The SAS System 1 16:38 Saturday, February 2, 2013 Obs subject eyelens y eye lens 1 1 l1 116 L 1 2 1 l2 119 L 2 3 1 l3 116 L 3 4 1 l4 124 L 4 5 1 r1 120 R 1 6 1 r2 117 R 2 7 1 r3 114 R 3 8 1 r4 122 R 4 9 2 l1 110 L 1 10 2 l2 110 L 2 11 2 l3 114 L 3 12 2 l4 115 L 4 13 2 r1 106 R 1 14 2 r2 112 R 2 15 2 r3 110 R 3 16 2 r4 110 R 4 17 3 l1 117 L 1 18 3 l2 118 L 2 19 3 l3 120 L 3 20 3 l4 120 L 4 21 3 r1 120 R 1 22 3 r2 120 R 2 23 3 r3 120 R 3 24 3 r4 124 R 4 25 4 l1 112 L 1 26 4 l2 116 L 2 27 4 l3 115 L 3 28 4 l4 113 L 4 29 4 r1 115 R 1 30 4 r2 116 R 2 31 4 r3 116 R 3 32 4 r4 119 R 4 33 5 l1 113 L 1 34 5 l2 114 L 2 35 5 l3 114 L 3 36 5 l4 118 L 4 37 5 r1 114 R 1 38 5 r2 117 R 2 39 5 r3 116 R 3 40 5 r4 112 R 4 41 6 l1 119 L 1 42 6 l2 115 L 2 43 6 l3 94 L 3 44 6 l4 116 L 4 45 6 r1 100 R 1 46 6 r2 99 R 2 47 6 r3 94 R 3 48 6 r4 97 R 4 49 7 l1 110 L 1 50 7 l2 110 L 2 The SAS System 2 16:38 Saturday, February 2, 2013 Obs subject eyelens y eye lens 51 7 l3 105 L 3 52 7 l4 118 L 4 53 7 r1 105 R 1 54 7 r2 105 R 2 55 7 r3 115 R 3 56 7 r4 115 R 4 Model 1: the RCBD model with random subject (block) effects 3 No adjustment for non-sphericity 16:38 Saturday, February 2, 2013 The Mixed Procedure Model Information Data Set WORK.TWO Dependent Variable y Covariance Structure Variance Components Estimation Method Type 3 Residual Variance Method Factor Fixed Effects SE Method Model-Based Degrees of Freedom Method Satterthwaite Class Level Information Class Levels Values subject 7 1 2 3 4 5 6 7 lens 4 1 2 3 4 eye 2 L R Dimensions Covariance Parameters 2 Columns in X 15 Columns in Z 7 Subjects 1 Max Obs Per Subject 56 Number of Observations Number of Observations Read 56 Number of Observations Used 56 Number of Observations Not Used 0 Type 3 Analysis of Variance Sum of Source DF Squares Mean Square Expected Mean Square lens 3 140.767857 46.922619 Var(Residual) + Q(lens,lens*eye) eye 1 46.446429 46.446429 Var(Residual) + Q(eye,lens*eye) lens*eye 3 40.625000 13.541667 Var(Residual) + Q(lens*eye) subject 6 1379.428571 229.904762 Var(Residual) + 8 Var(subject) Residual 42 964.285714 22.959184 Var(Residual) Model 1: the RCBD model with random subject (block) effects 4 No adjustment for non-sphericity 16:38 Saturday, February 2, 2013 The Mixed Procedure Type 3 Analysis of Variance Error Source Error Term DF F Value Pr > F lens MS(Residual) 42 2.04 0.1223 eye MS(Residual) 42 2.02 0.1623 lens*eye MS(Residual) 42 0.59 0.6251 subject MS(Residual) 42 10.01 <.0001 Residual . . . . Covariance Parameter Estimates Cov Parm Estimate subject 25.8682 Residual 22.9592 Fit Statistics -2 Res Log Likelihood 316.0 AIC (smaller is better) 320.0 AICC (smaller is better) 320.3 BIC (smaller is better) 319.9 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F lens 3 42 2.04 0.1223 eye 1 42 2.02 0.1623 lens*eye 3 42 0.59 0.6251 Least Squares Means Standard Effect eye lens Estimate Error DF t Value Pr > |t| lens 1 112.64 2.3098 10 48.77 <.0001 lens 2 113.43 