The SAS System The GLM Procedure Class Level Information Class Levels Values trt 2 0 1 id 34 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 timepnt 5 1 2 3 4 5 Number of Observations Read 170 Number of Observations Used 170 The SAS System The GLM Procedure Dependent Variable: y Sum of Source DF Squares Mean Square F Value Pr > F Model 41 2889.182353 70.467862 23.22 <.0001 Error 128 388.494118 3.035110 Corrected Total 169 3277.676471 R-Square Coeff Var Root MSE y Mean 0.881473 14.41200 1.742157 12.08824 Source DF Type I SS Mean Square F Value Pr > F trt 1 382.500000 382.500000 126.03 <.0001 id(trt) 32 2131.976471 66.624265 21.95 <.0001 timepnt 4 324.117647 81.029412 26.70 <.0001 trt*timepnt 4 50.588235 12.647059 4.17 0.0033 Source DF Type III SS Mean Square F Value Pr > F trt 1 382.500000 382.500000 126.03 <.0001 id(trt) 32 2131.976471 66.624265 21.95 <.0001 timepnt 4 324.117647 81.029412 26.70 <.0001 trt*timepnt 4 50.588235 12.647059 4.17 0.0033 Tests of Hypotheses Using the Type III MS for id(trt) as an Error Term Source DF Type III SS Mean Square F Value Pr > F trt 1 382.5000000 382.5000000 5.74 0.0226 The SAS System The Mixed Procedure Model Information Data Set WORK.UNI 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 trt 2 0 1 id 34 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 timepnt 5 1 2 3 4 5 Dimensions Covariance Parameters 2 Columns in X 18 Columns in Z 34 Subjects 1 Max Obs per Subject 170 Number of Observations Number of Observations Read 170 Number of Observations Used 170 Number of Observations Not Used 0 Iteration History Iteration Evaluations -2 Res Log Like Criterion 0 1 923.51679834 1 1 758.87438101 0.00000000 Convergence criteria met. The SAS System The Mixed Procedure Covariance Parameter Estimates Cov Parm Estimate id(trt) 12.7178 Residual 3.0351 Fit Statistics -2 Res Log Likelihood 758.9 AIC (Smaller is Better) 762.9 AICC (Smaller is Better) 763.0 BIC (Smaller is Better) 765.9 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F trt 1 32 5.74 0.0226 timepnt 4 128 26.70 <.0001 trt*timepnt 4 128 4.17 0.0033 The SAS System The Mixed Procedure Model Information Data Set WORK.UNI Dependent Variable y Covariance Structures Variance Components, Autoregressive Subject Effects id(trt), id(trt) Estimation Method REML Residual Variance Method Profile Fixed Effects SE Method Model-Based Degrees of Freedom Method Containment Class Level Information Class Levels Values trt 2 0 1 id 34 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 timepnt 5 1 2 3 4 5 Dimensions Covariance Parameters 3 Columns in X 18 Columns in Z per Subject 1 Subjects 34 Max Obs per Subject 5 Number of Observations Number of Observations Read 170 Number of Observations Used 170 Number of Observations Not Used 0 Iteration History Iteration Evaluations -2 Res Log Like Criterion 0 1 923.51679834 1 4 707.66451911 . 2 1 705.47944031 0.00355728 3 1 704.66585568 0.00013035 The SAS System The Mixed Procedure Iteration History Iteration Evaluations -2 Res Log Like Criterion 4 1 704.63846693 0.00000017 5 1 704.63843191 0.00000000 Convergence criteria met. Estimated R Matrix for id(trt) 2 0 Row Col1 Col2 Col3 Col4 Col5 1 15.7085 14.2116 12.8573 11.6321 10.5236 2 14.2116 15.7085 14.2116 12.8573 11.6321 3 12.8573 14.2116 15.7085 14.2116 12.8573 4 11.6321 12.8573 14.2116 15.7085 14.2116 5 10.5236 11.6321 12.8573 14.2116 15.7085 Estimated R Correlation Matrix for id(trt) 2 0 Row Col1 Col2 Col3 Col4 Col5 1 1.0000 0.9047 0.8185 0.7405 0.6699 2 0.9047 1.0000 0.9047 0.8185 0.7405 3 0.8185 0.9047 1.0000 0.9047 0.8185 4 0.7405 0.8185 0.9047 1.0000 0.9047 5 0.6699 0.7405 0.8185 0.9047 1.0000 Covariance Parameter Estimates Cov Parm Subject Estimate Intercept id(trt) 0 AR(1) id(trt) 0.9047 Residual 15.7085 Fit Statistics -2 Res Log Likelihood 704.6 AIC (Smaller is Better) 708.6 AICC (Smaller is Better) 708.7 BIC (Smaller is Better) 711.7 The SAS System The Mixed Procedure Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F trt 1 32 5.68 