The SAS System 1 14:46 Tuesday, April 15, 2014 The GLM Procedure Class Level Information Class Levels Values pop 2 1 2 trt 2 1 2 id 12 1 2 3 4 5 6 7 8 9 10 11 12 co2conc 7 95 175 250 350 500 675 1000 Number of Observations Read 84 Number of Observations Used 84 The SAS System 2 14:46 Tuesday, April 15, 2014 The GLM Procedure Dependent Variable: co2uptake Sum of Source DF Squares Mean Square F Value Pr > F Model 35 9518.347024 271.952772 69.20 <.0001 Error 48 188.628571 3.929762 Corrected Total 83 9706.975595 R-Square Coeff Var Root MSE co2uptake Mean 0.980568 7.284591 1.982363 27.21310 Source DF Type I SS Mean Square F Value Pr > F pop 1 3365.534405 3365.534405 856.42 <.0001 trt 1 988.114405 988.114405 251.44 <.0001 pop*trt 1 225.729643 225.729643 57.44 <.0001 id(pop*trt) 8 282.831429 35.353929 9.00 <.0001 co2conc 6 4068.771429 678.128571 172.56 <.0001 pop*co2conc 6 374.424762 62.404127 15.88 <.0001 trt*co2conc 6 100.981429 16.830238 4.28 0.0016 pop*trt*co2conc 6 111.959524 18.659921 4.75 0.0007 Source DF Type III SS Mean Square F Value Pr > F pop 1 3365.534405 3365.534405 856.42 <.0001 trt 1 988.114405 988.114405 251.44 <.0001 pop*trt 1 225.729643 225.729643 57.44 <.0001 id(pop*trt) 8 282.831429 35.353929 9.00 <.0001 co2conc 6 4068.771429 678.128571 172.56 <.0001 pop*co2conc 6 374.424762 62.404127 15.88 <.0001 trt*co2conc 6 100.981429 16.830238 4.28 0.0016 pop*trt*co2conc 6 111.959524 18.659921 4.75 0.0007 Tests of Hypotheses Using the Type III MS for id(pop*trt) as an Error Term Source DF Type III SS Mean Square F Value Pr > F pop 1 3365.534405 3365.534405 95.20 <.0001 trt 1 988.114405 988.114405 27.95 0.0007 pop*trt 1 225.729643 225.729643 6.38 0.0354 The SAS System 3 14:46 Tuesday, April 15, 2014 The GLM Procedure Class Level Information Class Levels Values pop 2 1 2 trt 2 1 2 Number of Observations Read 12 Number of Observations Used 12 The SAS System 4 14:46 Tuesday, April 15, 2014 The GLM Procedure Repeated Measures Analysis of Variance Repeated Measures Level Information Dependent Variable y95 y175 y250 y350 y500 y675 Level of conc 95 175 250 350 500 675 Repeated Measures Level Information Dependent Variable y1000 Level of conc 1000 Partial Correlation Coefficients from the Error SSCP Matrix / Prob > |r| DF = 8 y95 y175 y250 y350 y500 y675 y1000 y95 1.000000 0.009594 0.319363 -0.192999 0.067755 0.325766 0.000590 0.9805 0.4022 0.6188 0.8625 0.3923 0.9988 y175 0.009594 1.000000 0.347151 0.616349 0.349384 0.280327 0.309250 0.9805 0.3600 0.0771 0.3567 0.4650 0.4181 y250 0.319363 0.347151 1.000000 0.627956 0.919166 0.802506 0.634024 0.4022 0.3600 0.0702 0.0005 0.0092 0.0667 y350 -0.192999 0.616349 0.627956 1.000000 0.814085 0.694963 0.791941 0.6188 0.0771 0.0702 0.0076 0.0377 0.0110 y500 0.067755 0.349384 0.919166 0.814085 1.000000 0.884890 0.840527 0.8625 0.3567 0.0005 0.0076 0.0015 0.0045 y675 0.325766 0.280327 0.802506 0.694963 0.884890 