2.3098 10 49.11 <.0001 lens 3 111.64 2.3098 10 48.33 <.0001 lens 4 115.93 2.3098 10 50.19 <.0001 eye L 114.32 2.1250 7.25 53.80 <.0001 Model 1: the RCBD model with random subject (block) effects 5 No adjustment for non-sphericity 16:38 Saturday, February 2, 2013 The Mixed Procedure Least Squares Means Standard Effect eye lens Estimate Error DF t Value Pr > |t| eye R 112.50 2.1250 7.25 52.94 <.0001 lens*eye L 1 113.86 2.6411 16.2 43.11 <.0001 lens*eye R 1 111.43 2.6411 16.2 42.19 <.0001 lens*eye L 2 114.57 2.6411 16.2 43.38 <.0001 lens*eye R 2 112.29 2.6411 16.2 42.51 <.0001 lens*eye L 3 111.14 2.6411 16.2 42.08 <.0001 lens*eye R 3 112.14 2.6411 16.2 42.46 <.0001 lens*eye L 4 117.71 2.6411 16.2 44.57 <.0001 lens*eye R 4 114.14 2.6411 16.2 43.22 <.0001 Model 1 refit with PROC GLM 6 Here, adjustments for non-sphericity are done in RM-ANOVA 16:38 Saturday, February 2, 2013 The GLM Procedure Number of Observations Read 7 Number of Observations Used 7 Model 1 refit with PROC GLM 7 Here, adjustments for non-sphericity are done in RM-ANOVA 16:38 Saturday, February 2, 2013 The GLM Procedure Repeated Measures Analysis of Variance Repeated Measures Level Information Dependent Variable l1 l2 l3 l4 r1 r2 Level of eyelens 1 2 3 4 5 6 Repeated Measures Level Information Dependent Variable r3 r4 Level of eyelens 7 8 Partial Correlation Coefficients from the Error SSCP Matrix / Prob > |r| DF = 6 l1 l2 l3 l4 l1 1.000000 0.738152 -0.251188 0.390300 0.0582 0.5869 0.3867 l2 0.738152 1.000000 0.338093 0.511226 0.0582 0.4583 0.2409 l3 -0.251188 0.338093 1.000000 0.280867 0.5869 0.4583 0.5418 l4 0.390300 0.511226 0.280867 1.000000 0.3867 0.2409 0.5418 Partial Correlation Coefficients from the Error SSCP Matrix / Prob > |r| DF = 6 r1 r2 r3 r4 l1 0.141213 -0.097442 -0.430539 -0.180379 0.7627 0.8354 0.3349 0.6987 l2 0.720891 0.486205 0.150815 0.434423 0.0676 0.2686 0.7469 0.3301 l3 0.867283 0.972225 0.869557 0.861491 0.0115 0.0002 0.0110 0.0127 l4 0.532533 0.320528 0.273416 0.454301 0.2185 0.4834 0.5530 0.3058 Model 1 refit with PROC GLM 8 Here, adjustments for non-sphericity are done in RM-ANOVA 16:38 Saturday, February 2, 2013 The GLM Procedure Repeated Measures Analysis of Variance Partial Correlation Coefficients from the Error SSCP Matrix / Prob > |r| DF = 6 l1 l2 l3 l4 r1 0.141213 0.720891 0.867283 0.532533 0.7627 0.0676 0.0115 0.2185 r2 -0.097442 0.486205 0.972225 0.320528 0.8354 0.2686 0.0002 0.4834 r3 -0.430539 0.150815 0.869557 0.273416 0.3349 0.7469 0.0110 0.5530 r4 -0.180379 0.434423 0.861491 0.454301 0.6987 0.3301 0.0127 0.3058 Partial Correlation Coefficients from the Error SSCP Matrix / Prob > |r| DF = 6 r1 r2 r3 r4 r1 1.000000 0.929259 0.767399 0.879233 0.0025 0.0440 0.0091 r2 0.929259 1.000000 0.828353 0.825613 0.0025 0.0213 0.0222 r3 0.767399 0.828353 1.000000 0.910092 0.0440 0.0213 0.0044 r4 0.879233 0.825613 0.910092 1.000000 0.0091 0.0222 0.0044 E = Error SSCP Matrix eyelens_N represents the contrast between the nth