var Root MSE yield Mean 0.964443 13.93706 3.282953 23.55556 Source DF Anova SS Mean Square F Value Pr > F row 2 126.8888889 63.4444444 5.89 0.1452 column 2 89.5555556 44.7777778 4.15 0.1940 trt 2 368.2222222 184.1111111 17.08 0.0553 anova of each individual square 4 12:34 Wednesday, October 22, 2003 ------------------------------------------- square=2 ------------------------------------------- The ANOVA Procedure Class Level Information Class Levels Values row 3 1 2 3 column 3 1 2 3 trt 3 a b c Number of observations 9 anova of each individual square 5 12:34 Wednesday, October 22, 2003 ------------------------------------------- square=2 ------------------------------------------- The ANOVA Procedure Dependent Variable: yield Sum of Source DF Squares Mean Square F Value Pr > F Model 6 775.3333333 129.2222222 17.36 0.0555 Error 2 14.8888889 7.4444444 Corrected Total 8 790.2222222 R-Square Coeff Var Root MSE yield Mean 0.981159 18.74508 2.728451 14.55556 Source DF Anova SS Mean Square F Value Pr > F row 2 130.8888889 65.4444444 8.79 0.1021 column 2 110.2222222 55.1111111 7.40 0.1190 trt 2 534.2222222 267.1111111 35.88 0.0271 anova of each individual square 6 12:34 Wednesday, October 22, 2003 ------------------------------------------- square=3 ------------------------------------------- The ANOVA Procedure Class Level Information Class Levels Values row 3 1 2 3 column 3 1 2 3 trt 3 a b c Number of observations 9 anova of each individual square 7 12:34 Wednesday, October 22, 2003 ------------------------------------------- square=3 ------------------------------------------- The ANOVA Procedure Dependent Variable: yield Sum of Source DF Squares Mean Square F Value Pr > F Model 6 584.6666667 97.4444444 9.04 0.1029 Error 2 21.5555556 10.7777778 Corrected Total 8 606.2222222 R-Square Coeff Var Root MSE yield Mean 0.964443 12.84634 3.282953 25.55556 Source DF Anova SS Mean Square F Value Pr > F row 2 126.8888889 63.4444444 5.89 0.1452 column 2 89.5555556 44.7777778 4.15 0.1940 trt 2 368.2222222 184.1111111 17.08 0.0553 anova combined across squares assuming square and trt are fixed effects 8 12:34 Wednesday, October 22, 2003 The ANOVA Procedure Class Level Information Class Levels Values square 3 1 2 3 row 3 1 2 3 column 3 1 2 3 trt 3 a b c Number of observations 27 anova combined across squares assuming square and trt are fixed effects 9 12:34 Wednesday, October 22, 2003 The ANOVA Procedure Dependent Variable: yield Sum of Source DF Squares Mean Square F Value Pr > F Model 20 2562.666667 128.133333 13.26 0.0021 Error 6 58.000000 9.666667 Corrected Total 26 2620.666667 R-Square Coeff Var Root MSE yield Mean 0.977868 14.65033 3.109126 21.22222 Source DF Anova SS Mean Square F Value Pr > F square 2 618.000000 309.000000 31.97 0.0006 row(square) 6 384.666667 64.111111 6.63 0.0183 column(square) 6 289.333333 48.222222 4.99 0.0357 trt 2 1174.222222 587.111111 60.74 0.0001 square*trt 4 96.444444 24.111111 2.49 0.1522 anova combined across squares assuming square and trt are fixed effects 10 12:34 Wednesday, October 22, 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 6 Error Mean Square 9.666667 Critical Value of t 2.44691 Least Significant Difference 3.5863 Means with the same letter are not significantly different. t Grouping Mean N trt A 28.111 9 b B 23.222 9 c C 12.333 9 a anova combined across squares assuming square and trt are fixed effects 11 12:34 Wednesday, October 22, 2003 The ANOVA Procedure Level of Level of ------------yield------------ square trt N Mean Std Dev 1 a 3 15.6666667 4.0414519 1 b 3 31.3333333 10.0166528 1 c 3 23.6666667 1.5275252 2 a 3 3.6666667 0.5773503 2 b 3 19.6666667 9.7125349 2 c 3 20.3333333 5.7735027 3 a 3 17.6666667 4.0414519 3 b 3 33.3333333 10.0166528 3 c 3 25.6666667 1.5275252 anova combined across squares assuming square random and trt fixed 12 12:34 Wednesday, October 22, 2003 The ANOVA Procedure Class Level Information Class Levels Values square 3 1 2 3 row 3 1 2 3 column 3 1 2 3 trt 3 a b c Number of observations 27 anova combined across squares assuming square random and trt fixed 13 12:34 Wednesday, October 22, 2003 The ANOVA Procedure Dependent Variable: yield Sum of Source DF Squares Mean Square F Value Pr > F Model 20 2562.666667 128.133333 13.26 0.0021 Error 6 58.000000 9.666667 Corrected Total 26 2620.666667 R-Square Coeff Var Root MSE yield Mean 0.977868 14.65033 3.109126 21.22222 Source DF Anova SS Mean Square F Value Pr > F square 2 618.000000 309.000000 31.97 0.0006 row(square) 6 384.666667 64.111111 6.63 0.0183 column(square) 6 289.333333 48.222222 4.99 0.0357 trt 2 1174.222222 587.111111 60.74 0.0001 square*trt 4 96.444444 24.111111 2.49 0.1522 Tests of Hypotheses Using the Anova MS for square*trt as an Error Term Source DF Anova SS Mean Square F Value Pr > F trt 2 1174.222222 587.111111 24.35 0.0058 anova combined across squares assuming square random and trt fixed 14 12:34 Wednesday, October 22, 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 4 Error Mean Square 24.11111 Critical Value of t 2.77645 Least Significant Difference 6.4268 Means with the same letter are not significantly different. t Grouping Mean N trt A 28.111 9 b A A 23.222 9 c B 12.333 9 a anova combined across squares assuming square random and trt fixed 15 12:34 Wednesday, October 22, 2003 The ANOVA Procedure Level of Level of ------------yield------------ square trt N Mean Std Dev 1 a 3 15.6666667 4.0414519 1 b 3 31.3333333 10.0166528 1 c 3 23.6666667 1.5275252 2 a 3 3.6666667 0.5773503 2 b 3 19.6666667 9.7125349 2 c 3 20.3333333 5.7735027 3 a 3 17.6666667 4.0414519 3 b 3 33.3333333 10.0166528 3 c 3 25.6666667 1.5275252