1.000000 0.908565 0.3923 0.4650 0.0092 0.0377 0.0015 0.0007 y1000 0.000590 0.309250 0.634024 0.791941 0.840527 0.908565 1.000000 0.9988 0.4181 0.0667 0.0110 0.0045 0.0007 The SAS System 5 14:46 Tuesday, April 15, 2014 The GLM Procedure Repeated Measures Analysis of Variance E = Error SSCP Matrix conc_N represents the nth degree polynomial contrast for conc conc_1 conc_2 conc_3 conc_4 conc_5 conc_6 conc_1 61.6610 -23.2306 12.7439 8.1388 -5.3012 9.7052 conc_2 -23.2306 28.5820 -21.2107 -2.9242 -3.5552 -13.2740 conc_3 12.7439 -21.2107 32.0061 -3.4563 10.6391 -11.7376 conc_4 8.1388 -2.9242 -3.4563 7.4926 -6.9414 9.4487 conc_5 -5.3012 -3.5552 10.6391 -6.9414 10.5327 -6.8352 conc_6 9.7052 -13.2740 -11.7376 9.4487 -6.8352 48.3541 Partial Correlation Coefficients from the Error SSCP Matrix of the Variables Defined by the Specified Transformation / Prob > |r| DF = 8 conc_1 conc_2 conc_3 conc_4 conc_5 conc_6 conc_1 1.000000 -0.553361 0.286867 0.378651 -0.208017 0.177739 0.1222 0.4542 0.3149 0.5912 0.6473 conc_2 -0.553361 1.000000 -0.701280 -0.199824 -0.204904 -0.357059 0.1222 0.0353 0.6062 0.5969 0.3455 conc_3 0.286867 -0.701280 1.000000 -0.223190 0.579451 -0.298363 0.4542 0.0353 0.5638 0.1020 0.4355 conc_4 0.378651 -0.199824 -0.223190 1.000000 -0.781375 0.496406 0.3149 0.6062 0.5638 0.0129 0.1741 conc_5 -0.208017 -0.204904 0.579451 -0.781375 1.000000 -0.302878 0.5912 0.5969 0.1020 0.0129 0.4282 conc_6 0.177739 -0.357059 -0.298363 0.496406 -0.302878 1.000000 0.6473 0.3455 0.4355 0.1741 0.4282 Sphericity Tests Mauchly's Variables DF Criterion Chi-Square Pr > ChiSq Transformed Variates 20 0.0019393 36.084829 0.0150 Orthogonal Components 20 0.0019393 36.084829 0.0150 The SAS System 6 14:46 Tuesday, April 15, 2014 The GLM Procedure Repeated Measures Analysis of Variance MANOVA Test Criteria and Exact F Statistics for the Hypothesis of no conc Effect H = Type III SSCP Matrix for conc E = Error SSCP Matrix S=1 M=2 N=0.5 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.00451125 110.33 6 3 0.0013 Pillai's Trace 0.99548875 110.33 6 3 0.0013 Hotelling-Lawley Trace 220.66815723 110.33 6 3 0.0013 Roy's Greatest Root 220.66815723 110.33 6 3 0.0013 MANOVA Test Criteria and Exact F Statistics for the Hypothesis of no conc*pop Effect H = Type III SSCP Matrix for conc*pop E = Error SSCP Matrix S=1 M=2 N=0.5 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.03576022 13.48 6 3 0.0283 Pillai's Trace 0.96423978 13.48 6 3 0.0283 Hotelling-Lawley Trace 26.96403028 13.48 6 3 0.0283 Roy's Greatest Root 26.96403028 13.48 6 3 0.0283 MANOVA Test Criteria and Exact F Statistics for the Hypothesis of no conc*trt Effect H = Type III SSCP Matrix for conc*trt E = Error SSCP Matrix S=1 M=2 N=0.5 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.14668274 2.91 6 3 0.2048 Pillai's Trace 0.85331726 2.91 6 3 0.2048 Hotelling-Lawley Trace 5.81743460 2.91 6 3 0.2048 Roy's Greatest Root 