level of eyelens and the last eyelens_1 eyelens_2 eyelens_3 eyelens_4 eyelens_1 643.43 504.86 72.00 474.14 eyelens_2 504.86 405.71 63.00 364.29 eyelens_3 72.00 63.00 134.00 48.00 eyelens_4 474.14 364.29 48.00 397.71 eyelens_5 180.57 158.14 66.00 122.86 eyelens_6 174.29 149.57 131.00 118.43 eyelens_7 31.00 17.00 51.00 35.00 Model 1 refit with PROC GLM 9 Here, adjustments for non-sphericity are done in RM-ANOVA 16:38 Saturday, February 2, 2013 The GLM Procedure Repeated Measures Analysis of Variance E = Error SSCP Matrix eyelens_N represents the contrast between the nth level of eyelens and the last eyelens_5 eyelens_6 eyelens_7 eyelens_1 180.57 174.29 31.00 eyelens_2 158.14 149.57 17.00 eyelens_3 66.00 131.00 51.00 eyelens_4 122.86 118.43 35.00 eyelens_5 113.43 110.71 5.00 eyelens_6 110.71 158.86 53.00 eyelens_7 5.00 53.00 86.00 Partial Correlation Coefficients from the Error SSCP Matrix of the Variables Defined by the Specified Transformation / Prob > |r| DF = 6 eyelens_1 eyelens_2 eyelens_3 eyelens_4 eyelens_1 1.000000 0.988117 0.245205 0.937289 <.0001 0.5961 0.0018 eyelens_2 0.988117 1.000000 0.270195 0.906873 <.0001 0.5579 0.0048 eyelens_3 0.245205 0.270195 1.000000 0.207923 0.5961 0.5579 0.6546 Partial Correlation Coefficients from the Error SSCP Matrix of the Variables Defined by the Specified Transformation / Prob > |r| DF = 6 eyelens_5 eyelens_6 eyelens_7 eyelens_1 0.668402 0.545140 0.131784 0.1007 0.2057 0.7782 eyelens_2 0.737188 0.589163 0.091010 0.0587 0.1639 0.8461 eyelens_3 0.535341 0.897874 0.475082 0.2156 0.0061 0.2813 Model 1 refit with PROC GLM 10 Here, adjustments for non-sphericity are done in RM-ANOVA 16:38 Saturday, February 2, 2013 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 = 6 eyelens_1 eyelens_2 eyelens_3 eyelens_4 eyelens_4 0.937289 0.906873 0.207923 1.000000 0.0018 0.0048 0.6546 eyelens_5 0.668402 0.737188 0.535341 0.578434 0.1007 0.0587 0.2156 0.1737 eyelens_6 0.545140 0.589163 0.897874 0.471159 0.2057 0.1639 0.0061 0.2859 eyelens_7 0.131784 0.091010 0.475082 0.189249 0.7782 0.8461 0.2813 0.6844 Partial Correlation Coefficients from the Error SSCP Matrix of the Variables Defined by the Specified Transformation / Prob > |r| DF = 6 eyelens_5 eyelens_6 eyelens_7 eyelens_4 0.578434 0.471159 0.189249 0.1737 0.2859 0.6844 eyelens_5 1.000000 0.824782 0.050624 0.0224 0.9142 eyelens_6 0.824782 1.000000 0.453444 0.0224 0.3068 eyelens_7 0.050624 0.453444 1.000000 0.9142 0.3068 NOTE: Sphericity test not performed due to insufficient error degrees of freedom. Model 1 refit with PROC GLM 11 Here, adjustments for non-sphericity are done in RM-ANOVA 16:38 Saturday, February 2, 2013 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 eyelens 7 227.8392857 32.5484694 1.42 0.2239 Error(eyelens) 42 964.2857143 22.9591837 Adj Pr > F Source G - G H - F eyelens 0.2816 0.2769 Error(eyelens) Greenhouse-Geisser Epsilon 0.2478 Huynh-Feldt Epsilon 0.3397 Model 1 refit with PROC GLM 12 