The GLM Procedure Class Level Information Class Levels Values seed 2 1 2 farm 4 1 2 3 4 Number of observations 16 The GLM Procedure Dependent Variable: yield Sum of Source DF Squares Mean Square F Value Pr > F Model 7 154.4498985 22.0642712 12.23 0.0010 Error 8 14.4311175 1.8038897 Corrected Total 15 168.8810160 R-Square Coeff Var Root MSE yield Mean 0.914549 4.553523 1.343090 29.49561 Source DF Type I SS Mean Square F Value Pr > F seed 1 4.8149964 4.8149964 2.67 0.1409 farm 3 100.7858444 33.5952815 18.62 0.0006 seed*farm 3 48.8490577 16.2830192 9.03 0.0060 Source DF Type II SS Mean Square F Value Pr > F seed 1 4.8149964 4.8149964 2.67 0.1409 farm 3 100.7858444 33.5952815 18.62 0.0006 seed*farm 3 48.8490577 16.2830192 9.03 0.0060 Source DF Type III SS Mean Square F Value Pr > F seed 1 4.8149964 4.8149964 2.67 0.1409 farm 3 100.7858444 33.5952815 18.62 0.0006 seed*farm 3 48.8490577 16.2830192 9.03 0.0060 Standard Parameter Estimate Error t Value Pr > |t| Intercept 27.00339000 B 0.94970777 28.43 <.0001 seed 1 2.43996500 B 1.34308961 1.82 0.1068 seed 2 0.00000000 B . . . farm 1 4.66621000 B 1.34308961 3.47 0.0084 farm 2 6.33951500 B 1.34308961 4.72 0.0015 farm 3 1.15747500 B 1.34308961 0.86 0.4139 farm 4 0.00000000 B . . . seed*farm 1 1 -0.14021000 B 1.89941554 -0.07 0.9430 seed*farm 1 2 -7.61995000 B 1.89941554 -4.01 0.0039 seed*farm 1 3 -6.38832000 B 1.89941554 -3.36 0.0099 seed*farm 1 4 0.00000000 B . . . seed*farm 2 1 0.00000000 B . . . seed*farm 2 2 0.00000000 B . . . seed*farm 2 3 0.00000000 B . . . seed*farm 2 4 0.00000000 B . . . NOTE: The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by the letter 'B' are not uniquely estimable. The GLM Procedure Source Type III Expected Mean Square seed Var(Error) + 2 Var(seed*farm) + 8 Var(seed) farm Var(Error) + 2 Var(seed*farm) + 4 Var(farm) seed*farm Var(Error) + 2 Var(seed*farm) The GLM Procedure Tests of Hypotheses for Random Model Analysis of Variance Dependent Variable: yield Source DF Type III SS Mean Square F Value Pr > F seed 1 4.814996 4.814996 0.30 0.6244 farm 3 100.785844 33.595281 2.06 0.2836 Error: MS(seed*farm) 3 48.849058 16.283019 Source DF Type III SS Mean Square F Value Pr > F seed*farm 3 48.849058 16.283019 9.03 0.0060 Error: MS(Error) 8 14.431118 1.803890 Dependent Variable: yield Standard Parameter Estimate Error t Value Pr > |t| grand mean 29.4956125 0.33577240 87.84 <.0001 farm 1 32.8194775 0.67154480 48.87 <.0001 farm 2 30.7529125 0.67154480 45.79 <.0001 farm 3 26.1866875 0.67154480 38.99 <.0001 farm 4 28.2233725 0.67154480 42.03 <.0001 seed 1 farm 1 33.9693550 0.94970777 35.77 <.0001 seed 2 farm 1 31.6696000 0.94970777 33.35 <.0001 seed 1 farm 2 28.1629200 0.94970777 29.65 <.0001 seed 2 farm 2 33.3429050 0.94970777 35.11 <.0001 seed 1 farm 3 24.2125100 0.94970777 25.49 <.0001 seed 2 farm 3 28.1608650 0.94970777 29.65 <.0001 seed 1 farm 4 29.4433550 0.94970777 31.00 <.0001 seed 2 farm 4 27.0033900 0.94970777 28.43 <.0001 Variance Components Estimation Procedure Class Level Information Class Levels Values seed 2 1 2 farm 4 1 2 3 4 