5.81743460 2.91 6 3 0.2048 The SAS System 7 14:46 Tuesday, April 15, 2014 The GLM Procedure Repeated Measures Analysis of Variance MANOVA Test Criteria and Exact F Statistics for the Hypothesis of no conc*pop*trt Effect H = Type III SSCP Matrix for conc*pop*trt E = Error SSCP Matrix S=1 M=2 N=0.5 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.35082441 0.93 6 3 0.5743 Pillai's Trace 0.64917559 0.93 6 3 0.5743 Hotelling-Lawley Trace 1.85042881 0.93 6 3 0.5743 Roy's Greatest Root 1.85042881 0.93 6 3 0.5743 The SAS System 8 14:46 Tuesday, April 15, 2014 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 pop 1 3365.534405 3365.534405 95.20 <.0001 trt 1 988.114405 988.114405 27.95 0.0007 pop*trt 1 225.729643 225.729643 6.38 0.0354 Error 8 282.831429 35.353929 The SAS System 9 14:46 Tuesday, April 15, 2014 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 conc 6 4068.771429 678.128571 172.56 <.0001 conc*pop 6 374.424762 62.404127 15.88 <.0001 conc*trt 6 100.981429 16.830238 4.28 0.0016 conc*pop*trt 6 111.959524 18.659921 4.75 0.0007 Error(conc) 48 188.628571 3.929762 Adj Pr > F Source G - G H - F conc <.0001 <.0001 conc*pop <.0001 <.0001 conc*trt 0.0156 0.0016 conc*pop*trt 0.0103 0.0007 Error(conc) Greenhouse-Geisser Epsilon 0.4893 Huynh-Feldt Epsilon 1.0938 The SAS System 10 14:46 Tuesday, April 15, 2014 The GLM Procedure Repeated Measures Analysis of Variance Analysis of Variance of Contrast Variables conc_N represents the nth degree polynomial contrast for conc Contrast Variable: conc_1 Source DF Type III SS Mean Square F Value Pr > F Mean 1 2284.993964 2284.993964 296.46 <.0001 pop 1 207.997623 207.997623 26.99 0.0008 trt 1 31.870618 31.870618 4.13 0.0764 pop*trt 1 55.534682 55.534682 7.21 0.0277 Error 8 61.660987 7.707623 Contrast Variable: conc_2 Source DF Type III SS Mean Square F Value Pr > F Mean 1 1067.914664 1067.914664 298.91 <.0001 pop 1 83.375497 83.375497 23.34 0.0013 trt 1 48.451842 48.451842 13.56 0.0062 pop*trt 1 28.452860 28.452860 7.96 0.0224 Error 8 28.581995 3.572749 Contrast Variable: conc_3 Source DF Type III SS Mean Square F Value Pr > F Mean 1 606.3603520 606.3603520 151.56 <.0001 pop 1 70.1335228 70.1335228 17.53 0.0031 trt 1 18.9715752 18.9715752 4.74 0.0611 pop*trt 1 12.6208803 12.6208803 3.15 0.1136 Error 8 32.0060941 4.0007618 Contrast Variable: conc_4 Source DF Type III SS Mean Square F Value Pr > F Mean 1 98.84618474 98.84618474 105.54 <.0001 pop 1 10.30004768 10.30004768 11.00 0.0106 trt 1 0.94898124 0.94898124 1.01 0.3436 pop*trt 1 3.34312607 3.34312607 3.57 0.0955 The SAS System 11 14:46 Tuesday, April 15, 2014 The GLM Procedure Repeated Measures Analysis of Variance Analysis of Variance of Contrast Variables conc_N represents the nth degree polynomial contrast for conc Contrast Variable: conc_4 Source DF Type III SS Mean Square F Value Pr > F Error 8 7.49264191 0.93658024 Contrast Variable: conc_5 Source