Here, adjustments for non-sphericity are done in RM-ANOVA 16:38 Saturday, February 2, 2013 The GLM Procedure Multivariate Analysis of Variance M Matrix Describing Transformed Variables l1 l2 l3 l4 MVAR1 1 1 1 1 M Matrix Describing Transformed Variables r1 r2 r3 r4 MVAR1 -1 -1 -1 -1 Model 1 refit with PROC GLM 13 Here, adjustments for non-sphericity are done in RM-ANOVA 16:38 Saturday, February 2, 2013 The GLM Procedure Multivariate Analysis of Variance Characteristic Roots and Vectors of: E Inverse * H, where H = Type III SSCP Matrix for Intercept E = Error SSCP Matrix Variables have been transformed by the M Matrix Characteristic Characteristic Vector V'EV=1 Root Percent MVAR1 0.12994604 100.00 0.01870081 MANOVA Test Criteria and Exact F Statistics for the Hypothesis of No Overall Intercept Effect on the Variables Defined by the M Matrix Transformation H = Type III SSCP Matrix for Intercept E = Error SSCP Matrix S=1 M=-0.5 N=2 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.88499801 0.78 1 6 0.4112 Pillai's Trace 0.11500199 0.78 1 6 0.4112 Hotelling-Lawley Trace 0.12994604 0.78 1 6 0.4112 Roy's Greatest Root 0.12994604 0.78 1 6 0.4112 Model 1 refit with PROC GLM 14 Here, adjustments for non-sphericity are done in RM-ANOVA 16:38 Saturday, February 2, 2013 The GLM Procedure Multivariate Analysis of Variance M Matrix Describing Transformed Variables l1 l2 l3 l4 MVAR1 3 -1 -1 -1 MVAR2 0 2 -1 -1 MVAR3 0 0 1 -1 M Matrix Describing Transformed Variables r1 r2 r3 r4 MVAR1 3 -1 -1 -1 MVAR2 0 2 -1 -1 MVAR3 0 0 1 -1 Model 1 refit with PROC GLM 15 Here, adjustments for non-sphericity are done in RM-ANOVA 16:38 Saturday, February 2, 2013 The GLM Procedure Multivariate Analysis of Variance Characteristic Roots and Vectors of: E Inverse * H, where H = Type III SSCP Matrix for Intercept E = Error SSCP Matrix Variables have been transformed by the M Matrix Characteristic Characteristic Vector V'EV=1 Root Percent MVAR1 MVAR2 MVAR3 16.1175870 100.00 0.10008241 -0.09884917 0.12177950 0.0000000 0.00 -0.02754492 0.04981633 0.01143780 0.0000000 0.00 0.00864901 0.01151436 -0.00811752 MANOVA Test Criteria and Exact F Statistics for the Hypothesis of No Overall Intercept Effect on the Variables Defined by the M Matrix Transformation H = Type III SSCP Matrix for Intercept E = Error SSCP Matrix S=1 M=0.5 N=1 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.05841945 21.49 3 4 0.0063 Pillai's Trace 0.94158055 21.49 3 4 0.0063 Hotelling-Lawley Trace 16.11758703 21.49 3 4 0.0063 Roy's Greatest Root 16.11758703 21.49 3 4 0.0063 Model 1 refit with PROC GLM 16 Here, adjustments for non-sphericity are done in RM-ANOVA 16:38 Saturday, February 2, 2013 The GLM Procedure Multivariate Analysis of Variance M Matrix Describing Transformed Variables l1 l2 l3 l4 MVAR1 3 -1 -1 -1 MVAR2 0 2 -1 -1 MVAR3 0 0 1 -1 M Matrix Describing Transformed Variables r1 r2 r3 r4 MVAR1 -3 1 1 1 MVAR2 0 -2 1 1 MVAR3 0 0 -1 1 Model 1 refit with PROC GLM 17 Here, adjustments