General Linear Models Procedure Class Level Information Class Levels Values ROW 2 1 2 COL 3 1 2 3 Number of observations in data set = 14 General Linear Models Procedure Dependent Variable: Y Sum of Mean Source DF Squares Square F Value Pr > F Model 5 124.54761905 24.90952381 6.50 0.0106 Error 8 30.66666667 3.83333333 Corrected Total 13 155.21428571 R-Square C.V. Root MSE Y Mean 0.802424 13.37096 1.9578900 14.642857 Source DF Type I SS Mean Square F Value Pr > F ROW 1 0.64285714 0.64285714 0.17 0.6929 COL 2 14.75966387 7.37983193 1.93 0.2077 ROW*COL 2 109.14509804 54.57254902 14.24 0.0023 Source DF Type II SS Mean Square F Value Pr > F ROW 1 0.18823529 0.18823529 0.05 0.8302 COL 2 14.75966387 7.37983193 1.93 0.2077 ROW*COL 2 109.14509804 54.57254902 14.24 0.0023 Source DF Type III SS Mean Square F Value Pr > F ROW 1 0.16666667 0.16666667 0.04 0.8400 COL 2 8.90980392 4.45490196 1.16 0.3605 ROW*COL 2 109.14509804 54.57254902 14.24 0.0023 T for H0: Pr > |T| Std Error of Parameter Estimate Parameter=0 Estimate INTERCEPT 12.00000000 B 8.67 0.0001 1.38443731 ROW 1 8.00000000 B 4.09 0.0035 1.95789002 2 0.00000000 B . . . COL 1 5.00000000 B 2.55 0.0340 1.95789002 2 3.33333333 B 1.87 0.0992 1.78730088 3 0.00000000 B . . . ROW*COL 1 1 -14.00000000 B -5.28 0.0007 2.65099562 1 2 -9.33333333 B -3.52 0.0078 2.65099562 1 3 0.00000000 B . . . 2 1 0.00000000 B . . . 2 2 0.00000000 B . . . 2 3 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. Estimates followed by the letter 'B' are biased, and are not unique estimators of the parameters. General Linear Models Procedure Source Type III Expected Mean Square ROW Var(Error) + 2.25 Var(ROW*COL) + 6.75 Var(ROW) COL Var(Error) + 2.2588 Var(ROW*COL) + 4.5176 Var(COL) ROW*COL Var(Error) + 2.2588 Var(ROW*COL) General Linear Models Procedure Tests of Hypotheses for Random Model Analysis of Variance Dependent Variable: Y Source: ROW Error: 0.9961*MS(ROW*COL) + 0.0039*MS(Error) Denominator Denominator DF Type III MS DF MS F Value Pr > F 1 0.1666666667 2.00 54.374348958 0.003065 0.9609 Source: COL Error: MS(ROW*COL) Denominator Denominator DF Type III MS DF MS F Value Pr > F 2 4.4549019608 2 54.57254902 0.0816 0.9245 Source: ROW*COL Error: MS(Error) Denominator Denominator DF Type III MS DF MS F Value Pr > F 2 54.57254902 8 3.8333333333 14.2363 0.0023 Dependent Variable: Y T for H0: Pr > |T| Std Error of Parameter Estimate Parameter=0 Estimate grand mean 14.8888889 27.94 0.0001 0.53287017 row 1 col 1 11.0000000 9.73 0.0001 1.13038833 row 1 col 2 14.0000000 10.11 0.0001 1.38443731 row 1 col 3 20.0000000 14.45 0.0001 1.38443731 row 2 col 1 17.0000000 12.28 0.0001 1.38443731 row 2 col 2 15.3333333 13.56 0.0001 1.13038833 row 2 col 3 12.0000000 8.67 0.0001 1.38443731 Variance Components Estimation Procedure Class Level Information Class Levels Values ROW 2 1 2 COL 3 1 2 3 Number of observations in data set = 14 MIVQUE(0) Variance Component Estimation Procedure SSQ Matrix Source ROW COL ROW*COL ROW 49.00000000 1.00000000 17.00000000 COL 1.00000000 43.36734694 22.30612245 ROW*COL 17.00000000 22.30612245 27.61224490 Error 7.00000000 9.28571429 11.57142857 Source Error Y ROW 7.00000000 4.50000000 COL 9.28571429 68.70408163 ROW*COL 11.57142857 290.33673469 Error 13.00000000 155.21428571 Estimate Variance Component Y Var(ROW) -7.99544866 Var(COL) -10.54946171 Var(ROW*COL) 22.31965572 Var(Error) 3.91318551 Variance Components Estimation Procedure Class Level Information Class Levels Values ROW 2 1 2 COL 3 1 2 3 Number of observations in data set = 14 Variance Components Estimation Procedure Dependent Variable: Y Source DF Type I SS Type I MS ROW 1 0.64285714 0.64285714 COL 2 14.75966387 7.37983193 ROW*COL 2 