Print all the data for Ex9.1 08:30 Thursday, July 10, 2008 1 Obs drug plot Y 1 1 1 56 2 1 2 48 3 1 3 66 4 1 4 62 5 2 1 83 6 2 2 78 7 2 3 94 8 2 4 93 9 3 1 80 10 3 2 72 11 3 3 83 12 3 4 85 Example 9.1, both factors are in model 08:30 Thursday, July 10, 2008 2 The GLM Procedure Class Level Information Class Levels Values drug 3 1 2 3 plot 4 1 2 3 4 Number of Observations Read 12 Number of Observations Used 12 Example 9.1, both factors are in model 08:30 Thursday, July 10, 2008 3 The GLM Procedure Dependent Variable: Y Sum of Source DF Squares Mean Square F Value Pr > F Model 5 2270.000000 454.000000 104.77 <.0001 Error 6 26.000000 4.333333 Corrected Total 11 2296.000000 R-Square Coeff Var Root MSE Y Mean 0.988676 2.775555 2.081666 75.00000 Source DF Type I SS Mean Square F Value Pr > F drug 2 1832.000000 916.000000 211.38 <.0001 plot 3 438.000000 146.000000 33.69 0.0004 Source DF Type III SS Mean Square F Value Pr > F drug 2 1832.000000 916.000000 211.38 <.0001 plot 3 438.000000 146.000000 33.69 0.0004 Example 9.1, only plot in model 08:30 Thursday, July 10, 2008 4 The GLM Procedure Class Level Information Class Levels Values drug 3 1 2 3 plot 4 1 2 3 4 Number of Observations Read 12 Number of Observations Used 12 Example 9.1, only plot in model 08:30 Thursday, July 10, 2008 5 The GLM Procedure Dependent Variable: Y Sum of Source DF Squares Mean Square F Value Pr > F Model 3 438.000000 146.000000 0.63 0.6166 Error 8 1858.000000 232.250000 Corrected Total 11 2296.000000 R-Square Coeff Var Root MSE Y Mean 0.190767 20.31967 15.23975 75.00000 Source DF Type I SS Mean Square F Value Pr > F plot 3 438.0000000 146.0000000 0.63 0.6166 Source DF Type III SS Mean Square F Value Pr > F plot 3 438.0000000 146.0000000 0.63 0.6166 Example 9.1, only drug in model 08:30 Thursday, July 10, 2008 6 The GLM Procedure Class Level Information Class Levels Values drug 3 1 2 3 plot 4 1 2 3 4 Number of Observations Read 12 Number of Observations Used 12 Example 9.1, only drug in model 08:30 Thursday, July 10, 2008 7 The GLM Procedure Dependent Variable: Y Sum of Source DF Squares Mean Square F Value Pr > F Model 2 1832.000000 916.000000 17.77 0.0007 Error 9 464.000000 51.555556 Corrected Total 11 2296.000000 R-Square Coeff Var Root MSE Y Mean 0.797909 9.573626 7.180220 75.00000 Source DF Type I SS Mean Square F Value Pr > F drug 2 1832.000000 916.000000 17.77 0.0007 Source DF Type III SS Mean Square F Value Pr > F drug 2 1832.000000 916.000000 17.77 0.0007 One datum in Example 9.1 is deleted 08:30 Thursday, July 10, 2008 8 Obs drug p1 p2 p3 p4 plot Y 1 1 56 48 66 62 2 48 2 1 56 48 66 62 3 66 3 1 56 48 66 62 4 62 4 2 83 78 94 93 1 83 5 2 83 78 94 93 2 78 6 2 83 78 94 93 3 94 7 2 83 78 94 93 4 93 8 3 80 72 83 85 1 80 9 3 80 72 83 85 2 72 10 3 80 72 83 85 3 83 11 3 80 72 83 85 4 85 Incomplete data for Example 9.1, model = drug plot 9 08:30 Thursday, July 10, 2008 The GLM Procedure Class Level Information Class Levels Values drug 3 1 2 3 plot 4 1 2 3 4 Number of Observations Read 11 Number of Observations Used 11 Incomplete data for Example 9.1, model = drug plot 10 08:30 Thursday, July 10, 2008 The GLM Procedure Dependent Variable: Y Sum of Source DF Squares Mean Square F Value Pr > F Model 5 1876.181818 375.236364 72.16 0.0001 Error 5 26.000000 5.200000 Corrected Total 10 1902.181818 R-Square Coeff Var Root MSE Y Mean 0.986331 2.972021 2.280351 76.72727 Source DF Type I SS Mean Square F Value Pr > F drug 2 1443.515152 721.757576 138.80 <.0001 plot 3 432.666667 144.222222 27.74 0.0015 Source DF