for non-sphericity are done in RM-ANOVA 16:38 Saturday, February 2, 2013 The GLM Procedure Multivariate Analysis of Variance Characteristic Roots and Vectors of: E Inverse * H, where H = Type III SSCP Matrix for Intercept E = Error SSCP Matrix Variables have been transformed by the M Matrix Characteristic Characteristic Vector V'EV=1 Root Percent MVAR1 MVAR2 MVAR3 0.41423331 100.00 0.02539128 -0.00407830 0.06491833 0.00000000 0.00 0.04041616 -0.00473527 0.01939941 0.00000000 0.00 -0.01072622 0.04348656 0.01332707 MANOVA Test Criteria and Exact F Statistics for the Hypothesis of No Overall Intercept Effect on the Variables Defined by the M Matrix Transformation H = Type III SSCP Matrix for Intercept E = Error SSCP Matrix S=1 M=0.5 N=1 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.70709691 0.55 3 4 0.6733 Pillai's Trace 0.29290309 0.55 3 4 0.6733 Hotelling-Lawley Trace 0.41423331 0.55 3 4 0.6733 Roy's Greatest Root 0.41423331 0.55 3 4 0.6733 Model 2: the RCBD model with random subj, subj*lens and subj*eye effects 18 No adjustment for non-sphericity 16:38 Saturday, February 2, 2013 The Mixed Procedure Model Information Data Set WORK.TWO Dependent Variable y Covariance Structure Variance Components Estimation Method Type 3 Residual Variance Method Factor Fixed Effects SE Method Model-Based Degrees of Freedom Method Satterthwaite Class Level Information Class Levels Values subject 7 1 2 3 4 5 6 7 lens 4 1 2 3 4 eye 2 L R Dimensions Covariance Parameters 4 Columns in X 15 Columns in Z 49 Subjects 1 Max Obs Per Subject 56 Number of Observations Number of Observations Read 56 Number of Observations Used 56 Number of Observations Not Used 0 Type 3 Analysis of Variance Sum of Source DF Squares Mean Square lens 3 140.767857 46.922619 eye 1 46.446429 46.446429 lens*eye 3 40.625000 13.541667 subject 6 1379.428571 229.904762 subject*lens 18 375.857143 20.880952 subject*eye 6 357.428571 59.571429 Residual 18 231.000000 12.833333 Model 2: the RCBD model with random subj, subj*lens and subj*eye effects 19 No adjustment for non-sphericity 16:38 Saturday, February 2, 2013 The Mixed Procedure Type 3 Analysis of Variance Source Expected Mean Square lens Var(Residual) + 2 Var(subject*lens) + Q(lens,lens*eye) eye Var(Residual) + 4 Var(subject*eye) + Q(eye,lens*eye) lens*eye Var(Residual) + Q(lens*eye) subject Var(Residual) + 4 Var(subject*eye) + 2 Var(subject*lens) + 8 Var(subject) subject*lens Var(Residual) + 2 Var(subject*lens) subject*eye Var(Residual) + 4 Var(subject*eye) Residual Var(Residual) Type 3 Analysis of Variance Error Source Error Term DF F Value Pr > F lens MS(subject*lens) 18 2.25 0.1177 eye MS(subject*eye) 6 0.78 0.4112 lens*eye MS(Residual) 18 1.06 0.3925 subject MS(subject*lens) + MS(subject*eye) 7.3177 3.40 0.0636 - MS(Residual) subject*lens MS(Residual) 18 1.63 0.1554 subject*eye MS(Residual) 18 4.64 0.0051 Residual . . . . Covariance Parameter Estimates Cov Parm Estimate subject 20.2857 