EXST7015 Fall2011 Appendix 17

EXST7015 Fall2011 Appendix 17 - Statistical Techniques II...

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Unformatted text preview: Statistical Techniques II Appendix 17 SAS Example Split-plot and Repeated measures designs Page 311 1 dm 'log;clear;output;clear'; 2 options ps=512 ls=109 nocenter nodate nonumber 3 nolabel FORMCHAR="|----|+|---+=|-/\<>*"; 4 TITLE1 'Study of drug effect on asthma patients'; 5 6 ODS HTML style=minimal body='C:\SAS\Appendix17 Repeated (Asthma).HTML' ; NOTE: Writing HTML Body file: C:\SAS\Appendix17 Repeated (Asthma).HTML 7 *ODS rtf style=minimal body='C:\SAS\Appendix17 Repeated (Asthma).RTF' ; 8 *ODS PDF style=minimal body='C:\SAS\Appendix17 Repeated (Asthma).PDF' ; 9 filename input1 'C:\SAS\Appendix17 Repeated (Asthma).dat'; 10 FILENAME OUT1 'C:\SAS\Appendix17 Repeated (Asthma)01.CGM'; 11 FILENAME OUT2 'C:\SAS\Appendix17 Repeated (Asthma)02.CGM'; 12 13 ********************************************************************; 14 *** A pharmaceutical company wants to examine the effects of ***; 15 *** three drugs on the respiratory ability of asthma patients. ***; 16 *** The three drugs are labeled a, c, and p. Drug a is a ***; 17 *** standard drug used to treat asthma. Drug c is a potential ***; 18 *** competitor that was developed by the pharmaceutical company. ***; 19 *** Drug p is a placebo. Each of the three drugs is randomly ***; 20 *** assigned to 24 patients. A total of 72 patients are included ***; 21 *** in the study. The assigned drug is administered to each ***; 22 *** patient. Then a standard measure of respiratory ability ***; 23 *** called fev1 (forced exhaled volume in one second) is ***; 24 *** measured hourly for eight hours following treatment. Also, ***; 25 *** a baseline fev1 is measured immediately before administering ***; 26 *** the drugs. ***; 27 ********************************************************************; 28 29 data fev1mult; infile input1 missover; 30 input patient basefev1 fev11h fev12h fev13h fev14h 31 fev15h fev16h fev17h fev18h drug $; 32 label patient = patient identification number 33 basefev1 = baseline fev1 measurement taken before the treatment 34 fev11h = fev1 measurement one hour after giving the drug 35 fev12h = fev1 measurement two hours after giving the drug 36 fev13h = fev1 measurement three hours after giving the drug 37 fev14h = fev1 measurement four hours after giving the drug 38 fev15h = fev1 measurement five hours after giving the drug 39 fev16h = fev1 measurement six hours after giving the drug 40 fev17h = fev1 measurement seven hours after giving the drug 41 fev18h = fev1 measurement eight hours after giving the drug 42 drug = drug administered (a, c, or p); 43 datalines; NOTE: The infile INPUT1 is: Filename=C:\SAS\Appendix17 Repeated (Asthma).dat, RECFM=V,LRECL=256,File Size (bytes)=3744, Last Modified=13Jan2011:19:19:57, Create Time=13Jan2011:19:19:33 NOTE: 72 records were read from the infile INPUT1. The minimum record length was 50. The maximum record length was 50. NOTE: The data set WORK.FEV1MULT has 72 observations and 11 variables. NOTE: DATA statement used (Total process time): real time 0.73 seconds cpu time 0.07 seconds 44 run; 45 46 proc print data=fev1mult; run; NOTE: There were 72 observations read from the data set WORK.FEV1MULT. NOTE: The PROCEDURE PRINT printed page 1. NOTE: PROCEDURE PRINT used (Total process time): real time 0.68 seconds cpu time 0.04 seconds Study of drug effect on asthma patients Obs patient 1 201 2 202 3 203 4 204 5 205 . . . 68 221 69 222 basefev1 2.46 3.50 1.96 3.44 2.80 fev11h 2.68 3.95 2.28 4.08 4.09 fev12h 2.76 3.65 2.34 3.87 3.90 fev13h 2.50 2.93 2.29 3.79 3.54 fev14h 2.30 2.53 2.43 3.30 3.35 fev15h 2.14 3.04 2.06 3.80 3.15 fev16h 2.40 3.37 2.18 3.24 3.23 fev17h 2.33 3.14 2.28 2.98 3.46 fev18h 2.20 2.62 2.29 2.91 3.27 3.50 2.86 3.81 3.06 3.77 2.95 3.78 3.07 3.90 3.10 3.80 2.67 3.78 2.68 3.70 2.94 3.61 2.89 drug a a a a a p p James P. Geaghan - Copyright 2011 Statistical Techniques II Appendix 17 SAS Example Split-plot and Repeated measures designs 70 71 72 223 224 232 2.42 3.66 2.88 2.87 3.98 3.04 Page 312 3.08 3.77 3.00 3.02 3.65 3.24 3.14 3.81 3.37 3.67 3.77 2.69 3.84 3.89 2.89 3.55 3.63 2.89 3.75 3.74 2.76 p p p 48 ********************************************************************; 49 *** The dataset above, with all repeated measures on one line is ***; 50 *** referred to as a multivariate arrangement. We need a ***; 51 *** univariate arrangement, with only one measurement per line. ***; 52 ********************************************************************; 53 54 data fev1uni(drop=fev11h fev12h fev13h fev14h fev15h fev16h fev17h fev18h); 55 set fev1mult; 56 label patient = patient identification number 57 basefev1 = baseline fev1 measurement taken before giving the treatment 58 drug = the drug administrated (a, c, or p) to a patient. 