19:01 Wednesday, April 19, 1995 General Linear Models Procedure Class Level Information Class Levels Values TRT 3 ax23 bww9 control Number of observations in data set = 24 19:01 Wednesday, April 19, 1995 General Linear Models Procedure Dependent Variable: T1 Sum of Mean Source DF Squares Square F Value Pr > F Model 2 567.00000000 283.50000000 9.29 0.0013 Error 21 641.00000000 30.52380952 Corrected Total 23 1208.00000000 R-Square C.V. Root MSE T1 Mean 0.469371 7.366448 5.5248357 75.000000 Source DF Type I SS Mean Square F Value Pr > F TRT 2 567.00000000 283.50000000 9.29 0.0013 Source DF Type III SS Mean Square F Value Pr > F TRT 2 567.00000000 283.50000000 9.29 0.0013 19:01 Wednesday, April 19, 1995 General Linear Models Procedure Dependent Variable: T2 Sum of Mean Source DF Squares Square F Value Pr > F Model 2 569.08333333 284.54166667 7.25 0.0040 Error 21 823.87500000 39.23214286 Corrected Total 23 1392.95833333 R-Square C.V. Root MSE T2 Mean 0.408543 7.932737 6.2635567 78.958333 Source DF Type I SS Mean Square F Value Pr > F TRT 2 569.08333333 284.54166667 7.25 0.0040 Source DF Type III SS Mean Square F Value Pr > F TRT 2 569.08333333 284.54166667 7.25 0.0040 19:01 Wednesday, April 19, 1995 General Linear Models Procedure Dependent Variable: T3 Sum of Mean Source DF Squares Square F Value Pr > F Model 2 391.08333333 195.54166667 6.26 0.0074 Error 21 655.87500000 31.23214286 Corrected Total 23 1046.95833333 R-Square C.V. Root MSE T3 Mean 0.373542 7.253961 5.5885725 77.041667 Source DF Type I SS Mean Square F Value Pr > F TRT 2 391.08333333 195.54166667 6.26 0.0074 Source DF Type III SS Mean Square F Value Pr > F TRT 2 391.08333333 195.54166667 6.26 0.0074 19:01 Wednesday, April 19, 1995 General Linear Models Procedure Dependent Variable: T4 Sum of Mean Source DF Squares Square F Value Pr > F Model 2 319.08333333 159.54166667 5.09 0.0157 Error 21 657.87500000 31.32738095 Corrected Total 23 976.95833333 R-Square C.V. Root MSE T4 Mean 0.326609 7.491918 5.5970868 74.708333 Source DF Type I SS Mean Square F Value Pr > F TRT 2 319.08333333 159.54166667 5.09 0.0157 Source DF Type III SS Mean Square F Value Pr > F TRT 2 319.08333333 159.54166667 5.09 0.0157 19:01 Wednesday, April 19, 1995 General Linear Models Procedure Repeated Measures Analysis of Variance Repeated Measures Level Information Dependent Variable T1 T2 T3 T4 Level of TIME 1 2 3 4 Manova Test Criteria and Exact F Statistics for the Hypothesis of no TIME Effect H = Type III SS&CP Matrix for TIME E = Error SS&CP Matrix S=1 M=0.5 N=8.5 Statistic Value F Num DF Den DF Pr > F Wilks' Lambda 0.29886466 14.8580 3 19 0.0001 Pillai's Trace 0.70113534 14.8580 3 19 0.0001 Hotelling-Lawley Trace 2.34599609 14.8580 3 19 0.0001 Roy's Greatest Root 2.34599609 14.8580 3 19 0.0001 Manova Test Criteria and F Approximations for the Hypothesis of no TIME*TRT Effect H = Type III SS&CP Matrix for TIME*TRT E = Error SS&CP Matrix S=2 M=0 N=8.5 Statistic Value F Num DF Den DF Pr > F Wilks' Lambda 0.10831123 12.9107 6 38 0.0001 Pillai's Trace 1.09156533 8.0106 6 40 0.0001 Hotelling-Lawley Trace 6.38726223 19.1618 6 36 0.0001 Roy's Greatest Root 6.08394057 40.5596 3 20 0.0001 NOTE: F Statistic for Roy's Greatest Root is an upper bound. NOTE: F Statistic for Wilks' Lambda is exact. 