11:29 Thursday, April 30, 1998 General Linear Models Procedure Class Level Information Class Levels Values TRT 2 A B SEQ 2 1 2 PERSON 8 1 2 3 4 5 6 7 8 Number of observations in data set = 28 11:29 Thursday, April 30, 1998 General Linear Models Procedure Dependent Variable: Y Sum of Mean Source DF Squares Square F Value Pr > F Model 15 27.96583333 1.86438889 1.50 0.2435 Error 12 14.94416667 1.24534722 Corrected Total 27 42.91000000 R-Square C.V. Root MSE Y Mean 0.651732 -2231.903 1.1159513 -0.0500000 Source DF Type I SS Mean Square F Value Pr > F SEQ 1 4.57333333 4.57333333 3.67 0.0794 PERSON(SEQ) 12 12.00666667 1.00055556 0.80 0.6446 TRT 1 5.14285714 5.14285714 4.13 0.0649 TRT*SEQ 1 6.24297619 6.24297619 5.01 0.0449 Source DF Type III SS Mean Square F Value Pr > F SEQ 1 4.57333333 4.57333333 3.67 0.0794 PERSON(SEQ) 12 12.00666667 1.00055556 0.80 0.6446 TRT 1 3.56297619 3.56297619 2.86 0.1165 TRT*SEQ 1 6.24297619 6.24297619 5.01 0.0449 11:29 Thursday, April 30, 1998 General Linear Models Procedure Source Type III Expected Mean Square SEQ Var(Error) + 2 Var(PERSON(SEQ)) + Q(SEQ,TRT*SEQ) PERSON(SEQ) Var(Error) + 2 Var(PERSON(SEQ)) TRT Var(Error) + Q(TRT,TRT*SEQ) TRT*SEQ Var(Error) + Q(TRT*SEQ) 11:29 Thursday, April 30, 1998 General Linear Models Procedure Tests of Hypotheses for Mixed Model Analysis of Variance Dependent Variable: Y Source: SEQ * Error: MS(PERSON(SEQ)) Denominator Denominator DF Type III MS DF MS F Value Pr > F 1 4.5733333333 12 1.0005555556 4.5708 0.0538 * - This test assumes one or more other fixed effects are zero. Source: PERSON(SEQ) Error: MS(Error) Denominator Denominator DF Type III MS DF MS F Value Pr > F 12 1.0005555556 12 1.2453472222 0.8034 0.6446 Source: TRT * Error: MS(Error) Denominator Denominator DF Type III MS DF MS F Value Pr > F 1 3.5629761905 12 1.2453472222 2.8610 0.1165 * - This test assumes one or more other fixed effects are zero. Source: TRT*SEQ Error: MS(Error) Denominator Denominator DF Type III MS DF MS F Value Pr > F 1 6.2429761905 12 1.2453472222 5.0130 0.0449 11:29 Thursday, April 30, 1998 Least Squares Means SEQ Y LSMEAN 1 0.41666667 2 -0.40000000 11:29 Thursday, April 30, 1998 Least Squares Means TRT Y LSMEAN A 0.36875000 B -0.35208333 TRT SEQ Y LSMEAN A 1 0.30000000 A 2 0.43750000 B 1 0.53333333 B 2 -1.23750000 11:29 Thursday, April 30, 1998 Dependent Variable: Y Tests of Hypotheses using the Type III MS for PERSON(SEQ) as an error term Source DF Type III SS Mean Square F Value Pr > F SEQ 1 4.57333333 4.57333333 4.57 0.0538 11:29 Thursday, April 30, 1998 The MIXED Procedure Class Level Information Class Levels Values TRT 2 A B SEQ 2 1 2 PERSON 8 1 2 3 4 5 6 7 8 REML Estimation Iteration History Iteration Evaluations Objective Criterion 0 1 34.52545133 1 1 34.52545133 0.00000000 Convergence criteria met. Covariance Parameter Estimates (REML) Cov Parm Ratio Estimate Std Error Z Pr > |Z| PERSON(SEQ) 0.00000000 0.00000000 . . . Residual 1.00000000 1.12295139 0.32416814 3.46 0.0005 Model Fitting Information for Y Description Value Observations 28.0000 Variance Estimate 1.1230 Standard Deviation Estimate 1.0597 REML Log Likelihood -39.3173 Akaike's Information Criterion -41.3173 Schwarz's Bayesian Criterion -42.4953 -2 REML Log Likelihood 78.6345 11:29 Thursday, April 30, 1998 Tests of Fixed Effects Source NDF DDF Type III F Pr > F SEQ 1 24 4.07 0.0549 TRT 1 24 3.17 0.0875 TRT*SEQ 1 24 5.56 0.0269 Least Squares Means Level LSMEAN Std Error DDF T Pr > |T| SEQ 1 0.41666667 0.30590731 24 1.36 0.1858 SEQ 2 -0.40000000 0.26492350 24 -1.51 0.1441 TRT A 0.36875000 0.28615009 24 1.29 0.2098 TRT B -0.35208333 0.28615009 24 -1.23 0.2305 TRT*SEQ A 1 0.30000000 0.43261827 24 0.69 0.4947 TRT*SEQ A 2 0.43750000 0.37465841 24 1.17 0.2544 TRT*SEQ B 1 0.53333333 0.43261827 24 1.23 0.2296 TRT*SEQ B 2 -1.23750000 0.37465841 24 -3.30 0.0030 Differences of Least Squares Means Level 1 Level 2 Difference Std Error DDF T Pr > |T| TRT*SEQ A 1 TRT*SEQ A 2 -0.13750000 0.57230017 24 -0.24 0.8122 TRT*SEQ A 1 TRT*SEQ B 1 -0.23333333 0.61181462 24 -0.38 0.7063 TRT*SEQ A 1 TRT*SEQ B 2 1.53750000 0.57230017 24 2.69 0.0129 TRT*SEQ A 2 TRT*SEQ B 1 -0.09583333 0.57230017 24 -0.17 0.8684 TRT*SEQ A 2 TRT*SEQ B 2 1.67500000 0.52984700 24 3.16 0.0042 TRT*SEQ B 1 TRT*SEQ B 2 1.77083333 0.57230017 24 3.09 0.0050