59 hour = number of hours the measurement was taken after giving the drug 60 fev1 = forced exhaled volume in one second measurement.; 61 array fev[8] fev11h fev12h fev13h fev14h fev15h fev16h fev17h fev18h; 62 do hour = 1 to 8; 63 fev1 = fev[hour]; 64 output; 65 end; 66 run; NOTE: There were 72 observations read from the data set WORK.FEV1MULT. NOTE: The data set WORK.FEV1UNI has 576 observations and 5 variables. NOTE: DATA statement used (Total process time): real time 0.07 seconds cpu time 0.00 seconds 67 proc print data=fev1uni; run; NOTE: There were 576 observations read from the data set WORK.FEV1UNI. NOTE: The PROCEDURE PRINT printed pages 2-3. NOTE: PROCEDURE PRINT used (Total process time): real time 0.23 seconds cpu time 0.14 seconds Study of drug effect on asthma patients Obs 1 2 3 4 5 6 7 8 9 10 . . . 572 573 574 575 576 patient 201 201 201 201 201 201 201 201 202 202 basefev1 2.46 2.46 2.46 2.46 2.46 2.46 2.46 2.46 3.50 3.50 232 232 232 232 232 2.88 2.88 2.88 2.88 2.88 drug a a a a a a a a a a p p p p p hour 1 2 3 4 5 6 7 8 1 2 4 5 6 7 8 fev1 2.68 2.76 2.50 2.30 2.14 2.40 2.33 2.20 3.95 3.65 3.37 2.69 2.89 2.89 2.76 69 proc mixed data=fev1uni; class drug patient hour; 70 title2 'Repeated measures analysis with AR(1) covariance'; 71 model fev1=drug basefev1 drug*basefev1 hour drug*hour / ddfm=kr ; 72 repeated hour / type=ar(1) subject=patient(drug); 73 ods output FitStatistics=FitAR1(rename=(value=AR1)) 74 FitStatistics=FitAR1p 75 Dimensions=ParmAR1(rename=(value=NumAR1)); 76 run; NOTE:Convergence criteria met. NOTE: The data set WORK.PARMAR1 has 5 observations and 2 variables. NOTE: The data set WORK.FITAR1P has 4 observations and 2 variables. NOTE: The data set WORK.FITAR1 has 4 observations and 2 variables. NOTE: The PROCEDURE MIXED printed page 4. NOTE: PROCEDURE MIXED used (Total process time): real time 1.26 seconds cpu time 0.26 seconds James P. Geaghan - Copyright 2011 Statistical Techniques II Appendix 17 Split-plot and Repeated measures designs SAS Example Page 313 Study of drug effect on asthma patients Repeated measures analysis with AR(1) covariance The Mixed Procedure Model Information Data Set Dependent Variable Covariance Structure Subject Effect Estimation Method Residual Variance Method Fixed Effects SE Method Degrees of Freedom Method WORK.FEV1UNI fev1 Autoregressive patient(drug) REML Profile Kenward-Roger Kenward-Roger Class Level Information Class Levels Values drug patient 3 24 hour 8 a c 201 208 216 223 1 2 p 202 209 217 224 3 4 203 210 218 232 5 6 Dimensions Covariance Parameters Columns in X Columns in Z Subjects Max Obs Per Subject Number Number Number Number of of of of 204 205 206 207 211 212 214 215 219 220 221 222 7 8 2 40 0 72 8 Observations Observations Read Observations Used Observations Not Used Iteration History Iteration Evaluations 0 1 1 2 2 1 Convergence criteria met. 576 576 0 -2 Res Log Like 914.99974879 276.12192387 276.12191676 Criterion 0.00000002 0.00000000 Covariance Parameter Estimates Cov Parm Subject Estimate AR(1) patient(drug) 0.8573 Residual 0.2676 Fit Statistics -2 Res Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) 276.1 280.1 280.1 284.7 Null Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq 1 638.88 <.0001 Type 3 Tests of Fixed Effects Num Den Effect DF DF drug 2 74.8 basefev1 1 74.7 basefev1*drug 2 74.7 hour 7 479 drug*hour 14 482 77 78 79 80 81 82 83 84 F Value 0.62 90.33 0.72 7.27 2.42 Pr > F 0.5396 <.0001 0.4889 <.0001 0.0027 proc mixed data=fev1uni; class drug patient hour; title2 'Repeated measures analysis with Toeplitz covariance'; model fev1=drug basefev1 drug*basefev1 hour drug*hour / ddfm=kr; repeated hour / type=toep subject=patient(drug); ods output FitStatistics=FitToep(rename=(value=Toep)) FitStatistics=FitToepp Dimensions=ParmToep(rename=(value=NumToep)); James P. Geaghan - Copyright 2011 Statistical Techniques II Appendix 17 Split-plot and Repeated measures designs SAS Example Page 314 85 run; NOTE:Convergence criteria met. NOTE: The data set WORK.PARMTOEP has 5 observations and 2 variables. NOTE: The data set WORK.FITTOEPP has 4 observations and 2 variables. NOTE: The data set WORK.FITTOEP has 4 observations and 2 variables. NOTE: The PROCEDURE MIXED printed page 5. NOTE: PROCEDURE MIXED used (Total process time): real time 0.87 seconds cpu time 0.76 seconds Study of drug effect on asthma patients Repeated measures analysis with Toeplitz covariance The Mixed Procedure Model Information Data Set Dependent Variable Covariance Structure Subject Effect Estimation Method Residual Variance Method Fixed Effects SE Method Degrees of Freedom Method WORK.FEV1UNI fev1 Toeplitz patient(drug) REML Profile Kenward-Roger Kenward-Roger Class Level Information Class Levels Values drug patient 3 24 hour 8 a c 201 216 1 2 p 202 203 204 205 206 207 