Print all the data for fruit variety and pesticide 1 08:34 Monday, July 14, 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 Two Way without interaction by GLM 08:34 Monday, July 14, 2008 2 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 Two Way without interaction by GLM 08:34 Monday, July 14, 2008 3 The GLM Procedure Dependent Variable: y Sum of Source DF Squares Mean Square F Value Pr > F Model 5 6223.541667 1244.708333 23.23 <.0001 Error 18 964.416667 53.578704 Corrected Total 23 7187.958333 R-Square Coeff Var Root MSE y Mean 0.865829 11.91010 7.319748 61.45833 Source DF Type I SS Mean Square F Value Pr > F variety 2 3996.083333 1998.041667 37.29 <.0001 pestcide 3 2227.458333 742.486111 13.86 <.0001 Source DF Type III SS Mean Square F Value Pr > F variety 2 3996.083333 1998.041667 37.29 <.0001 pestcide 3 2227.458333 742.486111 13.86 <.0001 Twoway without intercation by MIXED with RANDOM variety 4 08:34 Monday, July 14, 2008 The Mixed Procedure Model Information Data Set WORK.FRUIT Dependent Variable y 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 variety 3 1 2 3 pestcide 4 1 2 3 4 Dimensions Covariance Parameters 2 Columns in X 5 Columns in Z 3 Subjects 1 Max Obs Per Subject 24 Number of Observations Number of Observations Read 24 Number of Observations Used 24 Number of Observations Not Used 0 Iteration History Iteration Evaluations -2 Res Log Like Criterion 0 1 174.19517016 1 1 150.78515489 0.00000000 Convergence criteria met. Covariance Parameter Estimates Cov Parm Estimate variety 243.06 Residual 53.5787 Twoway without intercation by MIXED with RANDOM variety 5 08:34 Monday, July 14, 2008 The Mixed Procedure Fit Statistics -2 Res Log Likelihood 150.8 AIC (smaller is better) 154.8 AICC (smaller is better) 155.5 BIC (smaller is better) 153.0 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F pestcide 3 18 13.86 <.0001 Duncan Multiple comaprisons for the main effects 6 08:34 Monday, July 14, 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 7 08:34 Monday, July 14, 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 8 08:34 Monday, July 14, 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 9 08:34 Monday, July 14, 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 pseticide with PROC MIXED 08:34 Monday, July 14, 2008 10 The Mixed Procedure Model Information Data Set WORK.FRUIT Dependent Variable y Covariance Structure Variance Components Estimation Method Type 3 Residual Variance Method Factor Fixed Effects SE Method Model-Based Degrees of Freedom Method Containment Class Level Information Class Levels Values variety 3 1 2 3 pestcide 4 1 2 3 4 Dimensions Covariance Parameters 3 Columns in X 5 Columns in Z 15 Subjects 1 Max Obs Per Subject 24 Number of Observations Number of Observations Read 24 Number of Observations Used 24 Number of Observations Not Used 0 Type 3 Analysis of Variance Sum of Source DF Squares Mean Square pestcide 3 2227.458333 742.486111 variety 2 3996.083333 1998.041667 variety*pestcide 6 456.916667 76.152778 Residual 12 507.500000 42.291667 Type 3 Analysis of Variance Source Expected Mean Square Error Term pestcide Var(Residual) + 2 MS(variety*pestcide) Var(variety*pestcide) + Q(pestcide) variety Var(Residual) + 2 MS(variety*pestcide) Var(variety*pestcide) + 8 Var(variety) variety*pestcide Var(Residual) + 2 MS(Residual) Var(variety*pestcide) pseticide with PROC MIXED 08:34 Monday, July 14, 2008 11 The Mixed Procedure Type 3 Analysis of Variance Source Expected Mean Square Error Term Residual Var(Residual) . Type 3 Analysis of Variance Error Source DF F Value Pr > F pestcide 6 9.75 0.0101 variety 6 26.24 0.0011 variety*pestcide 12 1.80 0.1817 Residual . . . Covariance Parameter Estimates Cov Parm Estimate variety 240.24 variety*pestcide 16.9306 Residual 42.2917 Fit Statistics -2 Res Log Likelihood 150.1 AIC (smaller is better) 156.1 AICC (smaller is better) 157.6 BIC (smaller is better) 153.4 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F pestcide 3 6 9.75 0.0101 Least Squares Means Standard Effect pestcide Estimate Error DF t Value Pr > |t| Alpha pestcide 1 53.0000 9.6318 6 5.50 0.0015 0.05 pestcide 2 67.8333 9.6318 6 7.04 0.0004 0.05 pestcide 3 51.1667 9.6318 6 5.31 0.0018 0.05 pestcide 4 73.8333 9.6318 6 7.67 0.0003 0.05 pseticide with PROC MIXED 08:34 Monday, July 14, 2008 12 The Mixed Procedure Least Squares Means Effect pestcide Lower Upper pestcide 1 29.4319 76.5681 pestcide 2 44.2653 91.4014 pestcide 3 27.5986 74.7347 pestcide 4 50.2653 97.4014 Differences of Least Squares Means Standard Effect pestcide _pestcide Estimate Error DF t Value Pr > |t| pestcide 1 2 -14.8333 5.0383 6 -2.94 0.0258 pestcide 1 3 1.8333 5.0383 6 0.36 0.7284 pestcide 1 4 -20.8333 5.0383 6 -4.14 0.0061 pestcide 2 3 16.6667 5.0383 6 3.31 0.0162 pestcide 2 4 -6.0000 5.0383 6 -1.19 0.2787 pestcide 3 4 -22.6667 5.0383 6 -4.50 0.0041 Differences of Least Squares Means Effect pestcide _pestcide Alpha Lower Upper pestcide 1 2 0.05 -27.1616 -2.5051 pestcide 1 3 0.05 -10.4949 14.1616 pestcide 1 4 0.05 -33.1616 -8.5051 pestcide 2 3 0.05 4.3384 28.9949 pestcide 2 4 0.05 -18.3282 6.3282 pestcide 3 4 0.05 -34.9949 -10.3384