Type III SS Mean Square F Value Pr > F drug 2 1398.500000 699.250000 134.47 <.0001 plot 3 432.666667 144.222222 27.74 0.0015 Incomplete data for Example 9.1, model = plot grug 11 08:30 Thursday, July 10, 2008 The GLM Procedure Class Level Information Class Levels Values drug 3 1 2 3 plot 4 1 2 3 4 Number of Observations Read 11 Number of Observations Used 11 Incomplete data for Example 9.1, model = plot grug 12 08:30 Thursday, July 10, 2008 The GLM Procedure Dependent Variable: Y Sum of Source DF Squares Mean Square F Value Pr > F Model 5 1876.181818 375.236364 72.16 0.0001 Error 5 26.000000 5.200000 Corrected Total 10 1902.181818 R-Square Coeff Var Root MSE Y Mean 0.986331 2.972021 2.280351 76.72727 Source DF Type I SS Mean Square F Value Pr > F plot 3 477.681818 159.227273 30.62 0.0012 drug 2 1398.500000 699.250000 134.47 <.0001 Source DF Type III SS Mean Square F Value Pr > F plot 3 432.666667 144.222222 27.74 0.0015 drug 2 1398.500000 699.250000 134.47 <.0001 Incomplete data for Example 9.1, only plot in model 13 08:30 Thursday, July 10, 2008 The GLM Procedure Class Level Information Class Levels Values drug 3 1 2 3 plot 4 1 2 3 4 Number of Observations Read 11 Number of Observations Used 11 Incomplete data for Example 9.1, only plot in model 14 08:30 Thursday, July 10, 2008 The GLM Procedure Dependent Variable: Y Sum of Source DF Squares Mean Square F Value Pr > F Model 3 477.681818 159.227273 0.78 0.5404 Error 7 1424.500000 203.500000 Corrected Total 10 1902.181818 R-Square Coeff Var Root MSE Y Mean 0.251123 18.59227 14.26534 76.72727 Source DF Type I SS Mean Square F Value Pr > F plot 3 477.6818182 159.2272727 0.78 0.5404 Source DF Type III SS Mean Square F Value Pr > F plot 3 477.6818182 159.2272727 0.78 0.5404 Incomplete data for Example 9.1, only drug in model 15 08:30 Thursday, July 10, 2008 The GLM Procedure Class Level Information Class Levels Values drug 3 1 2 3 plot 4 1 2 3 4 Number of Observations Read 11 Number of Observations Used 11 Incomplete data for Example 9.1, only drug in model 16 08:30 Thursday, July 10, 2008 The GLM Procedure Dependent Variable: Y Sum of Source DF Squares Mean Square F Value Pr > F Model 2 1443.515152 721.757576 12.59 0.0034 Error 8 458.666667 57.333333 Corrected Total 10 1902.181818 R-Square Coeff Var Root MSE Y Mean 0.758873 9.868561 7.571878 76.72727 Source DF Type I SS Mean Square F Value Pr > F drug 2 1443.515152 721.757576 12.59 0.0034 Source DF Type III SS Mean Square F Value Pr > F drug 2 1443.515152 721.757576 12.59 0.0034 Print all the data for fruit variety and pesticide 17 08:30 Thursday, July 10, 2008 Obs variety pestcide y 1 1 1 49 2 1 1 39 3 1 2 50 4 1 2 55 5 1 3 43 6 1 3 38 7 1 4 53 8 1 4 48 9 2 1 55 10 2 1 41 11 2 2 67 12 2 2 58 13 2 3 53 14 2 3 42 15 2 4 85 16 2 4 73 17 3 1 66 18 3 1 68 19 3 2 85 20 3 2 92 21 3 3 69 22 3 3 62 23 3 4 85 24 3 4 99 Duncan Multiple comaprisons for the main effects 18 08:30 Thursday, July 10, 2008 The GLM Procedure Class Level Information Class Levels Values variety 3 1 2 3 pestcide 4 1 2 3 4 Number of Observations Read 24 Number of Observations Used 24 Duncan Multiple comaprisons for the main effects 19 08:30 Thursday, July 10, 2008 The GLM Procedure Dependent Variable: y Sum of Source DF Squares Mean Square F Value Pr > F Model 11 6680.458333 607.314394 14.36 <.0001 Error 12 507.500000 42.291667 Corrected Total 23 7187.958333 R-Square Coeff Var Root MSE y Mean 0.929396 10.58149 6.503204 61.45833 Source DF Type I SS Mean Square F Value Pr > F variety 2 3996.083333 1998.041667 