1 EXAMPLE 21. TWO-FACTOR UNBALANCED MODEL: RATIONS DATA 1 15:06 Tuesday, August 21, 2001 The GLM Procedure Class Level Information Class Levels Values FEED 2 F1 F2 SIRE 3 S1 S2 S3 Number of observations 18 1 EXAMPLE 21. TWO-FACTOR UNBALANCED MODEL: RATIONS DATA 2 15:06 Tuesday, August 21, 2001 The GLM Procedure General Form of Estimable Functions Effect Coefficients Intercept L1 FEED F1 L2 FEED F2 L1-L2 SIRE S1 L4 SIRE S2 L5 SIRE S3 L1-L4-L5 FEED*SIRE F1 S1 L7 FEED*SIRE F1 S2 L8 FEED*SIRE F1 S3 L2-L7-L8 FEED*SIRE F2 S1 L4-L7 FEED*SIRE F2 S2 L5-L8 FEED*SIRE F2 S3 L1-L2-L4-L5+L7+L8 Type I Estimable Functions -----------------Coefficients----------------- Effect FEED SIRE FEED*SIRE Intercept 0 0 0 FEED F1 L2 0 0 FEED F2 -L2 0 0 SIRE S1 0.05*L2 L4 0 SIRE S2 0.325*L2 L5 0 SIRE S3 -0.375*L2 -L4-L5 0 FEED*SIRE F1 S1 0.25*L2 0.4101*L4-0.1236*L5 L7 FEED*SIRE F1 S2 0.625*L2 -0.1685*L4+0.3933*L5 L8 FEED*SIRE F1 S3 0.125*L2 -0.2416*L4-0.2697*L5 -L7-L8 FEED*SIRE F2 S1 -0.2*L2 0.5899*L4+0.1236*L5 -L7 FEED*SIRE F2 S2 -0.3*L2 0.1685*L4+0.6067*L5 -L8 FEED*SIRE F2 S3 -0.5*L2 -0.7584*L4-0.7303*L5 L7+L8 Type II Estimable Functions -----------------Coefficients------------------ Effect FEED SIRE FEED*SIRE Intercept 0 0 0 FEED F1 L2 0 0 FEED F2 -L2 0 0 SIRE S1 0 L4 0 SIRE S2 0 L5 0 1 EXAMPLE 21. TWO-FACTOR UNBALANCED MODEL: RATIONS DATA 3 15:06 Tuesday, August 21, 2001 The GLM Procedure Type II Estimable Functions -----------------Coefficients------------------ Effect FEED SIRE FEED*SIRE SIRE S3 0 -L4-L5 0 FEED*SIRE F1 S1 0.2697*L2 0.4101*L4-0.1236*L5 L7 FEED*SIRE F1 S2 0.5056*L2 -0.1685*L4+0.3933*L5 L8 FEED*SIRE F1 S3 0.2247*L2 -0.2416*L4-0.2697*L5 -L7-L8 FEED*SIRE F2 S1 -0.2697*L2 0.5899*L4+0.1236*L5 -L7 FEED*SIRE F2 S2 -0.5056*L2 0.1685*L4+0.6067*L5 -L8 FEED*SIRE F2 S3 -0.2247*L2 -0.7584*L4-0.7303*L5 L7+L8 Type III Estimable Functions --------------Coefficients--------------- Effect FEED SIRE FEED*SIRE Intercept 0 0 0 FEED F1 L2 0 0 FEED F2 -L2 0 0 SIRE S1 0 L4 0 SIRE S2 0 L5 0 SIRE S3 0 -L4-L5 0 FEED*SIRE F1 S1 0.3333*L2 0.5*L4 L7 FEED*SIRE F1 S2 0.3333*L2 0.5*L5 L8 FEED*SIRE F1 S3 0.3333*L2 -0.5*L4-0.5*L5 -L7-L8 FEED*SIRE F2 S1 -0.3333*L2 0.5*L4 -L7 FEED*SIRE F2 S2 -0.3333*L2 0.5*L5 -L8 FEED*SIRE F2 S3 -0.3333*L2 -0.5*L4-0.5*L5 L7+L8 Type IV Estimable Functions --------------Coefficients--------------- Effect FEED SIRE FEED*SIRE Intercept 0 0 0 FEED F1 L2 0 0 FEED F2 -L2 0 0 SIRE S1 0 L4 0 SIRE S2 0 L5 0 SIRE S3 0 -L4-L5 0 FEED*SIRE F1 S1 0.3333*L2 0.5*L4 L7 FEED*SIRE F1 S2 0.3333*L2 0.5*L5 L8 FEED*SIRE F1 S3 0.3333*L2 -0.5*L4-0.5*L5 -L7-L8 FEED*SIRE F2 S1 -0.3333*L2 0.5*L4 -L7 1 EXAMPLE 21. TWO-FACTOR UNBALANCED MODEL: RATIONS DATA 4 15:06 Tuesday, August 21, 2001 The GLM Procedure Type IV Estimable Functions --------------Coefficients--------------- Effect FEED SIRE FEED*SIRE FEED*SIRE F2 S2 -0.3333*L2 0.5*L5 -L8 FEED*SIRE F2 S3 -0.3333*L2 -0.5*L4-0.5*L5 L7+L8 1 EXAMPLE 21. TWO-FACTOR UNBALANCED MODEL: RATIONS DATA 5 15:06 Tuesday, August 21, 2001 The GLM Procedure Dependent Variable: WEIGHT Sum of Source DF Squares Mean Square F Value