The SAS System The GLM Procedure Class Level Information Class Levels Values trt 3 A S V Number of Observations Read 15 Number of Observations Used 15 The SAS System The GLM Procedure Repeated Measures Analysis of Variance Repeated Measures Level Information Dependent Variable y1 y2 y3 y4 Level of time 0 30 60 90 Partial Correlation Coefficients from the Error SSCP Matrix / Prob > |r| DF = 12 y1 y2 y3 y4 y1 1.000000 0.144091 -0.001938 -0.293278 0.6386 0.9950 0.3308 y2 0.144091 1.000000 0.337001 -0.007787 0.6386 0.2602 0.9799 y3 -0.001938 0.337001 1.000000 0.447737 0.9950 0.2602 0.1250 y4 -0.293278 -0.007787 0.447737 1.000000 0.3308 0.9799 0.1250 E = Error SSCP Matrix time_N represents the nth degree polynomial contrast for time time_1 time_2 time_3 time_1 9.14220 -0.93333 -1.43960 time_2 -0.93333 6.43900 -0.66366 time_3 -1.43960 -0.66366 5.23780 Partial Correlation Coefficients from the Error SSCP Matrix of the Variables Defined by the Specified Transformation / Prob > |r| DF = 12 time_1 time_2 time_3 time_1 1.000000 -0.121647 -0.208038 0.6922 0.4952 time_2 -0.121647 1.000000 -0.114279 0.6922 0.7101 time_3 -0.208038 -0.114279 1.000000 0.4952 0.7101 The SAS System The GLM Procedure Repeated Measures Analysis of Variance Sphericity Tests Mauchly's Variables DF Criterion Chi-Square Pr > ChiSq Transformed Variates 5 0.8516102 1.7222721 0.8861 Orthogonal Components 5 0.8516102 1.7222721 0.8861 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=0.5 N=4 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.32361566 6.97 3 10 0.0082 Pillai's Trace 0.67638434 6.97 3 10 0.0082 Hotelling-Lawley Trace 2.09008529 6.97 3 10 0.0082 Roy's Greatest Root 2.09008529 6.97 3 10 0.0082 MANOVA Test Criteria and F Approximations for the Hypothesis of no time*trt Effect H = Type III SSCP Matrix for time*trt E = Error SSCP Matrix S=2 M=0 N=4 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.39044824 2.00 6 20 0.1134 Pillai's Trace 0.72475865 2.08 6 22 0.0967 Hotelling-Lawley Trace 1.26609580 2.04 6 11.714 0.1406 Roy's Greatest Root 0.95814248 3.51 3 11 0.0527 NOTE: F Statistic for Roy's Greatest Root is an upper bound. NOTE: F Statistic for Wilks' Lambda is exact. 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 2 35.37733333 17.68866667 19.40 0.0002 Error 12 10.94100000 0.91175000 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 3 16.08333333 5.36111111 9.27 0.0001 time*trt 6 10.06266667 1.67711111 2.90 0.0207 Error(time) 36 20.81900000 0.57830556 Adj Pr > F Source G - G H - F time 0.0002 0.0001 time*trt 0.0253 0.0207 Error(time) Greenhouse-Geisser Epsilon 0.9073 Huynh-Feldt Epsilon 1.3949 The SAS System The GLM Procedure Class Level Information Class Levels Values trt 3 A S V rabbit 5 1 2 3 4 5 time 4 1 2 3 4 Number of Observations Read 60 Number of Observations Used 60 The SAS System The GLM Procedure Dependent Variable: y Sum of Source DF Squares Mean Square F Value Pr > F Model 23 72.46433333 3.15062319 5.45 <.0001 Error 36 20.81900000 0.57830556 Corrected Total 59 93.28333333 R-Square Coeff Var Root MSE y Mean 0.776820 240.1465 0.760464 0.316667 Source DF Type I SS Mean Square F Value Pr > F trt 2 35.37733333 17.68866667 30.59 <.0001 rabbit(trt) 12 10.94100000 0.91175000 1.58 0.1429 time 3 16.08333333 5.36111111 9.27 0.0001 trt*time 6 10.06266667 1.67711111 2.90 0.0207 Source DF Type III SS Mean Square F Value Pr > F trt 2 35.37733333 17.68866667 30.59 <.0001 rabbit(trt) 12 10.94100000 0.91175000 1.58 0.1429 time 3 16.08333333 5.36111111 9.27 0.0001 trt*time 6 10.06266667 1.67711111 2.90 0.0207 Tests of Hypotheses Using the Type III MS for rabbit(trt) as an Error Term Source DF Type III SS Mean Square F Value Pr > F trt 2 35.37733333 17.68866667 19.40 0.0002 The SAS System The Mixed Procedure Model Information Data Set WORK.ONE 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 3 A S V rabbit 5 1 2 3 4 5 time 4 1 2 3 4 Dimensions Covariance Parameters 2 Columns in X 20 Columns in Z 15 Subjects 1 Max Obs Per Subject 60 Number of Observations Number of Observations Read 60 Number of Observations Used 60 Number of Observations Not Used 0 Iteration History Iteration Evaluations -2 Res Log Like Criterion 0 1 135.70767216 1 1 134.70717609 0.00000000 Convergence criteria met. The SAS System The Mixed Procedure Covariance Parameter Estimates Cov Parm Estimate rabbit(trt) 0.08336 Residual 0.5783 Fit Statistics -2 Res Log Likelihood 134.7 AIC (smaller is better) 138.7 AICC (smaller is better) 139.0 BIC (smaller is better) 140.1 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F trt 2 12 19.40 0.0002 time 3 36 9.27 0.0001 trt*time 6 36 2.90 0.0207