DF Type III SS Mean Square F Value Pr > F Mean 1 1.91300171 1.91300171 1.45 0.2625 pop 1 0.71589146 0.71589146 0.54 0.4819 trt 1 0.13655809 0.13655809 0.10 0.7557 pop*trt 1 2.14622283 2.14622283 1.63 0.2375 Error 8 10.53270516 1.31658815 Contrast Variable: conc_6 Source DF Type III SS Mean Square F Value Pr > F Mean 1 8.74326196 8.74326196 1.45 0.2635 pop 1 1.90218007 1.90218007 0.31 0.5902 trt 1 0.60185438 0.60185438 0.10 0.7604 pop*trt 1 9.86175268 9.86175268 1.63 0.2373 Error 8 48.35414844 6.04426855 The SAS System 12 14:46 Tuesday, April 15, 2014 The Mixed Procedure Model Information Data Set WORK.UNI Dependent Variable co2uptake Covariance Structure Spatial Power Subject Effect id Estimation Method REML Residual Variance Method Profile Fixed Effects SE Method Model-Based Degrees of Freedom Method Between-Within Class Level Information Class Levels Values pop 2 1 2 trt 2 1 2 id 12 1 2 3 4 5 6 7 8 9 10 11 12 co2conc 7 95 175 250 350 500 675 1000 Dimensions Covariance Parameters 2 Columns in X 72 Columns in Z 0 Subjects 12 Max Obs Per Subject 7 Number of Observations Number of Observations Read 84 Number of Observations Used 84 Number of Observations Not Used 0 Iteration History Iteration Evaluations -2 Res Log Like Criterion 0 1 308.98928384 1 2 296.95948339 0.00000335 2 1 296.95915755 0.00000000 The SAS System 13 14:46 Tuesday, April 15, 2014 The Mixed Procedure Convergence criteria met. Estimated R Matrix for id 1 Row Col1 Col2 Col3 Col4 Col5 Col6 Col7 1 9.2385 6.1721 4.2288 2.5542 1.1990 0.4962 0.09639 2 6.1721 9.2385 6.3297 3.8232 1.7947 0.7427 0.1443 3 4.2288 6.3297 9.2385 5.5801 2.6194 1.0840 0.2106 4 2.5542 3.8232 5.5801 9.2385 4.3367 1.7947 0.3486 5 1.1990 1.7947 2.6194 4.3367 9.2385 3.8232 0.7427 6 0.4962 0.7427 1.0840 1.7947 3.8232 9.2385 1.7947 7 0.09639 0.1443 0.2106 0.3486 0.7427 1.7947 9.2385 Estimated R Correlation Matrix for id 1 Row Col1 Col2 Col3 Col4 Col5 Col6 Col7 1 1.0000 0.6681 0.4577 0.2765 0.1298 0.05371 0.01043 2 0.6681 1.0000 0.6851 0.4138 0.1943 0.08039 0.01562 3 0.4577 0.6851 1.0000 0.6040 0.2835 0.1173 0.02279 4 0.2765 0.4138 0.6040 1.0000 0.4694 0.1943 0.03774 5 0.1298 0.1943 0.2835 0.4694 1.0000 0.4138 0.08039 6 0.05371 0.08039 0.1173 0.1943 0.4138 1.0000 0.1943 7 0.01043 0.01562 0.02279 0.03774 0.08039 0.1943 1.0000 Covariance Parameter Estimates Cov Parm Subject Estimate SP(POW) id 0.6040 Residual 9.2385 Fit Statistics -2 Res Log Likelihood 297.0 AIC (smaller is better) 301.0 AICC (smaller is better) 301.2 BIC (smaller is better) 301.9 The SAS System 14 14:46 Tuesday, April 15, 2014 The Mixed Procedure Null Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq 1 12.03 0.0005 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F pop 1 8 143.21 <.0001 trt 1 8 42.05 0.0002 pop*trt 1 8 9.61 0.0147 co2conc 6 48 81.34 <.0001 pop*co2conc 6 48 7.72 <.0001 trt*co2conc 6 48 2.15 0.0651 pop*trt*co2conc 6 48 2.40 0.0415