0.0233 timepnt 4 128 12.45 <.0001 trt*timepnt 4 128 2.05 0.0914 The SAS System The GLM Procedure Class Level Information Class Levels Values trt 2 0 1 Number of Observations Read 34 Number of Observations Used 34 The SAS System The GLM Procedure Repeated Measures Analysis of Variance Repeated Measures Level Information Dependent Variable es1 es2 es3 es4 es5 Level of time 1 2 3 4 5 Partial Correlation Coefficients from the Error SSCP Matrix / Prob > |r| DF = 32 es1 es2 es3 es4 es5 es1 1.000000 0.814974 0.716624 0.685973 0.612815 <.0001 <.0001 <.0001 0.0001 es2 0.814974 1.000000 0.877020 0.839045 0.793701 <.0001 <.0001 <.0001 <.0001 es3 0.716624 0.877020 1.000000 0.935804 0.901526 <.0001 <.0001 <.0001 <.0001 es4 0.685973 0.839045 0.935804 1.000000 0.962108 <.0001 <.0001 <.0001 <.0001 es5 0.612815 0.793701 0.901526 0.962108 1.000000 0.0001 <.0001 <.0001 <.0001 E = Error SSCP Matrix time_N represents the nth degree polynomial contrast for time time_1 time_2 time_3 time_4 time_1 263.9059 -42.1682 -16.2529 1.1539 time_2 -42.1682 55.1429 -10.9423 -5.3872 time_3 -16.2529 -10.9423 40.2706 -6.2209 time_4 1.1539 -5.3872 -6.2209 29.1748 The SAS System The GLM Procedure Repeated Measures Analysis of Variance Partial Correlation Coefficients from the Error SSCP Matrix of the Variables Defined by the Specified Transformation / Prob > |r| DF = 32 time_1 time_2 time_3 time_4 time_1 1.000000 -0.349556 -0.157657 0.013150 0.0461 0.3809 0.9421 time_2 -0.349556 1.000000 -0.232203 -0.134313 0.0461 0.1935 0.4561 time_3 -0.157657 -0.232203 1.000000 -0.181490 0.3809 0.1935 0.3121 time_4 0.013150 -0.134313 -0.181490 1.000000 0.9421 0.4561 0.3121 Sphericity Tests Mauchly's Variables DF Criterion Chi-Square Pr > ChiSq Transformed Variates 9 0.1374381 60.364366 <.0001 Orthogonal Components 9 0.1374381 60.364366 <.0001 MANOVA Test Criteria and Exact F Statistics for the Hypothesis of no time Effect H = Type III SSCP Matrix for time E = Error SSCP Matrix S=1 M=1 N=13.5 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.44971994 8.87 4 29 <.0001 Pillai's Trace 0.55028006 8.87 4 29 <.0001 Hotelling-Lawley Trace 1.22360609 8.87 4 29 <.0001 Roy's Greatest Root 1.22360609 8.87 4 29 <.0001 The SAS System The GLM Procedure Repeated Measures Analysis of Variance MANOVA Test Criteria and Exact F Statistics for the Hypothesis of no time*trt Effect H = Type III SSCP Matrix for time*trt E = Error SSCP Matrix S=1 M=1 N=13.5 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.74601276 2.47 4 29 0.0669 Pillai's Trace 0.25398724 2.47 4 29 0.0669 Hotelling-Lawley Trace 0.34045965 2.47 4 29 0.0669 Roy's Greatest Root 0.34045965 2.47 4 29 0.0669 The SAS System The GLM 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 1 382.500000 382.500000 5.74 0.0226 Error 32 2131.976471 66.624265 The SAS System The GLM Procedure Repeated Measures Analysis of Variance Univariate Tests of Hypotheses for Within Subject Effects Source DF Type III SS Mean Square F Value Pr > F time 4 324.1176471 81.0294118 26.70 <.0001 time*trt 4 50.5882353 12.6470588 4.17 0.0033 Error(time) 128 388.4941176 3.0351103 Adj Pr > F Source G - G H-F-L time <.0001 <.0001 time*trt 0.0219 0.0197 Error(time) Greenhouse-Geisser Epsilon 0.4739 Huynh-Feldt-Lecoutre Epsilon 0.5029 The SAS System The GLM 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 1 318.3558824 318.3558824 38.60 <.0001 trt 1 47.4382353 47.4382353 5.75 0.0225 Error 32 263.9058824 8.2470588 Contrast Variable: time_2 Source DF Type III SS Mean Square F Value Pr > F Mean 1 4.64075630 4.64075630 2.69 0.1106 trt 1 2.57352941 2.57352941 1.49 0.2306 Error 32 55.14285714 1.72321429 Contrast Variable: time_3 Source DF Type III SS Mean Square F Value Pr > F Mean 1 0.95294118 0.95294118 0.76 0.3907 trt 1 0.57647059 0.57647059 0.46 0.5034 Error 32 40.27058824 1.25845588 Contrast Variable: time_4 Source DF Type III SS Mean Square F Value Pr > F Mean 1 0.16806723 0.16806723 0.18 0.6705 trt 1 0.00000000 0.00000000 0.00 1.0000 Error 32 29.17478992 0.91171218