109.14509804 54.57254902 Error 8 30.66666667 3.83333333 Corrected Total 13 155.21428571 Source Expected Mean Square ROW Var(Error) + 2.4286 Var(ROW*COL) + 0.1429 Var(COL) + 7 Var(ROW) COL Var(Error) + 2.3126 Var(ROW*COL) + 4.5714 Var(COL) ROW*COL Var(Error) + 2.2588 Var(ROW*COL) Error Var(Error) Variance Component Estimate Var(ROW) -8.03287982 Var(COL) -10.58767361 Var(ROW*COL) 22.46267361 Var(Error) 3.83333333 Variance Components Estimation Procedure Class Level Information Class Levels Values ROW 2 1 2 COL 3 1 2 3 Number of observations in data set = 14 Maximum Likelihood Variance Components Estimation Procedure Dependent Variable: Y Iteration Objective Var(ROW) Var(COL) Var(ROW*COL) Var(Error) 0 30.42524037 0 0 16.13588181 2.82901760 1 29.17637216 0 0 9.64010487 3.38029575 2 28.99804765 0 0 7.62929410 3.78310930 3 28.99573754 0 0 7.41300810 3.84121220 4 28.99573585 0 0 7.40708040 3.84285698 5 28.99573585 0 0 7.40708040 3.84285698 Convergence criteria met. Asymptotic Covariance Matrix of Estimates Var(ROW) Var(COL) Var(ROW*COL) Var(Error) Var(ROW) 0 0 0 0 Var(COL) 0 0 0 0 Var(ROW*COL) 0 0 28.556163696 -1.687465684 Var(Error) 0 0 -1.687465684 3.7075698983 Variance Components Estimation Procedure Class Level Information Class Levels Values ROW 2 1 2 COL 3 1 2 3 Number of observations in data set = 14 Restricted Maximum Likelihood Variance Components Estimation Procedure Dependent Variable: Y Iteration Objective Var(ROW) Var(COL) Var(ROW*COL) Var(Error) 0 27.68543031 0 0 17.37710349 3.04663434 1 26.88229305 0 0 10.38165140 3.64031850 2 26.85065583 0 0 9.30252163 3.82786099 3 26.85055629 0 0 9.24185674 3.83990075 4 26.85055627 0 0 9.24264463 3.83974323 5 26.85055627 0 0 9.24264463 3.83974323 Convergence criteria met. Asymptotic Covariance Matrix of Estimates Var(ROW) Var(COL) Var(ROW*COL) Var(Error) Var(ROW) 0 0 0 0 Var(COL) 0 0 0 0 Var(ROW*COL) 0 0 48.894011957 -1.687038596 Var(Error) 0 0 -1.687038596 3.6969691337 The MIXED Procedure Class Level Information Class Levels Values ROW 2 1 2 COL 3 1 2 3 REML Estimation Iteration History Iteration Evaluations Objective Criterion 0 1 47.87720214 1 3 42.52135037 0.00177521 2 2 42.49279452 0.00014277 3 1 42.48962827 0.00000069 4 1 42.48961360 0.00000000 Convergence criteria met. Covariance Parameter Estimates (REML) Cov Parm Ratio Estimate Std Error Z Pr > |Z| ROW 0.00000000 0.00000000 . . . COL 0.00000000 0.00000000 . . . ROW*COL 2.40705585 9.24253106 6.99228964 1.32 0.1862 Residual 1.00000000 3.83976593 1.92276177 2.00 0.0458 Model Fitting Information for Y Description Value Observations 14.0000 Variance Estimate 3.8398 Standard Deviation Estimate 1.9595 REML Log Likelihood -33.1910 Akaike's Information Criterion -37.1910 Schwarz's Bayesian Criterion -38.3209 -2 REML Log Likelihood 66.3820 Solution for Random Effects Parameter Estimate SE Pred DDF T Pr > |T| ROW 1 0.00000000 . . . . ROW 2 0.00000000 . . . . COL 1 0.00000000 . . . . COL 2 0.00000000 . . . . COL 3 0.00000000 . . . . ROW*COL 1 1 -3.38579711 1.59092908 8 -2.13 0.0660 ROW*COL 1 2 -0.70766931 1.68517204 8 -0.42 0.6856 ROW*COL 1 3 4.26035877 1.68517204 8 2.53 0.0354 ROW*COL 2 1 1.77634473 1.68517204 8 1.05 0.3226 ROW*COL 2 2 0.42044159 1.59092908 8 0.26 0.7982 ROW*COL 2 3 -2.36367867 1.68517204 8 -1.40 0.1983 ESTIMATE Statement Results Parameter Estimate Std Error DDF T Pr > |T| grand mean 14.85466825 1.35034664 1 11.00 0.0577 row 1 col 1 11.46887115 1.07294673 1 10.69 0.0594 row 1 col 2 14.14699894 1.28203498 1 11.03 0.0575 row 1 col 3 19.11502702 1.28203498 1 14.91 0.0426 row 2 col 1 16.63101298 1.28203498 1 12.97 0.0490 row 2 col 2 15.27510984 1.07294673 1 14.24 0.0446 row 2 col 3 12.49098958 1.28203498 1 9.74 0.0651