208 209 210 211 212 214 215 217 218 219 220 221 222 223 224 232 3 4 5 6 7 8 Dimensions Covariance Parameters Columns in X Columns in Z Subjects Max Obs Per Subject Number Number Number Number of of of of 8 40 0 72 8 Observations Observations Read Observations Used Observations Not Used Iteration History Iteration Evaluations 0 1 1 2 2 1 3 1 4 1 Convergence criteria met. 576 576 0 -2 Res Log Like 914.99974879 232.74147713 229.29333247 229.03013689 229.02803484 Criterion 0.00771564 0.00063950 0.00000536 0.00000000 Covariance Parameter Estimates Cov Parm Subject Estimate TOEP(2) patient(drug) 0.2314 TOEP(3) patient(drug) 0.2191 TOEP(4) patient(drug) 0.2099 TOEP(5) patient(drug) 0.1937 TOEP(6) patient(drug) 0.1858 TOEP(7) patient(drug) 0.1724 TOEP(8) patient(drug) 0.1612 Residual 0.2694 Fit Statistics -2 Res Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) 229.0 245.0 245.3 263.2 Null Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq 7 685.97 <.0001 James P. Geaghan - Copyright 2011 Statistical Techniques II Appendix 17 SAS Example Split-plot and Repeated measures designs Type 3 Tests of Fixed Effects Num Den Effect DF DF drug 2 66 basefev1 1 65.9 basefev1*drug 2 65.9 hour 7 186 drug*hour 14 249 Page 315 F Value 0.41 74.53 0.51 13.50 3.73 Pr > F 0.6667 <.0001 0.6026 <.0001 <.0001 86 87 proc mixed data=fev1uni; class drug patient hour; 88 title2 'Repeated measures analysis with compound symmetry covariance'; 89 model fev1=drug basefev1 drug*basefev1 hour drug*hour / ddfm=kr ; 90 repeated hour / type=CS subject=patient(drug); 91 ods output FitStatistics=FitCS(rename=(value=CS)) 92 FitStatistics=FitCSp 93 Dimensions=ParmUN(rename=(value=NumCS)); 94 run; NOTE:Convergence criteria met. NOTE: The data set WORK.PARMUN has 5 observations and 2 variables. NOTE: The data set WORK.FITCSP has 4 observations and 2 variables. NOTE: The data set WORK.FITCS has 4 observations and 2 variables. NOTE: The PROCEDURE MIXED printed page 6. NOTE: PROCEDURE MIXED used (Total process time): real time 0.31 seconds cpu time 0.21 seconds 95 Study of drug effect on asthma patients Repeated measures analysis with compound symmetry covariance The Mixed Procedure Model Information Data Set Dependent Variable Covariance Structure Subject Effect Estimation Method Residual Variance Method Fixed Effects SE Method Degrees of Freedom Method WORK.FEV1UNI fev1 Compound Symmetry patient(drug) REML Profile Kenward-Roger Kenward-Roger Class Level Information Class Levels Values drug patient 3 24 hour 8 a c 201 216 1 2 p 202 203 204 205 206 207 208 209 210 211 212 214 215 217 218 219 220 221 222 223 224 232 3 4 5 6 7 8 Dimensions Covariance Parameters Columns in X Columns in Z Subjects Max Obs Per Subject Number Number Number Number of of of of 2 40 0 72 8 Observations Observations Read Observations Used Observations Not Used Iteration History Iteration Evaluations 0 1 1 1 Convergence criteria met. 576 576 0 -2 Res Log Like 914.99974879 348.18647731 Criterion 0.00000000 Covariance Parameter Estimates Cov Parm Subject Estimate CS patient(drug) 0.2088 Residual 0.06313 James P. Geaghan - Copyright 2011 Statistical Techniques II Appendix 17 Split-plot and Repeated measures designs Fit Statistics -2 Res Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) SAS Example Page 316 348.2 352.2 352.2 356.7 Null Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq 1 566.81 <.0001 Type 3 Tests of Fixed Effects Num Den Effect DF DF drug 2 66 basefev1 1 66 basefev1*drug 2 66 hour 7 483 drug*hour 14 483 F Value 0.41 75.36 0.59 38.86 7.11 Pr > F 0.6674 <.0001 0.5547 <.0001 <.0001 96 proc mixed data=fev1uni; class drug patient hour; 97 title2 'Repeated measures analysis with unstructured covariance'; 98 model fev1 = drug basefev1 drug*basefev1 hour drug*hour / ddfm=kr outp=resids; 99 repeated hour / type=un subject=patient(drug); 100 ods output FitStatistics=FitUn(rename=(value=UN)) 101 FitStatistics=FitUNp 102 Dimensions=ParmUN(rename=(value=NumUN)); 103 lsmeans drug | hour / adjust=tukey pdiff cl; 104 ods output diffs=ppp lsmeans=mmm; 105 ods listing exclude diffs;* lsmeans; 106 run; NOTE: With DDFM=SATTERTHWAITE or DDFM=KENWADROGER, unadjusted p-values in tests are based on the degrees of freedom specific to that comparison. P-values that are adjusted for multiplicity, however, are by default based on the denominator degrees of freedom for the Type 3 test of the fixed effect. If you specify the ADJDFE=ROW option in the LSMEANS statement, the adjusted p-values take into account the row-wise degrees of freedom. NOTE:Convergence criteria met. NOTE: The data set WORK.MMM has 35 observations and 11 variables. NOTE: The data set WORK.PPP has 307 observations and 17 variables. NOTE: The data set WORK.PARMUN has 5 observations and 2 variables. NOTE: The data set WORK.FITUNP has 4 observations and 2 variables. NOTE: The data set WORK.FITUN has 4 observations and 2 variables. NOTE: The data set WORK.RESIDS has 576 observations and 12 variables. NOTE: The PROCEDURE MIXED printed page 7. NOTE: PROCEDURE MIXED used (Total process time): real time 7.32 seconds cpu time 6.92 seconds 107 %include 'C:\SAS\pdmix800.sas'; 780 %pdmix800(ppp,mmm,alpha=0.05,sort=yes); run; PDMIX800 08.08.2003 processing 3.3915683266 Tukey-Kramer values for drug are 0.32327 (avg) 0.32322 (min) 0.32332 (max). 