47.24 <.0001 pestcide 3 2227.458333 742.486111 17.56 0.0001 variety*pestcide 6 456.916667 76.152778 1.80 0.1817 Source DF Type III SS Mean Square F Value Pr > F variety 2 3996.083333 1998.041667 47.24 <.0001 pestcide 3 2227.458333 742.486111 17.56 0.0001 variety*pestcide 6 456.916667 76.152778 1.80 0.1817 Duncan Multiple comaprisons for the main effects 20 08:30 Thursday, July 10, 2008 The GLM Procedure Duncan's Multiple Range Test for y NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.01 Error Degrees of Freedom 12 Error Mean Square 42.29167 Number of Means 2 3 Critical Range 9.93 10.36 Means with the same letter are not significantly different. D u n c a n G r o u p i n g Mean N variety A 78.250 8 3 B 59.250 8 2 C 46.875 8 1 Duncan Multiple comaprisons for the main effects 21 08:30 Thursday, July 10, 2008 The GLM Procedure Duncan's Multiple Range Test for y NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.01 Error Degrees of Freedom 12 Error Mean Square 42.29167 Number of Means 2 3 4 Critical Range 11.47 11.96 12.27 Means with the same letter are not significantly different. D u n c a n G r o u p i n g Mean N pestcide A 73.833 6 4 A A 67.833 6 2 B 53.000 6 1 B B 51.167 6 3 Duncan Multiple comaprisons for the main effects 22 08:30 Thursday, July 10, 2008 Obs variety pestcide _TYPE_ _FREQ_ mu 1 1 1 0 2 44.0 2 1 2 0 2 52.5 3 1 3 0 2 40.5 4 1 4 0 2 50.5 5 2 1 0 2 48.0 6 2 2 0 2 62.5 7 2 3 0 2 47.5 8 2 4 0 2 79.0 9 3 1 0 2 67.0 10 3 2 0 2 88.5 11 3 3 0 2 65.5 12 3 4 0 2 92.0 Plot of the means for the fruit data 08:30 Thursday, July 10, 2008 23 Plot of mu*pestcide. Symbol is value of variety. mu | | 100 + | | | | | | 3 90 + | 3 | | | | | 80 + | 2 | | | | | 70 + | | 3 | 3 | | 2 | 60 + | | | | | 1 | 50 + 1 | 2 | 2 | | 1 | | 40 + 1 | ---+-----------------+-----------------+-----------------+-- 1 2 3 4 pestcide Duncan Multiple comaprisons for the interaction 24 08:30 Thursday, July 10, 2008 The GLM Procedure Class Level Information Class Levels Values combined 12 11 12 13 14 21 22 23 24 31 32 33 34 Number of Observations Read 24 Number of Observations Used 24 Duncan Multiple comaprisons for the interaction 25 08:30 Thursday, July 10, 2008 The GLM Procedure Dependent Variable: y Sum of Source DF Squares Mean Square F Value Pr > F Model 11 6680.458333 607.314394 14.36 <.0001 Error 12 507.500000 42.291667 Corrected Total 23 7187.958333 R-Square Coeff Var Root MSE y Mean 0.929396 10.58149 6.503204 61.45833 Source DF Type I SS Mean Square F Value Pr > F combined 11 6680.458333 607.314394 14.36 <.0001 Source DF Type III SS Mean Square F Value Pr > F combined 11 6680.458333 607.314394 14.36 <.0001 Duncan Multiple comaprisons for the interaction 26 08:30 Thursday, July 10, 2008 The GLM Procedure Duncan's Multiple Range Test for y NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error rate. Alpha 0.01 Error Degrees of Freedom 12 Error Mean Square 42.29167 Number of Means 2 3 4 5 6 7 Critical Range 19.86 20.71 21.25 21.64 21.92 22.14 Number of Means 8 9 10 11 12 Critical Range 22.31 22.45 22.56 22.66 22.73 Means with the same letter are not significantly different. Duncan Grouping Mean N combined A 92.000 2 34 A A 88.500 2 32 A B A 79.000 2 24 B B C 67.000 2 31 B C B C D 65.500 2 33 B C D B E C D 62.500 2 22 E C D E C D 52.500 2 12 E C D E C D 50.500 2 14 E C D E C D 48.000 2 21 E C D E C D 47.500 2 23 E D E D 44.000 2 11 E E 40.500 2 13 Estimate pesticide (1+2) - (3+4) 08:30 Thursday, July 10, 2008 27 The GLM Procedure Class Level Information Class Levels Values