The SAS System 1 Correlation Analysis 5 'VAR' Variables: TIME1 TIME2 TIME3 TIME4 TIME5 Covariance Matrix DF = 7 TIME1 TIME2 TIME3 TIME4 TIME5 TIME1 48.00000000 17.35714286 30.07142857 9.28571429 5.50000000 TIME2 17.35714286 11.41071429 15.12500000 7.21428571 14.33928571 TIME3 30.07142857 15.12500000 38.26785714 15.78571429 16.91071429 TIME4 9.28571429 7.21428571 15.78571429 10.57142857 16.35714286 TIME5 5.50000000 14.33928571 16.91071429 16.35714286 38.69642857 Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum TIME1 8 23.5000 6.9282 188.0000 11.0000 33.0000 TIME2 8 24.6250 3.3780 197.0000 18.0000 28.0000 TIME3 8 22.6250 6.1861 181.0000 15.0000 31.0000 TIME4 8 19.5000 3.2514 156.0000 15.0000 24.0000 TIME5 8 18.1250 6.2206 145.0000 10.0000 29.0000 Pearson Correlation Coefficients / N = 8 TIME1 TIME2 TIME3 TIME4 TIME5 TIME1 1.00000 0.74165 0.70164 0.41222 0.12762 TIME2 0.74165 1.00000 0.72381 0.65686 0.68239 TIME3 0.70164 0.72381 1.00000 0.78484 0.43945 TIME4 0.41222 0.65686 0.78484 1.00000 0.80873 TIME5 0.12762 0.68239 0.43945 0.80873 1.00000 The SAS System 2 T2 FCRIT PVAL 55.705418 44.71763 0.0346035 QQ 0.4472136 -0.632456 0.5345225 -0.316228 0.1195229 0.4472136 -0.316228 -0.267261 0.6324555 -0.478091 0.4472136 0 -0.534522 -2.85E-15 0.7171372 0.4472136 0.3162278 -0.267261 -0.632456 -0.478091 0.4472136 0.6324555 0.5345225 0.3162278 0.1195229 PP -0.632456 0.5345225 -0.316228 0.1195229 -0.316228 -0.267261 0.6324555 -0.478091 0 -0.534522 -2.85E-15 0.7171372 0.3162278 -0.267261 -0.632456 -0.478091 0.6324555 0.5345225 0.3162278 0.1195229 LAMBDA LR test statistic = 0.0820302 PVAL p-value for H-F conditions = 0.1817749 Hotellings T2 and test of H-F conditions using PROC GLM 3 General Linear Models Procedure Number of observations in data set = 8 Hotellings T2 and test of H-F conditions using PROC GLM 4 General Linear Models Procedure Repeated Measures Analysis of Variance Repeated Measures Level Information Dependent Variable TIME1 TIME2 TIME3 TIME4 TIME5 Level of TIME 1 2 3 4 5 Hotellings T2 and test of H-F conditions using PROC GLM 5 General Linear Models Procedure Repeated Measures Analysis of Variance Partial Correlation Coefficients from the Error SS&CP Matrix / Prob > |r| DF = 7 TIME1 TIME2 TIME3 TIME4 TIME5 TIME1 1.000000 0.741654 0.701643 0.412219 0.127616 0.0001 0.0352 0.0524 0.3102 0.7633 TIME2 0.741654 1.000000 0.723806 0.656856 0.682395 0.0352 0.0001 0.0424 0.0768 0.0622 TIME3 0.701643 0.723806 1.000000 0.784839 0.439450 0.0524 0.0424 0.0001 0.0211 0.2760 TIME4 0.412219 0.656856 0.784839 1.000000 0.808733 0.3102 0.0768 0.0211 0.0001 0.0151 TIME5 0.127616 0.682395 0.439450 0.808733 1.000000 0.7633 0.0622 0.2760 0.0151 0.0001 E = Error SS&CP Matrix TIME.N represents the contrast between the nth level of TIME and the last TIME.1 TIME.2 TIME.3 TIME.4 TIME.1 529.8750000 253.5000000 324.5000000 182.8750000 TIME.2 253.5000000 150.0000000 158.0000000 106.5000000 TIME.3 324.5000000 158.0000000 302.0000000 148.5000000 TIME.4 182.8750000 106.5000000 148.5000000 115.8750000 Hotellings T2 and test of H-F conditions using PROC GLM 6 General Linear Models Procedure Repeated Measures Analysis of Variance Partial Correlation Coefficients from the Error SS&CP Matrix of the Variables Defined by the Specified Transformation / Prob > |r| DF = 7 TIME.1 TIME.2 TIME.3 TIME.4 TIME.1 1.000000 0.899178 0.811194 0.738028 0.0001 0.0024 0.0145 0.0366 TIME.2 0.899178 1.000000 0.742349 0.807810 0.0024 0.0001 0.0349 0.0153 TIME.3 0.811194 0.742349 1.000000 0.793831 0.0145 0.0349 0.0001 0.0187 TIME.4 0.738028 0.807810 0.793831 1.000000 0.0366 0.0153 0.0187 0.0001 Test for Sphericity: Mauchly's Criterion = 0.0078765 Chisquare Approximation = 26.237604 with 9 df Prob > Chisquare = 0.0019 Applied to Orthogonal Components: Test for Sphericity: Mauchly's Criterion = 0.0820302 Chisquare Approximation = 13.545284 with 9 df Prob > Chisquare = 0.1394 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=1 N=1 Statistic Value F Num DF Den DF Pr > F Wilks' Lambda 0.11163310 7.9579 4 4 0.0346 Pillai's Trace 0.88836690 7.9579 4 4 0.0346 Hotelling-Lawley Trace 7.95791682 7.9579 4 4 0.0346 Roy's Greatest Root 7.95791682 7.9579 4 4 0.0346 Hotellings T2 and test of H-F conditions using PROC GLM 7 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 4 242.15000000 60.53750000 4.15 0.0092 0.0426 0.0266 Source: Error(TIME) DF Type III SS Mean Square 28 408.65000000 14.59464286 Greenhouse-Geisser Epsilon = 0.4653 Huynh-Feldt Epsilon = 0.6270 RCB Analysis using PROC GLM 8 General Linear Models Procedure Class Level Information Class Levels Values PATIENT 8 1 2 3 4 5 6 7 8 TIME 5 TIME1 TIME2 TIME3 TIME4 TIME5 Number of observations in data set = 40 RCB Analysis using PROC GLM 9 General Linear Models Procedure Dependent Variable: RESPONSE Sum of Mean Source DF Squares Square F Value Pr > F Model 11 862.1250000 78.3750000 5.37 0.0002 Error 28 408.6500000 14.5946429 Corrected Total 39 1270.7750000 R-Square C.V. Root MSE RESPONSE Mean 0.678425 17.62535 3.820294 21.67500 Source DF Type I SS Mean Square F Value Pr > F TIME 4 242.1500000 60.5375000 4.15 0.0092 PATIENT 7 619.9750000 88.5678571 6.07 0.0002 Source DF Type III SS Mean Square F Value Pr > F TIME 4 242.1500000 60.5375000 4.15 0.0092 PATIENT 7 619.9750000 88.5678571 6.07 0.0002 RCB Analysis using PROC GLM 10 General Linear Models Procedure Source Type III Expected Mean Square TIME Var(Error) + Q(TIME) PATIENT Var(Error) + 5 Var(PATIENT)