4.4205807351 Tukey-Kramer values for hour are 0.12796 (avg) 0.07992 (min) 0.18091 (max). 5.2860955037 Tukey-Kramer values for drug*hour are 0.47288 (avg) 0.16553 (min) 0.59466 (max). Study of drug effect on asthma patients Repeated measures analysis with unstructured covariance The Mixed Procedure Model Information Data Set Dependent Variable Covariance Structure Subject Effect Estimation Method Residual Variance Method Fixed Effects SE Method Degrees of Freedom Method WORK.FEV1UNI fev1 Unstructured patient(drug) REML None Kenward-Roger Kenward-Roger James P. Geaghan - Copyright 2011 Statistical Techniques II Appendix 17 SAS Example Split-plot and Repeated measures designs Page 317 Class Level Information Class Levels Values drug 3 a c p patient 24 201 202 203 204 205 206 207 208 209 210 211 212 214 215 216 217 218 219 220 221 222 223 224 232 hour 8 1 2 3 4 5 6 7 8 Dimensions Covariance Parameters Columns in X Columns in Z Subjects Max Obs Per Subject Number Number Number Number of of of of 36 40 0 72 8 Observations Observations Read Observations Used Observations Not Used Iteration History Iteration Evaluations 0 1 1 2 2 1 Convergence criteria met. 576 576 0 -2 Res Log Like 914.99974879 150.44318726 150.44307540 Criterion 0.00000026 0.00000000 Covariance Parameter Estimates Cov Parm Subject Estimate UN(1,1) patient(drug) 0.2321 UN(2,1) patient(drug) 0.2210 UN(2,2) patient(drug) 0.2629 UN(3,1) patient(drug) 0.2162 UN(3,2) patient(drug) 0.2372 UN(3,3) patient(drug) 0.2586 UN(4,1) patient(drug) 0.2091 UN(4,2) patient(drug) 0.2469 UN(4,3) patient(drug) 0.2566 UN(4,4) patient(drug) 0.3033 UN(5,1) patient(drug) 0.1789 UN(5,2) patient(drug) 0.2226 UN(5,3) patient(drug) 0.2224 UN(5,4) patient(drug) 0.2434 UN(5,5) patient(drug) 0.2879 UN(6,1) patient(drug) 0.1680 UN(6,2) patient(drug) 0.1845 UN(6,3) patient(drug) 0.1951 Fit Statistics -2 Res Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) UN(6,4) UN(6,5) UN(6,6) UN(7,1) UN(7,2) UN(7,3) UN(7,4) UN(7,5) UN(7,6) UN(7,7) UN(8,1) UN(8,2) UN(8,3) UN(8,4) UN(8,5) UN(8,6) UN(8,7) UN(8,8) patient(drug) patient(drug) patient(drug) patient(drug) patient(drug) patient(drug) patient(drug) patient(drug) patient(drug) patient(drug) patient(drug) patient(drug) patient(drug) patient(drug) patient(drug) patient(drug) patient(drug) patient(drug) 0.2083 0.2351 0.2620 0.1328 0.1602 0.1729 0.1948 0.2069 0.2187 0.2748 0.1731 0.1992 0.2090 0.2300 0.2502 0.2491 0.2375 0.3035 150.4 222.4 227.6 304.4 Null Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq 35 764.56 <.0001 Type 3 Tests of Fixed Effects Num Den Effect DF DF drug 2 66.8 basefev1 1 66 basefev1*drug 2 66 hour 7 63 drug*hour 14 98.1 F Value 0.04 74.30 0.10 12.53 3.66 Pr > F 0.9594 <.0001 0.9068 <.0001 <.0001 Least Squares Means Effect drug drug drug hour hour hour hour drug a c p hour 1 2 3 4 Estimate 3.1054 3.3319 2.8236 3.3295 3.3043 3.2188 3.1195 Standard Error 0.09534 0.09529 0.09532 0.05679 0.06045 0.05995 0.06492 DF 65.4 65.4 65.4 66.3 66.4 65.6 65.4 t Value 32.57 34.97 29.62 58.63 54.66 53.69 48.05 Pr > |t| <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 Alpha 0.05 0.05 0.05 0.05 0.05 0.05 0.05 Lower 2.9150 3.1416 2.6332 3.2161 3.1837 3.0991 2.9898 Upper 3.2957 3.5222 3.0139 3.4428 3.4250 3.3385 3.2491 James P. Geaghan - Copyright 2011 Statistical Techniques II Appendix 17 SAS Example Split-plot and Repeated measures designs hour hour hour hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour a a a a a a a a c c c c c c c c p p p p p p p p 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 3.0228 2.9591 2.8757 2.8659 3.4713 3.3947 3.1818 3.0443 3.0513 2.9772 2.8663 2.8559 3.6904 3.6259 3.5767 3.4429 3.2488 3.0846 2.9763 3.0096 2.8266 2.8925 2.8979 2.8712 2.7683 2.8154 2.7845 2.7320 Page 318 0.06325 0.06034 0.06179 0.06494 0.09839 0.1047 0.1039 0.1125 0.1096 0.1045 0.1071 0.1125 0.09834 0.1047 0.1038 0.1124 0.1095 0.1045 0.1070 0.1125 0.09836 0.1047 0.1038 0.1124 0.1095 0.1045 0.1070 0.1125 65 67 67.4 65.5 66.3 66.5 65.6 65.4 65 67 67.5 65.5 66.3 66.4 65.6 65.3 64.9 66.9 67.4 65.5 66.3 66.4 65.6 65.4 65 67 67.5 65.5 47.79 49.04 46.54 44.13 35.28 32.41 30.64 27.07 27.85 28.48 26.78 25.38 37.53 34.64 34.46 30.63 29.66 29.52 27.82 26.76 28.74 27.63 27.91 25.53 25.27 26.94 26.02 24.29 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 2.8965 2.8386 2.7524 2.7362 3.2749 3.1856 2.9744 2.8197 2.8325 2.7685 