Model 5 51.04444444 10.20888889 4.70 Error 12 26.06666667 2.17222222 Corrected Total 17 77.11111111 Source Pr > F Model 0.0131 Error Corrected Total R-Square Coeff Var Root MSE WEIGHT Mean 0.661960 28.22258 1.473846 5.222222 Source DF Type I SS Mean Square F Value FEED 1 5.13611111 5.13611111 2.36 SIRE 2 15.68286517 7.84143258 3.61 FEED*SIRE 2 30.22546816 15.11273408 6.96 Source Pr > F FEED 0.1501 SIRE 0.0592 FEED*SIRE 0.0099 Source DF Type II SS Mean Square F Value FEED 1 9.70786517 9.70786517 4.47 SIRE 2 15.68286517 7.84143258 3.61 FEED*SIRE 2 30.22546816 15.11273408 6.96 Source Pr > F FEED 0.0561 SIRE 0.0592 FEED*SIRE 0.0099 Source DF Type III SS Mean Square F Value FEED 1 3.59186992 3.59186992 1.65 SIRE 2 21.00074906 10.50037453 4.83 1 EXAMPLE 21. TWO-FACTOR UNBALANCED MODEL: RATIONS DATA 6 15:06 Tuesday, August 21, 2001 The GLM Procedure Dependent Variable: WEIGHT Source DF Type III SS Mean Square F Value FEED*SIRE 2 30.22546816 15.11273408 6.96 Source Pr > F FEED 0.2227 SIRE 0.0289 FEED*SIRE 0.0099 Source DF Type IV SS Mean Square F Value FEED 1 3.59186992 3.59186992 1.65 SIRE 2 21.00074906 10.50037453 4.83 FEED*SIRE 2 30.22546816 15.11273408 6.96 Source Pr > F FEED 0.2227 SIRE 0.0289 FEED*SIRE 0.0099 Standard Parameter Estimate Error t Value Pr > |t| Intercept 5.400000000 B 0.65912400 8.19 <.0001 FEED F1 -2.400000000 B 1.61451747 -1.49 0.1629 FEED F2 0.000000000 B . . . SIRE S1 -2.900000000 B 1.23310809 -2.35 0.0366 SIRE S2 2.933333333 B 1.07634498 2.73 0.0184 SIRE S3 0.000000000 B . . . FEED*SIRE F1 S1 5.400000000 B 2.18606699 2.47 0.0295 FEED*SIRE F1 S2 -1.333333333 B 1.94040851 -0.69 0.5051 FEED*SIRE F1 S3 0.000000000 B . . . FEED*SIRE F2 S1 0.000000000 B . . . FEED*SIRE F2 S2 0.000000000 B . . . FEED*SIRE F2 S3 0.000000000 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. 1 EXAMPLE 21. TWO-FACTOR UNBALANCED MODEL: RATIONS DATA 7 15:06 Tuesday, August 21, 2001 The GLM Procedure Level of ------------WEIGHT----------- FEED N Mean Std Dev F1 8 4.62500000 1.76776695 F2 10 5.70000000 2.35937845 Level of ------------WEIGHT----------- SIRE N Mean Std Dev S1 4 4.00000000 1.82574186 S2 8 6.00000000 2.50713268 S3 6 5.00000000 1.54919334 1 EXAMPLE 21. TWO-FACTOR UNBALANCED MODEL: RATIONS DATA 8 15:06 Tuesday, August 21, 2001 The GLM Procedure Least Squares Means WEIGHT Standard FEED LSMEAN Error Pr > |t| F1 4.36666667 0.64055339 <.0001 F2 5.41111111 0.49940294 <.0001 WEIGHT Standard SIRE LSMEAN Error Pr > |t| S1 4.00000000 0.73692303 0.0002 S2 6.46666667 0.53817249 <.0001 S3 4.20000000 0.80725874 0.0002 1 EXAMPLE 21. TWO-FACTOR UNBALANCED MODEL: RATIONS DATA 9 15:06 Tuesday, August 21, 2001 The GLM Procedure Dependent Variable: WEIGHT Contrast DF Contrast SS Mean Square F Value ALL FEED 1 3.59186992 3.59186992 1.65 ALL SIRE 2 21.00074906 10.50037453 4.83 SIRE1 VS SIRE2, SIRE3 1 4.96124031 4.96124031 2.28 SIRE2 VS SIRE3 1 11.85641026 11.85641026 5.46 FEED*SIRE 2 VS SIRE3 1 1.02564103 1.02564103 0.47 Contrast Pr > F ALL FEED 0.2227 ALL SIRE 0.0289 SIRE1 VS SIRE2, SIRE3 0.1566 SIRE2 VS SIRE3 0.0376 FEED*SIRE 2 VS SIRE3 0.5051