19:01 Wednesday, April 19, 1995 General Linear Models Procedure Repeated Measures Analysis of Variance Tests of Hypotheses for Between Subjects Effects Source DF Type III SS Mean Square F Value Pr > F TRT 2 1315.083333 657.541667 5.95 0.0090 Error 21 2320.156250 110.483631 19:01 Wednesday, April 19, 1995 General Linear Models Procedure Repeated Measures Analysis of Variance Univariate Tests of Hypotheses for Within Subject Effects Source: TIME Adj Pr > F DF Type III SS Mean Square F Value Pr > F G - G H - F 3 282.61458333 94.20486111 12.95 0.0001 0.0001 0.0001 Source: TIME*TRT Adj Pr > F DF Type III SS Mean Square F Value Pr > F G - G H - F 6 531.16666667 88.52777778 12.16 0.0001 0.0001 0.0001 Source: Error(TIME) DF Type III SS Mean Square 63 458.46875000 7.27728175 Greenhouse-Geisser Epsilon = 0.7986 Huynh-Feldt Epsilon = 0.9944 19:01 Wednesday, April 19, 1995 General Linear Models Procedure Repeated Measures Analysis of Variance Analysis of Variance of Contrast Variables TIME.N represents the nth degree polynomial contrast for TIME Contrast Variable: TIME.1 Source DF Type III SS Mean Square F Value Pr > F MEAN 1 9.35208333 9.35208333 0.80 0.3809 TRT 2 82.01666667 41.00833333 3.51 0.0483 Error 21 245.18125000 11.67529762 Contrast Variable: TIME.2 Source DF Type III SS Mean Square F Value Pr > F MEAN 1 237.51041667 237.51041667 48.35 0.0001 TRT 2 404.08333333 202.04166667 41.13 0.0001 Error 21 103.15625000 4.91220238 Contrast Variable: TIME.3 Source DF Type III SS Mean Square F Value Pr > F MEAN 1 35.75208333 35.75208333 6.82 0.0163 TRT 2 45.06666667 22.53333333 4.30 0.0273 Error 21 110.13125000 5.24434524 19:01 Wednesday, April 19, 1995 General Linear Models Procedure Least Squares Means TRT T1 T2 T3 T4 LSMEAN LSMEAN LSMEAN LSMEAN ax23 70.5000000 80.5000000 81.0000000 73.1250000 bww9 81.7500000 84.0000000 78.6250000 79.7500000 control 72.7500000 72.3750000 71.5000000 71.2500000 19:01 Wednesday, April 19, 1995 Plot of LSMEAN*PERIOD. Symbol is value of TRT. LSMEAN | | 84 + b | | | | 82 + | b | a | | a 80 + | b | | b | 78 + | | | | 76 + | | | | 74 + | | a | c | c 72 + | c | c | | a 70 + | ---+-----------------+-----------------+-----------------+-- 1 2 3 4 PERIOD 19:01 Wednesday, April 19, 1995 OBS TRT PERSON Y PERIOD 1 ax23 1 72 1 2 ax23 1 86 2 3 ax23 1 81 3 4 ax23 1 77 4 5 ax23 2 78 1 6 ax23 2 83 2 7 ax23 2 88 3 8 ax23 2 81 4 9 ax23 3 71 1 10 ax23 3 82 2 11 ax23 3 81 3 12 ax23 3 75 4 13 ax23 4 72 1 14 ax23 4 83 2 15 ax23 4 83 3 16 ax23 4 69 4 17 ax23 5 66 1 18 ax23 5 79 2 19 ax23 5 77 3 20 ax23 5 66 4 21 ax23 6 74 1 22 ax23 6 83 2 23 ax23 6 84 3 24 ax23 6 77 4 25 ax23 7 62 1 26 ax23 7 73 2 27 ax23 7 78 3 28 ax23 7 70 4 29 ax23 8 69 1 30 ax23 8 75 2 31 ax23 8 76 3 32 ax23 8 70 4 33 bww9 9 85 1 34 bww9 9 86 2 35 bww9 9 83 3 36 bww9 9 80 4 37 bww9 10 82 1 38 bww9 10 86 2 39 bww9 10 80 3 40 bww9 10 84 4 41 bww9 11 71 1 42 bww9 11 78 2 43 bww9 11 70 3 44 bww9 11 75 4 45 bww9 12 83 1 19:01 Wednesday, April 19, 1995 OBS TRT PERSON Y PERIOD 46 bww9 12 88 2 47 bww9 12 79 3 48 bww9 12 81 4 49 bww9 13 86 1 50 bww9 13 85 2 51 bww9 13 76 3 52 bww9 13 76 4 53 bww9 14 85 1 54 bww9 14 82 2 55 bww9 14 83 3 56 bww9 14 80 4 57 bww9 15 79 1 58 bww9 15 83 2 59 bww9 15 80 3 60 bww9 15 81 4 61 bww9 16 83 1 62 bww9 16 84 2 63 bww9 16 78 3 64 bww9 16 81 4 65 control 17 69 1 66 control 17 73 2 67 control 17 72 3 68 control 17 74 4 69 control 18 66 1 70 control 18 62 2 71 control 18 67 3 72 control 18 73 4 