Number of observations 16 MIVQUE(0) SSQ Matrix Source seed farm seed*farm seed 64.00000 0 16.00000 farm 0 48.00000 24.00000 seed*farm 16.00000 24.00000 28.00000 Error 8.00000 12.00000 14.00000 MIVQUE(0) SSQ Matrix Source Error yield seed 8.00000 38.51997 farm 12.00000 403.14338 seed*farm 14.00000 308.89980 Error 15.00000 168.88102 MIVQUE(0) Estimates Variance Component yield Var(seed) -1.43350 Var(farm) 4.32807 Var(seed*farm) 7.23956 Var(Error) 1.80389 Variance Components Estimation Procedure Class Level Information Class Levels Values seed 2 1 2 farm 4 1 2 3 4 Number of observations 16 Dependent Variable: yield Type 1 Analysis of Variance Sum of Source DF Squares Mean Square seed 1 4.814996 4.814996 farm 3 100.785844 33.595281 seed*farm 3 48.849058 16.283019 Error 8 14.431118 1.803890 Corrected Total 15 168.881016 . Type 1 Analysis of Variance Source Expected Mean Square seed Var(Error) + 2 Var(seed*farm) + 8 Var(seed) farm Var(Error) + 2 Var(seed*farm) + 4 Var(farm) seed*farm Var(Error) + 2 Var(seed*farm) Error Var(Error) Corrected Total . Type 1 Estimates Variance Component Estimate Var(seed) -1.43350 Var(farm) 4.32807 Var(seed*farm) 7.23956 Var(Error) 1.80389 Variance Components Estimation Procedure Class Level Information Class Levels Values seed 2 1 2 farm 4 1 2 3 4 Number of observations 16 Dependent Variable: yield Maximum Likelihood Iterations Iteration Objective Var(seed) Var(farm) Var(seed*farm) 0 28.1355243967 0 3.8670472136 6.4684183704 1 28.0133585946 0 2.9814128811 5.8995935126 2 28.0121726801 0 2.9455381892 5.8071633856 3 28.0121725125 0 2.9451117110 5.8060614354 4 28.0121725125 0 2.9451117110 5.8060614354 Maximum Likelihood Iterations Iteration Var(Error) 0 1.6117423594 1 1.7821901594 2 1.8036286592 3 1.8038898028 4 1.8038898028 Convergence criteria met. Maximum Likelihood Estimates Variance Component Estimate Var(seed) 0 Var(farm) 2.94511 Var(seed*farm) 5.80606 Var(Error) 1.80389 Asymptotic Covariance Matrix of Estimates Var(seed) Var(farm) Var(seed*farm) Var(Error) Var(seed) 0 0 0 0 Var(farm) 0 25.46408955672 -11.2493358807 8.349686054E-8 Var(seed*farm) 0 -11.2493358807 22.70204763908 -0.40675211238 Var(Error) 0 8.349686054E-8 -0.40675211238 0.813504605119 Variance Components Estimation Procedure Class Level Information Class Levels Values seed 2 1 2 farm 4 1 2 3 4 Number of observations 16 Dependent Variable: yield REML Iterations Iteration Objective Var(seed) Var(farm) Var(seed*farm) 0 25.7018460564 0 4.1248503611 6.8996462617 1 25.6487590889 0 5.0757532518 5.8519819319 2 25.6485151845 0 5.0449792416 5.8063030408 3 25.6485151777 0 5.0448169729 5.8060618915 REML Iterations Iteration Var(Error) 0 1.7191918501 1 1.7943204937 2 1.8038389271 3 1.8038896940 Convergence criteria met. REML Estimates Variance Component Estimate Var(seed) 0 Var(farm) 5.04482 Var(seed*farm) 5.80606 Var(Error) 1.80389 Asymptotic Covariance Matrix of Estimates Var(seed) Var(farm) Var(seed*farm) Var(Error) Var(seed) 0 0 0 0 Var(farm) 0 52.65145774731 -11.2493385374 6.766259997E-9 Var(seed*farm) 0 -11.2493385374 