subject*lens 4.0238 subject*eye 11.6845 Residual 12.8333 Fit Statistics -2 Res Log Likelihood 309.6 AIC (smaller is better) 317.6 AICC (smaller is better) 318.5 BIC (smaller is better) 317.4 Model 2: the RCBD model with random subj, subj*lens and subj*eye effects 20 No adjustment for non-sphericity 16:38 Saturday, February 2, 2013 The Mixed Procedure Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F lens 3 18 2.25 0.1177 eye 1 6 0.78 0.4112 lens*eye 3 18 1.06 0.3925 Least Squares Means Standard Effect eye lens Estimate Error DF t Value Pr > |t| lens 1 112.64 2.2856 9.48 49.28 <.0001 lens 2 113.43 2.2856 9.48 49.63 <.0001 lens 3 111.64 2.2856 9.48 48.85 <.0001 lens 4 115.93 2.2856 9.48 50.72 <.0001 eye L 114.32 2.2736 8.91 50.28 <.0001 eye R 112.50 2.2736 8.91 49.48 <.0001 lens*eye L 1 113.86 2.6411 15.7 43.11 <.0001 lens*eye R 1 111.43 2.6411 15.7 42.19 <.0001 lens*eye L 2 114.57 2.6411 15.7 43.38 <.0001 lens*eye R 2 112.29 2.6411 15.7 42.51 <.0001 lens*eye L 3 111.14 2.6411 15.7 42.08 <.0001 lens*eye R 3 112.14 2.6411 15.7 42.46 <.0001 lens*eye L 4 117.71 2.6411 15.7 44.57 <.0001 lens*eye R 4 114.14 2.6411 15.7 43.22 <.0001 Model 2 refit with PROC GLM 21 Here, adjustments for non-sphericity are done in RM-ANOVA 16:38 Saturday, February 2, 2013 The GLM Procedure Number of Observations Read 7 Number of Observations Used 7 Model 2 refit with PROC GLM 22 Here, adjustments for non-sphericity are done in RM-ANOVA 16:38 Saturday, February 2, 2013 The GLM Procedure Repeated Measures Analysis of Variance Repeated Measures Level Information Dependent Variable l1 l2 l3 l4 r1 r2 Level of eye 1 1 1 1 2 2 Level of lens 1 2 3 4 1 2 Repeated Measures Level Information Dependent Variable r3 r4 Level of eye 2 2 Level of lens 3 4 Partial Correlation Coefficients from the Error SSCP Matrix / Prob > |r| DF = 6 l1 l2 l3 l4 l1 1.000000 0.738152 -0.251188 0.390300 0.0582 0.5869 0.3867 l2 0.738152 1.000000 0.338093 0.511226 0.0582 0.4583 0.2409 l3 -0.251188 0.338093 1.000000 0.280867 0.5869 0.4583 0.5418 Partial Correlation Coefficients from the Error SSCP Matrix / Prob > |r| DF = 6 r1 r2 r3 r4 l1 0.141213 -0.097442 -0.430539 -0.180379 0.7627 0.8354 0.3349 0.6987 l2 0.720891 0.486205 0.150815 0.434423 0.0676 0.2686 0.7469 0.3301 l3 0.867283 0.972225 0.869557 0.861491 0.0115 0.0002 0.0110 0.0127 Model 2 refit with PROC GLM 23 Here, adjustments for non-sphericity are done in RM-ANOVA 16:38 Saturday, February 2, 2013 The GLM Procedure Repeated Measures Analysis of Variance Partial Correlation Coefficients from the Error SSCP Matrix / Prob > |r| DF = 6 l1 l2 l3 l4 l4 0.390300 0.511226 0.280867 1.000000 0.3867 0.2409 0.5418 r1 0.141213 0.720891 0.867283 0.532533 0.7627 0.0676 0.0115 0.2185 r2 -0.097442 0.486205 0.972225 0.320528 0.8354 0.2686 0.0002 0.4834 r3 -0.430539 0.150815 0.869557 0.273416 0.3349 0.7469 0.0110 0.5530 r4 -0.180379 0.434423 0.861491 0.454301 0.6987 0.3301 0.0127 0.3058 Partial Correlation Coefficients from the