variety 3 1 2 3 pestcide 4 1 2 3 4 Number of Observations Read 24 Number of Observations Used 24 Estimate pesticide (1+2) - (3+4) 08:30 Thursday, July 10, 2008 28 The GLM Procedure Coefficients for Contrast Variety 1 vs 2 Row 1 Intercept 0 variety 1 1 variety 2 -1 variety 3 0 pestcide 1 0 pestcide 2 0 pestcide 3 0 pestcide 4 0 variety*pestcide 1 1 0.25 variety*pestcide 1 2 0.25 variety*pestcide 1 3 0.25 variety*pestcide 1 4 0.25 variety*pestcide 2 1 -0.25 variety*pestcide 2 2 -0.25 variety*pestcide 2 3 -0.25 variety*pestcide 2 4 -0.25 variety*pestcide 3 1 0 variety*pestcide 3 2 0 variety*pestcide 3 3 0 variety*pestcide 3 4 0 Estimate pesticide (1+2) - (3+4) 08:30 Thursday, July 10, 2008 29 The GLM Procedure Coefficients for Contrast Variety 1 vs 2 Row 1 Intercept 0 variety 1 0.5 variety 2 -0.5 variety 3 0 pestcide 1 0 pestcide 2 0 pestcide 3 0 pestcide 4 0 variety*pestcide 1 1 0.125 variety*pestcide 1 2 0.125 variety*pestcide 1 3 0.125 variety*pestcide 1 4 0.125 variety*pestcide 2 1 -0.125 variety*pestcide 2 2 -0.125 variety*pestcide 2 3 -0.125 variety*pestcide 2 4 -0.125 variety*pestcide 3 1 0 variety*pestcide 3 2 0 variety*pestcide 3 3 0 variety*pestcide 3 4 0 Estimate pesticide (1+2) - (3+4) 08:30 Thursday, July 10, 2008 30 The GLM Procedure Coefficients for Estimate pesticide 1+2 vs 3+4 Row 1 Intercept 0 variety 1 0 variety 2 0 variety 3 0 pestcide 1 1 pestcide 2 1 pestcide 3 -1 pestcide 4 -1 variety*pestcide 1 1 0.3333333333 variety*pestcide 1 2 0.3333333333 variety*pestcide 1 3 -0.333333333 variety*pestcide 1 4 -0.333333333 variety*pestcide 2 1 0.3333333333 variety*pestcide 2 2 0.3333333333 variety*pestcide 2 3 -0.333333333 variety*pestcide 2 4 -0.333333333 variety*pestcide 3 1 0.3333333333 variety*pestcide 3 2 0.3333333333 variety*pestcide 3 3 -0.333333333 variety*pestcide 3 4 -0.333333333 Estimate pesticide (1+2) - (3+4) 08:30 Thursday, July 10, 2008 31 The GLM Procedure Coefficients for Estimate pest Av(1+2) - Av(3+4) Row 1 Intercept 0 variety 1 0 variety 2 0 variety 3 0 pestcide 1 0.5 pestcide 2 0.5 pestcide 3 -0.5 pestcide 4 -0.5 variety*pestcide 1 1 0.1666666667 variety*pestcide 1 2 0.1666666667 variety*pestcide 1 3 -0.166666667 variety*pestcide 1 4 -0.166666667 variety*pestcide 2 1 0.1666666667 variety*pestcide 2 2 0.1666666667 variety*pestcide 2 3 -0.166666667 variety*pestcide 2 4 -0.166666667 variety*pestcide 3 1 0.1666666667 variety*pestcide 3 2 0.1666666667 variety*pestcide 3 3 -0.166666667 variety*pestcide 3 4 -0.166666667 Estimate pesticide (1+2) - (3+4) 08:30 Thursday, July 10, 2008 32 The GLM Procedure Dependent Variable: y Sum of Source DF Squares Mean Square F Value Pr > F Model 11 6680.458333 607.314394 14.36 <.0001 Error 12 507.500000 42.291667 Corrected Total 23 7187.958333 R-Square Coeff Var Root MSE y Mean 0.929396 10.58149 6.503204 61.45833 Source DF Type I SS Mean Square F Value Pr > F variety 2 3996.083333 1998.041667 47.24 <.0001 pestcide 3 2227.458333 742.486111 17.56 0.0001 variety*pestcide 6 456.916667 76.152778 1.80 0.1817 Source DF Type III SS Mean Square F Value Pr > F variety 2 3996.083333 1998.041667 47.24 <.0001 pestcide 3 2227.458333 742.486111 17.56 0.0001 variety*pestcide 6 456.916667 76.152778 1.80 0.1817 Contrast DF Contrast SS Mean Square F Value Pr > F Variety 1 vs 2 1 612.5625000 612.5625000 14.48 0.0025 Variety 1 vs 2 1 612.5625000 612.5625000 14.48 0.0025 Standard Parameter Estimate Error t Value Pr > |t| pesticide 1+2 vs 3+4 -4.16666667 5.30984411 -0.78 0.4478 pest Av(1+2) - Av(3+4) -2.08333333 2.65492205 -0.78 0.4478