proc glm data=sim; class rep block trt; model y=rep block(rep) trt; estimate 'trt 1 vs 4' trt 1 0 0 -1 0 0; means trt; lsmeans trt/stderr; title 'Simulated Data. Compare 6 treatments'; title2 'Intra-block analysis of variance -- BIB design'; proc mixed data=sim; class rep block trt; model y=trt; random rep block(rep); estimate 'trt 1 vs 4' trt 1 0 0 -1 0 0; lsmeans trt; title2 'Analysis of variance with recovery of interblock information'; title3 'Reps and blocks(rep) are random effects'; run; Simulated Data. Compare 6 treatments 13:42 Saturday, November 2, 2002 13 Analysis of variance with recovery of interblock information Reps and blocks(rep) are random effects Simulated Data. Compare 6 treatments Intra-block analysis of variance -- BIB design The GLM Procedure Class Level Information Class Levels Values rep 5 1 2 3 4 5 block 3 1 2 3 trt 6 1 2 3 4 5 6 Dependent Variable: y Sum of Source DF Squares Mean Square F Value Pr > F Model 19 33.45633333 1.76085965 5.96 0.0031 Error 10 2.95333333 0.29533333 Corrected Total 29 36.40966667 R-Square Coeff Var Root MSE y Mean 0.918886 26.68310 0.543446 2.036667 Source DF Type I SS Mean Square F Value Pr > F rep 4 21.53800000 5.38450000 18.23 0.0001 block(rep) 10 7.96666667 0.79666667 2.70 0.0666 trt 5 3.95166667 0.79033333 2.68 0.0870 Dependent Variable: y Source DF Type III SS Mean Square F Value Pr > F rep 4 21.53800000 5.38450000 18.23 0.0001 block(rep) 10 6.81266667 0.68126667 2.31 0.1018 trt 5 3.95166667 0.79033333 2.68 0.0870 Standard Parameter Estimate Error t Value Pr > |t| trt 1 vs 4 0.33333333 0.44372163 0.75 0.4698 Level of --------------y-------------- trt N Mean Std Dev 1 5 1.76000000 1.07842478 2 5 2.14000000 1.36124943 3 5 2.06000000 1.07842478 4 5 1.42000000 1.29884564 5 5 2.06000000 1.09681357 6 5 2.78000000 0.87005747 Least Squares Means Standard trt y LSMEAN Error Pr > |t| 1 1.88666667 0.30311958 <.0001 2 2.33666667 0.30311958 <.0001 3 1.77000000 0.30311958 0.0002 4 1.55333333 0.30311958 0.0004 5 1.73666667 0.30311958 0.0002 6 2.93666667 0.30311958 <.0001 Simulated Data. Compare 6 treatments Analysis of variance with recovery of interblock information Reps and blocks(rep) are random effects The Mixed Procedure Model Information Data Set WORK.SIM 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 rep 5 1 2 3 4 5 block 3 1 2 3 trt 6 1 2 3 4 5 6 Dimensions Covariance Parameters 3 Columns in X 7 Columns in Z 20 Subjects 1 Max Obs Per Subject 30 Observations Used 30 Observations Not Used 0 Total Observations 30 Iteration History Iteration Evaluations -2 Res Log Like Criterion 0 1 84.14228638 1 3 68.03630360 0.00059006 2 1 68.02888764 0.00000388 3 1 68.02884106 0.00000000 Convergence criteria met. Covariance Parameter Estimates Cov Parm Estimate rep 0.7686 block(rep) 0.2426 Residual 0.2879 Fit Statistics -2 Res Log Likelihood 68.0 AIC (smaller is better) 74.0 AICC (smaller is better) 75.2 BIC (smaller is better) 72.9 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F trt 5 10 2.86 0.0741 Estimates Standard Label Estimate Error DF t Value Pr > |t| trt 1 vs 4 0.3366 0.3921 10 0.86 0.4107 Least Squares Means Standard Effect trt Estimate Error DF t Value Pr > |t| trt 1 1.8237 0.4935 10 3.70 0.0041 trt 2 2.2389 0.4935 10 4.54 0.0011 trt 3 1.9142 0.4935 10 3.88 0.0031 trt 4 1.4870 0.4935 10 3.01 0.0130 trt 5 1.8974 0.4935 10 3.84 0.0032 trt 6 2.8588 0.4935 10 5.79 0.0002