22.70205318574 -0.40675224454 Var(Error) 0 6.766259997E-9 -0.40675224454 0.813504507069 The Mixed Procedure Model Information Data Set WORK.TWOWAY Dependent Variable yield 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 seed 2 1 2 farm 4 1 2 3 4 Dimensions Covariance Parameters 4 Columns in X 1 Columns in Z 14 Subjects 1 Max Obs Per Subject 16 Observations Used 16 Observations Not Used 0 Total Observations 16 Iteration History Iteration Evaluations -2 Res Log Like Criterion 0 1 81.65790800 1 3 71.00585889 0.00067943 2 1 70.98967075 0.00001855 3 1 70.98926025 0.00000002 4 1 70.98925990 0.00000000 Convergence criteria met. Covariance Parameter Estimates Cov Parm Estimate seed 0 farm 5.0448 seed*farm 5.8061 Residual 1.8039 Fitting Information Res Log Likelihood -35.5 Akaike's Information Criterion -38.5 The Mixed Procedure Fitting Information Schwarz's Bayesian Criterion -36.5 -2 Res Log Likelihood 71.0 Solution for Random Effects Std Err Effect seed farm Estimate Pred DF t Value Pr > |t| seed 1 0 . . . . seed 2 0 . . . . farm 1 1.9965 1.6650 8 1.20 0.2648 farm 2 0.7552 1.6650 8 0.45 0.6622 farm 3 -1.9875 1.6650 8 -1.19 0.2668 farm 4 -0.7642 1.6650 8 -0.46 0.6585 seed*farm 1 1 2.1442 1.5940 8 1.35 0.2155 seed*farm 1 2 -1.8072 1.5940 8 -1.13 0.2897 seed*farm 1 3 -2.8525 1.5940 8 -1.79 0.1113 seed*farm 1 4 0.6162 1.5940 8 0.39 0.7091 seed*farm 2 1 0.1536 1.5940 8 0.10 0.9256 seed*farm 2 2 2.6763 1.5940 8 1.68 0.1317 seed*farm 2 3 0.5650 1.5940 8 0.35 0.7322 seed*farm 2 4 -1.4957 1.5940 8 -0.94 0.3755 Estimates Standard Label Estimate Error DF t Value Pr > |t| grand mean 29.4956 1.4490 1 20.36 0.0313 farm 1 32.6410 0.6579 1 49.62 0.0128 farm 2 30.6854 0.6579 1 46.64 0.0136 farm 3 26.3644 0.6579 1 40.07 0.0159 farm 4 28.2917 0.6579 1 43.00 0.0148 seed 1 farm 1 33.6363 0.9073 1 37.07 0.0172 seed 2 farm 1 31.6457 0.9073 1 34.88 0.0182 seed 1 farm 2 28.4437 0.9073 1 31.35 0.0203 seed 2 farm 2 32.9271 0.9073 1 36.29 0.0175 seed 1 farm 3 24.6556 0.9073 1 27.18 0.0234 seed 2 farm 3 28.0731 0.9073 1 30.94 0.0206 seed 1 farm 4 29.3476 0.9073 1 32.35 0.0197 seed 2 farm 4 27.2357 0.9073 1 30.02 0.0212 StdErr Obs seed farm yield Pred Pred L95 U95 Resid 1 1 1 32.9892 33.6363 0.90727 31.5441 35.7284 -0.64703 2 2 1 30.8765 31.6457 0.90727 29.5536 33.7379 -0.76926 3 1 2 27.8242 28.4437 0.90727 26.3515 30.5358 -0.61947 4 2 2 31.3995 32.9271 0.90727 30.8350 35.0193 -1.52770 5 1 3 24.5781 24.6556 0.90727 22.5634 26.7478 -0.07757 6 2 3 29.1700 28.0731 0.90727 25.9809 30.1653 1.09689 7 1 4 30.1395 29.3476 0.90727 27.2555 31.4398 0.79182 8 2 4 26.6909 27.2357 0.90727 25.1436 29.3279 -0.54483 9 1 1 34.9495 33.6363 0.90727 31.5441 35.7284 1.31320 10 2 1 32.4627 31.6457 0.90727 29.5536 33.7379 0.81698 11 1 2 28.5017 28.4437 0.90727 26.3515 30.5358 0.05801 12 2 2 35.2864 32.9271 0.90727 30.8350 35.0193 2.35921 13 1 3 23.8470 24.6556 0.90727 22.5634 26.7478 -0.80867 14 2 3 27.1518 28.0731 0.90727 25.9809 30.1653 -0.92134 15 1 4 28.7473 29.3476 0.90727 27.2555 31.4398 -0.60037 16 2 4 27.3159 27.2357 0.90727 25.1436 29.3279 0.08013