2.6527 2.6313 3.4941 3.4169 3.3694 3.2184 3.0300 2.8761 2.7627 2.7850 2.6302 2.6834 2.6905 2.6467 2.5495 2.6068 2.5709 2.5074 3.1491 3.0795 2.9990 2.9955 3.6678 3.6037 3.3891 3.2689 3.2702 3.1858 3.0800 3.0806 3.8868 3.8348 3.7840 3.6674 3.4675 3.2932 3.1898 3.2342 3.0230 3.1015 3.1052 3.0958 2.9871 3.0240 2.9981 2.9567 Study of drug effect on asthma patients Repeated measures analysis with unstructured covariance Effect=drug ADJUSTMENT=Tukey-Kramer(P<0.05) bygroup=1 Obs drug hour Estimate StdErr Alpha 1 c _ 3.3319 0.09529 0.05 2 a _ 3.1054 0.09534 0.05 3 p _ 2.8236 0.09532 0.05 Lower 3.1416 2.9150 2.6332 Upper 3.5222 3.2957 3.0139 MSGROUP A AB B Effect=hour ADJUSTMENT=Tukey-Kramer(P<0.05) bygroup=2 Obs drug hour Estimate StdErr Alpha 4 1 3.3295 0.05679 0.05 5 2 3.3043 0.06045 0.05 6 3 3.2188 0.05995 0.05 7 4 3.1195 0.06492 0.05 8 5 3.0228 0.06325 0.05 9 6 2.9591 0.06034 0.05 10 7 2.8757 0.06179 0.05 11 8 2.8659 0.06494 0.05 Lower 3.2161 3.1837 3.0991 2.9898 2.8965 2.8386 2.7524 2.7362 Upper 3.4428 3.4250 3.3385 3.2491 3.1491 3.0795 2.9990 2.9955 MSGROUP A A B C CD DE E E Effect=drug*hour ADJUSTMENT=Tukey-Kramer(P<0.05) bygroup=3 Obs drug hour Estimate StdErr Alpha Lower 12 c 1 3.6904 0.09834 0.05 3.4941 13 c 2 3.6259 0.1047 0.05 3.4169 14 c 3 3.5767 0.1038 0.05 3.3694 15 a 1 3.4713 0.09839 0.05 3.2749 16 c 4 3.4429 0.1124 0.05 3.2184 17 a 2 3.3947 0.1047 0.05 3.1856 18 c 5 3.2488 0.1095 0.05 3.0300 19 a 3 3.1818 0.1039 0.05 2.9744 20 c 6 3.0846 0.1045 0.05 2.8761 21 a 5 3.0513 0.1096 0.05 2.8325 22 a 4 3.0443 0.1125 0.05 2.8197 23 c 8 3.0096 0.1125 0.05 2.7850 24 a 6 2.9772 0.1045 0.05 2.7685 25 c 7 2.9763 0.1070 0.05 2.7627 26 p 3 2.8979 0.1038 0.05 2.6905 27 p 2 2.8925 0.1047 0.05 2.6834 28 p 4 2.8712 0.1124 0.05 2.6467 29 a 7 2.8663 0.1071 0.05 2.6527 30 a 8 2.8559 0.1125 0.05 2.6313 31 p 1 2.8266 0.09836 0.05 2.6302 32 p 6 2.8154 0.1045 0.05 2.6068 33 p 7 2.7845 0.1070 0.05 2.5709 34 p 5 2.7683 0.1095 0.05 2.5495 35 p 8 2.7320 0.1125 0.05 2.5074 Upper 3.8868 3.8348 3.7840 3.6678 3.6674 3.6037 3.4675 3.3891 3.2932 3.2702 3.2689 3.2342 3.1858 3.1898 3.1052 3.1015 3.0958 3.0800 3.0806 3.0230 3.0240 2.9981 2.9871 2.9567 MSGROUP AB AB ABC ADEF ABCDGH ADEFI DEGHJ BCGJK EFIJL CGHJK CGHJK FIKL GHJKL EFIJL GHIJ GHIJ GHIJ GHJKL HL JKL JKL JKL JKL JKL James P. Geaghan - Copyright 2011 Statistical Techniques II Appendix 17 SAS Example Split-plot and Repeated measures designs Page 319 781 782 options ps=512 ls=132; 783 PROC UNIVARIATE DATA=Resids PLOT NORMAL; VAR resid; 784 ods exclude basicmeasures extremeobs quantiles testsforlocation; 785 TITLE2 'Analysis of residuals from PROC MIXED'; 786 RUN; NOTE: The PROCEDURE UNIVARIATE printed page 9. NOTE: PROCEDURE UNIVARIATE used (Total process time): real time 0.20 seconds cpu time 0.03 seconds 786 ! QUIT; Study of drug effect on asthma patients Analysis of residuals from PROC MIXED The UNIVARIATE Procedure Variable: Resid Moments N Mean Std Deviation Skewness Uncorrected SS Coeff Variation 576 0 0.50436299 0.42501612 146.269665 . Tests for Normality Test Shapiro-Wilk Kolmogorov-Smirnov Cramer-von Mises Anderson-Darling Sum Weights Sum Observations Variance Kurtosis Corrected SS Std Error Mean --Statistic--W 0.984847 D 0.068424 W-Sq 0.480759 A-Sq 2.84676 Histogram Boxplot 1.5+* .*** .**** .********* .********* .************* .******************** 0.1+****************************** .************************************* .************************** .********************** .************* .***** .*** -1.3+* ----+----+----+----+----+----+----+-* may represent up to 3 counts 576 0 0.25438203 0.11368615 146.269665 0.02101512 -----p Value-----Pr < W <0.0001 Pr > D <0.0100 Pr > W-Sq <0.0050 Pr > A-Sq <0.0050 3 7 12 25 27 38 59 90 111 78 66 37 14 7 0 0 | | | | +-----+ | + | *-----* +-----+ | | | | 2 | Normal Probability Plot 1.5+ * | ***** | ****++ | *****+ | ****+ | +*** | +***** 0.1+ +***** | ****** | ***** | ****** | *****+ | ****++ |****++ -1.3+*+ +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 787 788 proc print data=mmm; run; NOTE: There were 35 observations read from the data set WORK.MMM. NOTE: The PROCEDURE PRINT printed page 10. NOTE: PROCEDURE PRINT used (Total process time): real time 0.14 seconds cpu time 0.03 seconds Study of drug effect on asthma patients Analysis of residuals from PROC MIXED Obs 1 2 3 4 5 6 7 8 9 10 11 12 13 Effect drug drug drug hour hour hour hour hour hour hour hour drug*hour drug*hour drug a c p a a hour _ _ _ 1 2 3 4 5 6 7 8 1 2 Estimate 3.1054 3.3319 2.8236 3.3295 3.3043 3.2188 3.1195 3.0228 2.9591 2.8757 2.8659 3.4713 3.3947 StdErr 0.09534 0.09529 0.09532 0.05679 0.06045 0.05995 0.06492 0.06325 0.06034 0.06179 0.06494 0.09839 0.1047 DF 65.4 65.4 65.4 66.3 66.4 65.6 65.4 65 67 67.4 65.5 66.3 66.5 tValue 32.57 34.97 29.62 58.63 54.66 53.69 48.05 47.79 49.04 46.54 44.13 35.28 32.41 Probt <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 Alpha 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 Lower 2.9150 3.1416 2.6332 3.2161 3.1837 3.0991 2.9898 2.8965 2.8386 2.7524 2.7362 3.2749 3.1856 Upper 3.2957 3.5222 3.0139 3.4428 3.4250 3.3385 3.2491 3.1491 3.0795 2.9990 2.9955 3.6678 3.6037 James P. Geaghan - Copyright 2011 Statistical Techniques II Appendix 17 SAS Example Split-plot and Repeated measures designs 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour drug*hour a a a a a a c c c c c c c c p p p p p p p p 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 Page 320 3.1818 3.0443 3.0513 2.9772 2.8663 2.8559 3.6904 3.6259 3.5767 3.4429 3.2488 3.0846 2.9763 3.0096 2.8266 2.8925 2.8979 2.8712 2.7683 2.8154 2.7845 2.7320 0.1039 0.1125 0.1096 0.1045 0.1071 0.1125 0.09834 0.1047 0.1038 0.1124 0.1095 0.1045 0.1070 0.1125 0.09836 0.1047 0.1038 0.1124 0.1095 0.1045 0.1070 0.1125 65.6 65.4 65 67 67.5 65.5 66.3 66.4 65.6 65.3 64.9 66.9 67.4 65.5 66.3 66.4 65.6 65.4 65 67 67.5 65.5 30.64 27.07 27.85 28.48 26.78 25.38 37.53 34.64 34.46 30.63 29.66 29.52 27.82 26.76 28.74 27.63 27.91 25.53 25.27 26.94 26.02 24.29 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 2.9744 2.8197 2.8325 2.7685 2.6527 2.6313 3.4941 3.4169 3.3694 3.2184 3.0300 2.8761 2.7627 2.7850 2.6302 2.6834 2.6905 2.6467 2.5495 2.6068 2.5709 2.5074 3.3891 3.2689 3.2702 3.1858 3.0800 3.0806 3.8868 3.8348 3.7840 3.6674 3.4675 3.2932 3.1898 3.2342 3.0230 3.1015 3.1052 3.0958 2.9871 3.0240 2.9981 2.9567 789 options ps=52 ls=132; 790 proc plot data=resids; plot resid*pred=drug / vref=0; run; 791 NOTE: There were 576 observations read from the data set WORK.RESIDS. NOTE: The PROCEDURE PLOT printed page 11. NOTE: PROCEDURE PLOT used (Total process time): real time 0.06 seconds cpu time 0.01 seconds Study of drug effect on asthma patients Analysis of residuals from PROC MIXED Plot of Resid*Pred. Symbol is value of drug. Resid | | | c 1.5 + c | c | a c c | ap ca a cc | a pp c c ac 1.0 + p p a a a | a p p aa ca p p c c a c | a ap p p a a ca c | a a pp pp p pa c a a a c | p p a a pa ppa c c a 0.5 + pp apc a a c a a a c | p pac p ppccacp c p a a c acac ac c c | a a p acc c p apaapc c c c c | c p p a a aa caca ca pcc cp ccc c | c a p p a aa a apa acac paa a ac ap paa c c a c c 0.0 +-------c--------------ccac-p-apc-a-ppca-pc-ppcacap--aappaa-------c-p--aa--aa-aca-a-----ac--------------------| c p cp pppcca ppcpapap cc caa aac a cc c a ac a c | c pp ap p pp pac a pa p c ccc a c cca cc cc a c | p aa c acaapappap ac cc c c a c c a c | ap aa a p a aa p c ca a a capa cc a a a c -0.5 + a pp a p p c a pa a a paaccp apa a a a a c c | p a p p a c p paa c c ca c aca cac c | p a a a pp apc ac cc pp aaa | p p c c a a | a p p apa pc -1.0 + pc c a a | c p pc | | c a | -1.5 + ---+--------------+--------------+--------------+--------------+--------------+--------------+--------------+-1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Pred NOTE: 146 obs hidden. 792 data drug_hour; set mmm; if effect = 'drug*hour'; run; NOTE: There were 35 observations read from the data set WORK.MMM. NOTE: The data set WORK.DRUG_HOUR has 24 observations and 11 variables. NOTE: DATA statement used (Total process time): real time 0.00 seconds cpu time 0.00 seconds 793 proc plot data=drug_hour; plot estimate*hour=drug; run; James P. Geaghan - Copyright 2011 Statistical Techniques II Appendix 17 Split-plot and Repeated measures designs SAS Example Page 321 794 options ps=512 ls=109; 795 NOTE: There were 24 observations read from the data set WORK.DRUG_HOUR. NOTE: The PROCEDURE PLOT printed page 12. NOTE: PROCEDURE PLOT used (Total process time): real time 0.03 seconds cpu time 0.00 seconds Study of drug effect on asthma patients Analysis of residuals from PROC MIXED Plot of Estimate*hour. Symbol is value of drug. Estimate | | 3.8000 + | | | c | | c 3.6000 + | c | | | a | c 3.4000 + a | | | | | c 3.2000 + | a | | c | a | a 3.0000 + c | a c | | p p | p a a | p 2.8000 + p p | p | p | | | 2.6000 + | ---+--------------+--------------+--------------+--------------+--------------+--------------+--------------+ 1 2 3 4 5 6 7 8 hour 796 NOTE: NOTE: NOTE: NOTE: NOTE: NOTE: data fits; merge FitAR1 FitToep FitCS FitUn; by descr; run; There were 4 observations read from the data set WORK.FITAR1. There were 4 observations read from the data set WORK.FITTOEP. There were 4 observations read from the data set WORK.FITCS. There were 4 observations read from the data set WORK.FITUN. The data set WORK.FITS has 4 observations and 5 variables. DATA statement used (Total process time): real time 0.01 seconds cpu time 0.01 seconds 797 798 proc print data=fits; run; NOTE: There were 4 observations read from the data set WORK.FITS. NOTE: The PROCEDURE PRINT printed page 13. NOTE: PROCEDURE PRINT used (Total process time): real time 0.03 seconds cpu time 