Error SSCP Matrix / Prob > |r| DF = 6 r1 r2 r3 r4 l4 0.532533 0.320528 0.273416 0.454301 0.2185 0.4834 0.5530 0.3058 r1 1.000000 0.929259 0.767399 0.879233 0.0025 0.0440 0.0091 r2 0.929259 1.000000 0.828353 0.825613 0.0025 0.0213 0.0222 r3 0.767399 0.828353 1.000000 0.910092 0.0440 0.0213 0.0044 r4 0.879233 0.825613 0.910092 1.000000 0.0091 0.0222 0.0044 E = Error SSCP Matrix eye_N represents the contrast between the nth level of eye and the last eye_1 eye_1 2859.4 Model 2 refit with PROC GLM 24 Here, adjustments for non-sphericity are done in RM-ANOVA 16:38 Saturday, February 2, 2013 The GLM Procedure Repeated Measures Analysis of Variance E = Error SSCP Matrix lens_N represents the contrast between the nth level of lens and the last lens_1 lens_2 lens_3 lens_1 321.71 266.00 -108.29 lens_2 266.00 296.00 96.00 lens_3 -108.29 96.00 553.71 Partial Correlation Coefficients from the Error SSCP Matrix of the Variables Defined by the Specified Transformation / Prob > |r| DF = 6 lens_1 lens_2 lens_3 lens_1 1.000000 0.861987 -0.256562 0.0126 0.5786 lens_2 0.861987 1.000000 0.237128 0.0126 0.6087 lens_3 -0.256562 0.237128 1.000000 0.5786 0.6087 Sphericity Tests Mauchly's Variables DF Criterion Chi-Square Pr > ChiSq Transformed Variates 5 0.0266065 17.125616 0.0043 Orthogonal Components 5 0.0251719 17.387347 0.0038 E = Error SSCP Matrix eye_N represents the contrast between the nth level of eye and the last lens_N represents the contrast between the nth level of lens and the last eye_1*lens_1 eye_1*lens_2 eye_1*lens_3 eye_1*lens_1 90.857 83.714 13.429 eye_1*lens_2 83.714 171.429 106.857 eye_1*lens_3 13.429 106.857 489.714 Model 2 refit with PROC GLM 25 Here, adjustments for non-sphericity are done in RM-ANOVA 16:38 Saturday, February 2, 2013 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 = 6 eye_1*lens_1 eye_1*lens_2 eye_1*lens_3 eye_1*lens_1 1.000000 0.670777 0.063662 0.0991 0.8921 eye_1*lens_2 0.670777 1.000000 0.368800 0.0991 0.4156 eye_1*lens_3 0.063662 0.368800 1.000000 0.8921 0.4156 Sphericity Tests Mauchly's Variables DF Criterion Chi-Square Pr > ChiSq Transformed Variates 5 0.2138038 7.2849558 0.2003 Orthogonal Components 5 0.2305064 6.9297505 0.2259 Model 2 refit with PROC GLM 26 Here, adjustments for non-sphericity are done in RM-ANOVA 16:38 Saturday, February 2, 2013 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 eye 1 46.4464286 46.4464286 0.78 0.4112 Error(eye) 6 357.4285714 59.5714286 Source DF Type III SS Mean Square F Value Pr > F lens 3 140.7678571 46.9226190 2.25 0.1177 Error(lens) 18 375.8571429 20.8809524 Adj Pr > F Source G - G H - F lens 0.1665 0.1528 Error(lens) Greenhouse-Geisser Epsilon 0.4966 Huynh-Feldt Epsilon 0.6229 Source DF Type III SS Mean Square F Value Pr > F eye*lens 3 40.6250000 13.5416667 1.06 0.3925 Error(eye*lens) 18 231.0000000 12.8333333 Adj Pr > F Source G - G H - F eye*lens 0.3700 0.3819 Error(eye*lens) Greenhouse-Geisser Epsilon 0.5493 Huynh-Feldt Epsilon 0.7303