73 control 19 84 1 74 control 19 90 2 75 control 19 88 3 76 control 19 87 4 77 control 20 80 1 78 control 20 81 2 79 control 20 77 3 80 control 20 72 4 81 control 21 72 1 82 control 21 72 2 83 control 21 69 3 84 control 21 70 4 85 control 22 65 1 86 control 22 62 2 87 control 22 65 3 88 control 22 61 4 89 control 23 75 1 90 control 23 69 2 19:01 Wednesday, April 19, 1995 OBS TRT PERSON Y PERIOD 91 control 23 69 3 92 control 23 68 4 93 control 24 71 1 94 control 24 70 2 95 control 24 65 3 96 control 24 65 4 19:01 Wednesday, April 19, 1995 The MIXED Procedure Class Level Information Class Levels Values TRT 3 ax23 bww9 control PERIOD 4 1 2 3 4 PERSON 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 The MIXED Procedure REML Estimation Iteration History Iteration Evaluations Objective Criterion 0 1 402.86045172 1 1 332.79522992 0.00000000 Convergence criteria met. The MIXED Procedure Covariance Parameter Estimates (REML) Cov Parm Ratio Estimate Std Error Z Pr > |Z| DIAG CS 3.54549792 25.80158730 8.53015856 3.02 0.0025 Residual 1.00000000 7.27728175 1.29662357 5.61 0.0000 The MIXED Procedure Model Fitting Information for Y Description Value Observations 96.0000 Variance Estimate 7.2773 Standard Deviation Estimate 2.6976 REML Log Likelihood -243.588 Akaike's Information Criterion -245.588 19:01 Wednesday, April 19, 1995 The MIXED Procedure Model Fitting Information for Y Description Value Schwarz's Bayesian Criterion -248.019 -2 REML Log Likelihood 487.1769 Null Model LRT Chi-Square 70.0652 Null Model LRT DF 1.0000 Null Model LRT P-Value 0.0000 The MIXED Procedure Tests of Fixed Effects Source NDF DDF Type III F Pr > F TRT 2 84 5.95 0.0038 PERIOD 3 84 12.95 0.0000 TRT*PERIOD 6 84 12.16 0.0000 The MIXED Procedure Least Squares Means Level LSMEAN Std Error DDF T Pr > |T| TRT*PERIOD ax23 1 70.50000000 2.03343518 84 34.67 0.0000 TRT*PERIOD ax23 2 80.50000000 2.03343518 84 39.59 0.0000 TRT*PERIOD ax23 3 81.00000000 2.03343518 84 39.83 0.0000 TRT*PERIOD ax23 4 73.12500000 2.03343518 84 35.96 0.0000 TRT*PERIOD bww9 1 81.75000000 2.03343518 84 40.20 0.0000 TRT*PERIOD bww9 2 84.00000000 2.03343518 84 41.31 0.0000 TRT*PERIOD bww9 3 78.62500000 2.03343518 84 38.67 0.0000 TRT*PERIOD bww9 4 79.75000000 2.03343518 84 39.22 0.0000 TRT*PERIOD control 1 72.75000000 2.03343518 84 35.78 0.0000 TRT*PERIOD control 2 72.37500000 2.03343518 84 35.59 0.0000 TRT*PERIOD control 3 71.50000000 2.03343518 84 35.16 0.0000 TRT*PERIOD control 4 71.25000000 2.03343518 84 35.04 0.0000 19:01 Wednesday, April 19, 1995 The MIXED Procedure Class Level Information Class Levels Values TRT 3 ax23 bww9 control PERIOD 4 1 2 3 4 PERSON 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 The MIXED Procedure REML Estimation Iteration History Iteration Evaluations Objective Criterion 0 1 402.86045172 1 1 332.79522992 0.00000000 Convergence criteria met. The MIXED Procedure Covariance Parameter Estimates (REML) Cov Parm Ratio Estimate Std Error Z Pr > |Z| PERSON(TRT) 3.54549792 25.80158730 8.53015856 3.02 0.0025 Residual 1.00000000 7.27728175 1.29662357 5.61 0.0000 The MIXED Procedure Model Fitting Information for Y Description Value Observations 96.0000 Variance Estimate 7.2773 Standard Deviation Estimate 2.6976 REML Log Likelihood -243.588 Akaike's Information Criterion -245.588 19:01 Wednesday, April 19, 1995 The MIXED Procedure Model Fitting