0.00 seconds James P. Geaghan - Copyright 2011 Statistical Techniques II Appendix 17 SAS Example Split-plot and Repeated measures designs Page 322 Study of drug effect on asthma patients Analysis of residuals from PROC MIXED Obs 1 2 3 4 Descr -2 Res Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) AR1 276.1 280.1 280.1 284.7 Toep 229.0 245.0 245.3 263.2 CS 348.2 352.2 352.2 356.7 UN 150.4 222.4 227.6 304.4 799 800 801 802 803 804 805 806 807 808 809 810 811 NOTE: NOTE: NOTE: NOTE: NOTE: NOTE: NOTE: NOTE: proc mixed data=fev1uni; class drug patient; title2 'Repeated measures analysis with covariable'; model fev1 = drug basefev1 drug*basefev1 hour drug*hour / ddfm=kr outp=resids; ods output FitStatistics=FitUn(rename=(value=UN)) FitStatistics=FitUNp Dimensions=ParmUN(rename=(value=NumUN)); lsmeans drug / adjust=tukey pdiff cl; lsmeans drug / adjust=tukey pdiff cl at hour=1; lsmeans drug / adjust=tukey pdiff cl at hour=8; ods output diffs=ppp lsmeans=mmm; ods listing exclude diffs;* lsmeans; run; The data set WORK.MMM has 9 observations and 12 variables. The data set WORK.PPP has 9 observations and 17 variables. The data set WORK.PARMUN has 5 observations and 2 variables. The data set WORK.FITUNP has 4 observations and 2 variables. The data set WORK.FITUN has 4 observations and 2 variables. The data set WORK.RESIDS has 576 observations and 12 variables. The PROCEDURE MIXED printed page 14. PROCEDURE MIXED used (Total process time): real time 0.34 seconds cpu time 0.26 seconds 812 %include 'C:\SAS\pdmix800.sas'; 1485 %pdmix800(ppp,mmm,alpha=0.05,sort=yes); run; PDMIX800 08.08.2003 processing . Tukey-Kramer values for drug are . (avg) . (min) . (max). Effect=drug DF=567 Adjustment=Tukey-Kramer _TYPE_=0 _FREQ_=9 numcomp=9 meanse=0.08044 maxse=0.09472 minse=0.05189 critt=. prob=. numdf=4.7720018727 AvgSigDiff=. MaxSigDiff=. MinSigDiff=. _ERROR_=1 _N_=1 Study of drug effect on asthma patients Repeated measures analysis with covariable The Mixed Procedure Model Information Data Set Dependent Variable Covariance Structure Estimation Method Residual Variance Method Fixed Effects SE Method Degrees of Freedom Method WORK.FEV1UNI fev1 Diagonal REML Profile Model-Based Residual Class Level Information Class Levels Values drug patient 3 24 a c p 201 202 203 204 205 206 207 208 209 210 211 212 214 215 216 217 218 219 220 221 222 223 224 232 Dimensions Covariance Parameters Columns in X Columns in Z Subjects Max Obs Per Subject Number Number Number Number of of of of Observations Observations Read Observations Used Observations Not Used 1 12 0 1 576 576 576 0 James P. Geaghan - Copyright 2011 Statistical Techniques II Appendix 17 SAS Example Split-plot and Repeated measures designs Page 323 Covariance Parameter Estimates Cov Parm Estimate Residual 0.2583 Fit Statistics -2 Res Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) 890.1 892.1 892.1 896.4 Type 3 Tests of Fixed Effects Num Den Effect DF DF drug 2 567 basefev1 1 567 basefev1*drug 2 567 hour 1 567 hour*drug 2 567 F Value 4.84 505.77 3.99 65.10 9.83 Pr > F 0.0083 <.0001 0.0190 <.0001 <.0001 Estimate 3.1080 3.3323 2.8238 3.4228 3.7358 2.8885 2.7931 2.9288 2.7592 Standard Error 0.03670 0.03668 0.03669 0.06698 0.06697 0.06698 0.06698 0.06697 0.06698 Least Squares Means Effect drug drug drug drug drug drug drug drug drug drug a c p a c p a c p basefev1 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 hour 4.50 4.50 4.50 1.00 1.00 1.00 8.00 8.00 8.00 DF 567 567 567 567 567 567 567 567 567 t Value 84.68 90.84 76.96 51.10 55.78 43.13 41.70 43.73 41.20 Pr > |t| <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 Alpha 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 Lower 3.0359 3.2602 2.7518 3.2912 3.6042 2.7570 2.6616 2.7972 2.6276 Upper 3.1801 3.4043 2.8959 3.5544 3.8673 3.0201 2.9247 3.0603 2.8907 Study of drug effect on asthma patients Repeated measures analysis with covariable Effect=drug ADJUSTMENT=Tukey-Kramer(P<0.05) bygroup=1 Obs drug basefev1 hour Estimate StdErr 1 c 2.65 4.50 3.3323 0.03668 2 a 2.65 4.50 3.1080 0.03670 3 p 2.65 4.50 2.8238 0.03669 Alpha 0.05 0.05 0.05 Lower 3.2602 3.0359 2.7518 Upper 3.4043 3.1801 2.8959 MSGROUP A B C Effect=drug ADJUSTMENT=Tukey-Kramer(P<0.05) bygroup=2 Obs drug basefev1 hour Estimate StdErr 4 c 2.65 1.00 3.7358 0.06697 5 a 2.65 1.00 3.4228 0.06698 6 p 2.65 1.00 2.8885 0.06698 Alpha 0.05 0.05 0.05 Lower 3.6042 3.2912 2.7570 Upper 3.8673 3.5544 3.0201 MSGROUP A B C Effect=drug ADJUSTMENT=Tukey-Kramer(P<0.05) bygroup=3 Obs drug basefev1 hour Estimate StdErr 7 c 2.65 8.00 2.9288 0.06697 8 a 2.65 8.00 2.7931 0.06698 9 p 2.65 8.00 2.7592 0.06698 Alpha 0.05 0.05 0.05 Lower 2.7972 2.6616 2.6276 Upper 3.0603 2.9247 2.8907 MSGROUP A A A 1487 ods html close; 1488 ods rtf close; 1489 ods PDF close; 1490 1491 GOPTIONS DEVICE=CGMLT97L ctitle=black ctext=black htext=1 htitle=1 1492 ftext='TimesRoman' ftitle='TimesRoman'; 1493 1494 data fev1uni; set fev1uni; 1495 if drug = 'a' then a = fev1; else a = .; 1496 if drug = 'c' then c = fev1; else c = .; 1497 if drug = 'p' then p = fev1; else p = .; 1498 RUN; NOTE: There were 576 observations read from the data set WORK.FEV1UNI. NOTE: The data set WORK.FEV1UNI has 576 observations and 8 variables. NOTE: DATA statement used (Total process time): real time 0.00 seconds cpu time 0.00 seconds 1499 1500 GOPTIONS GSFNAME=OUT1; 1501 PROC GPLOT DATA=fev1uni; 1502 TITLE2 'Plot of means with standard errors'; James P. Geaghan - Copyright 2011 Statistical Techniques II Split-plot and Repeated measures designs Appendix 17 SAS Example Page 324 1503 PLOT a*hour=1 c*hour=2 p*hour=3 / OVERLAY HAXIS=AXIS1 VAXIS=AXIS2; 1504 AXIS1 LABEL=( 'Time in hours') WIDTH=5 MINOR=(N=4); 1505 AXIS2 LABEL=('Mean fiv1') WIDTH=6 1506 MINOR=(N=4) ORDER= 2.5 TO 4 BY 0.25; 1507 SYMBOL1 C=RED L=1 V=NONE I=STD1mjtp W=1 H=1 mode=include; 1508 SYMBOL2 C=BLUE L=1 V=NONE I=STD1mjtp W=1 H=1 mode=include; 1509 SYMBOL3 C=GREEN L=1 V=NONE I=STD1mjtp W=1 H=1 mode=include; 1510 **** V = dot would place a dot for each point; 1511 **** P = variance calculations uses a pooled calculation as in ANOVA; 1512 **** I = requests STD (std dev) 1 (1 width, 2 or 3) M (of mean=std err) 1513 J (join means of bars) t (add top & bottom hash) p (use pooled variance); 1514 **** Other options: omit M=std dev, use B to get bar for min/max; 1515 * SYMBOL1 C=green L=1 V=dot I=none W=1 H=1 mode=include; 1516 * SYMBOL2 C=magenta L=1 V=dot I=none W=1 H=1 mode=include; 1517 RUN; NOTE: The axis frame outline was drawn with line width 6 as specified on the left vertical axis. Any other axis line widths were ignored. NOTE: 384 observation(s) contained a MISSING value for the a * hour request. NOTE: 47 observation(s) outside the axis range for the a * hour request. NOTE: 384 observation(s) contained a MISSING value for the c * hour request. NOTE: 77 observation(s) outside the axis range for the c * hour request. NOTE: 384 observation(s) contained a MISSING value for the p * hour request. NOTE: 46 observation(s) outside the axis range for the p * hour request. NOTE: 13 records written to C:\SAS\Appendix17 Repeated (Asthma)01.CGM 1517 ! QUIT; NOTE: There were 576 observations read from the data set WORK.FEV1UNI. NOTE: PROCEDURE GPLOT used (Total process time): real time 0.87 seconds cpu time 0.07 seconds 1518 1519 GOPTIONS GSFNAME=OUT2; 1520 PROC GPLOT DATA=fev1uni; 1521 TITLE2 'Plot of regression lines'; 1522 PLOT a*hour=1 c*hour=2 p*hour=3 / OVERLAY HAXIS=AXIS1 VAXIS=AXIS2; 1523 AXIS1 LABEL=( 'Time in hours') WIDTH=5 MINOR=(N=4); 1524 AXIS2 LABEL=('Mean fiv1') WIDTH=6 1525 MINOR=(N=4) ORDER= 2.5 TO 4 BY 0.25; 1526 SYMBOL1 C=RED L=1 V=dot I=rl W=1 H=1 mode=include; 1527 SYMBOL2 C=BLUE L=1 V=dot I=rl W=1 H=1 mode=include; 1528 SYMBOL3 C=GREEN L=1 V=dot I=rl W=1 H=1 mode=include; 1529 **** V = dot would place a dot for each point; 1530 **** P = variance calculations uses a pooled calculation as in ANOVA; 1531 **** I = requests STD (std dev) 1 (1 width, 2 or 3) M (of mean=std err) 1532 J (join means of bars) t (add top & bottom hash) p (use pooled variance); 1533 **** Other options: omit M=std dev, use B to get bar for min/max; 1534 * SYMBOL1 C=green L=1 V=dot I=none W=1 H=1 mode=include; 1535 * SYMBOL2 C=magenta L=1 V=dot I=none W=1 H=1 mode=include; 1536 RUN; NOTE: The axis frame outline was drawn with line width 6 as specified on the left vertical axis. Any other axis line widths were ignored. NOTE: Regression equation : a = 3.52756 - 0.089955*hour. NOTE: 384 observation(s) contained a MISSING value for the a * hour request. NOTE: 47 observation(s) outside the axis range for the a * hour request. NOTE: Regression equation : c = 3.845253 - 0.115288*hour. NOTE: 384 observation(s) contained a MISSING value for the c * hour request. NOTE: 77 observation(s) outside the axis range for the c * hour request. NOTE: Regression equation : p = 2.895074 - 0.018477*hour. NOTE: 384 observation(s) contained a MISSING value for the p * hour request. NOTE: 46 observation(s) outside the axis range for the p * hour request. NOTE: 284 records written to C:\SAS\Appendix17 Repeated (Asthma)02.CGM 1536 ! QUIT; NOTE: There were 576 observations read from the data set WORK.FEV1UNI. NOTE: PROCEDURE GPLOT used (Total process time): real time 0.10 seconds cpu time 0.03 seconds 1537 1538 run; quit; 1540 NOTE: SAS Institute Inc., SAS Campus Drive, Cary, NC USA 27513-2414 NOTE: The SAS System used: real time 24.46 seconds cpu time 9.88 seconds James P. Geaghan - Copyright 2011 ...
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This note was uploaded on 12/29/2011 for the course EXST 7015 taught by Professor Wang,j during the Fall '08 term at LSU.

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