Information for Y Description Value Schwarz's Bayesian Criterion -248.019 -2 REML Log Likelihood 487.1769 The MIXED Procedure Tests of Fixed Effects Source NDF DDF Type III F Pr > F TRT 2 21 5.95 0.0090 PERIOD 3 63 12.95 0.0000 TRT*PERIOD 6 63 12.16 0.0000 The MIXED Procedure Least Squares Means Level LSMEAN Std Error DDF T Pr > |T| TRT*PERIOD ax23 1 70.50000000 2.03343518 63 34.67 0.0000 TRT*PERIOD ax23 2 80.50000000 2.03343518 63 39.59 0.0000 TRT*PERIOD ax23 3 81.00000000 2.03343518 63 39.83 0.0000 TRT*PERIOD ax23 4 73.12500000 2.03343518 63 35.96 0.0000 TRT*PERIOD bww9 1 81.75000000 2.03343518 63 40.20 0.0000 TRT*PERIOD bww9 2 84.00000000 2.03343518 63 41.31 0.0000 TRT*PERIOD bww9 3 78.62500000 2.03343518 63 38.67 0.0000 TRT*PERIOD bww9 4 79.75000000 2.03343518 63 39.22 0.0000 TRT*PERIOD control 1 72.75000000 2.03343518 63 35.78 0.0000 TRT*PERIOD control 2 72.37500000 2.03343518 63 35.59 0.0000 TRT*PERIOD control 3 71.50000000 2.03343518 63 35.16 0.0000 TRT*PERIOD control 4 71.25000000 2.03343518 63 35.04 0.0000 19:01 Wednesday, April 19, 1995 General Linear Models Procedure Class Level Information Class Levels Values TRT 3 ax23 bww9 control PERIOD 4 1 2 3 4 PERSON 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Number of observations in data set = 96 19:01 Wednesday, April 19, 1995 General Linear Models Procedure Dependent Variable: Y Sum of Mean Source DF Squares Square F Value Pr > F Model 32 4449.0208333 139.0319010 19.10 0.0001 Error 63 458.4687500 7.2772817 Corrected Total 95 4907.4895833 R-Square C.V. Root MSE Y Mean 0.906578 3.529696 2.6976437 76.427083 Source DF Type I SS Mean Square F Value Pr > F TRT 2 1315.0833333 657.5416667 90.36 0.0001 PERSON(TRT) 21 2320.1562500 110.4836310 15.18 0.0001 PERIOD 3 282.6145833 94.2048611 12.95 0.0001 TRT*PERIOD 6 531.1666667 88.5277778 12.16 0.0001 Source DF Type III SS Mean Square F Value Pr > F TRT 2 1315.0833333 657.5416667 90.36 0.0001 PERSON(TRT) 21 2320.1562500 110.4836310 15.18 0.0001 PERIOD 3 282.6145833 94.2048611 12.95 0.0001 TRT*PERIOD 6 531.1666667 88.5277778 12.16 0.0001 Tests of Hypotheses using the Type III MS for PERSON(TRT) as an error term Source DF Type III SS Mean Square F Value Pr > F TRT 2 1315.0833333 657.5416667 5.95 0.0090 19:01 Wednesday, April 19, 1995 General Linear Models Procedure Source Type III Expected Mean Square TRT Var(Error) + 4 Var(PERSON(TRT)) + Q(TRT,TRT*PERIOD) PERSON(TRT) Var(Error) + 4 Var(PERSON(TRT)) PERIOD Var(Error) + Q(PERIOD,TRT*PERIOD) TRT*PERIOD Var(Error) + Q(TRT*PERIOD) 19:01 Wednesday, April 19, 1995 General Linear Models Procedure Tests of Hypotheses for Mixed Model Analysis of Variance Dependent Variable: Y Source: TRT * Error: MS(PERSON(TRT)) Denominator Denominator DF Type III MS DF MS F Value Pr > F 2 657.54166667 21 110.48363095 5.9515 0.0090 * - This test assumes one or more other fixed effects are zero. Source: PERSON(TRT) Error: MS(Error) Denominator Denominator DF Type III MS DF MS F Value Pr > F 21 110.48363095 63 7.277281746 15.1820 0.0001 Source: PERIOD * Error: MS(Error) Denominator Denominator DF Type III MS DF MS F Value Pr > F 3 94.204861111 63 7.277281746 12.9451 0.0001 * - This test assumes one or more other fixed effects are zero. Source: TRT*PERIOD Error: MS(Error) Denominator Denominator DF Type III MS DF MS F Value Pr > F 6 88.527777778 63 7.277281746 12.1650 0.0001