EXST7015 : Statistical Techniques II Geaghan ANOVA – Design Analysis of Covariance (revisited) Page 1 25d-AnCova&Design.doc 1 ****************************************************; 2 *** Example of Analysis of Covariance ***; 3 *** Steel and Torrie (1980) example (pg. 424) ***; 4 *** Analysis of three diet treatments on two ***; 5 *** sexes, where X is the initial weight, ***; 6 *** and Y is the weight gain in pounds. ***; 7 ****************************************************; 8 OPTIONS NOCENTER PS=256 LS=132 nodate nonumber; 9 DATA HOGS; INFILE CARDS MISSOVER; 10 Title1 'Analysis of Covariance example from Steel & Torrie, 1980'; 11 INPUT PEN SEX $ RATION $ X Y; 12 CARDS; NOTE: The data set WORK.HOGS has 30 observations and 5 variables. NOTE: DATA statement used: real time 0.05 seconds cpu time 0.05 seconds 12 ! RUN; 43 ; 44 PROC PRINT DATA=HOGS; Title2 'Raw data listing'; RUN; NOTE: There were 30 observations read from the data set WORK.HOGS. NOTE: The PROCEDURE PRINT printed page 1. NOTE: PROCEDURE PRINT used: real time 0.04 seconds cpu time 0.04 seconds Analysis of Covariance example from Steel & Torrie, 1980 Raw data listing Obs PEN SEX RATION X Y 1 1 M a1 38 9.52 2 1 F a1 48 9.94 3 1 M a2 39 8.51 4 1 F a2 48 10.00 5 1 M a3 48 9.11 6 1 F a3 48 9.75 7 2 M a1 35 8.21 8 2 F a1 32 9.48 9 2 M a2 38 9.95 10 2 F a2 32 9.24 11 2 M a3 37 8.50 12 2 F a3 28 8.66 13 3 M a1 41 9.32 14 3 F a1 35 9.32 15 3 M a2 46 8.43 16 3 F a2 41 9.34 17 3 M a3 42 8.90 18 3 F a3 33 7.63 19 4 M a1 48 10.56 20 4 F a1 46 10.90 21 4 M a2 40 8.86 22 4 F a2 46 9.68 23 4 M a3 42 9.51 24 4 F a3 50 10.37 25 5 M a1 43 10.42 26 5 F a1 32 8.82 27 5 M a2 40 9.20 28 5 F a2 37 9.67 29 5 M a3 40 8.76 30 5 F a3 30 8.57 46 PROC MIXED DATA=HOGS; CLASSES RATION SEX PEN; 47 TITLE2 'Analysis of Covariance Example'; 48 TITLE3 'Design done in PROC MIXED without a covariable'; 49 MODEL Y = RATION|SEX / htype=1 3 DDFM=Satterthwaite; 50 random PEN; 51 LSMEANS RATION|SEX / ADJUST=TUKEY PDIFF; 52 ods output diffs=ppp; 53 ods output lsmeans=mmm; 54 ods listing exclude diffs; 55 ods listing exclude lsmeans; 56 run; NOTE: Convergence criteria met. NOTE: The data set WORK.MMM has 11 observations and 8 variables. NOTE: The data set WORK.PPP has 19 observations and 12 variables. NOTE: The PROCEDURE MIXED printed page 2. NOTE: PROCEDURE MIXED used: real time 0.22 seconds cpu time 0.22 seconds 57 %include 'C:\Program Files\SAS Institute\SAS\V8\stat\sample\pdmix800.sas'; 673 %pdmix800(ppp,mmm,alpha=.05,sort=yes);EXST7015 : Statistical Techniques II Geaghan ANOVA – Design Analysis of Covariance (revisited) Page 2 25d-AnCova&Design.doc Analysis of Covariance example from Steel & Torrie, 1980 Analysis of Covariance Example Design done in PROC MIXED without a covariable The Mixed Procedure Model Information Data Set WORK.HOGS Dependent Variable Y Covariance Structure Variance Components Estimation Method REML Residual Variance Method Profile Fixed Effects SE Method Model-Based Degrees of Freedom Method Satterthwaite Class Level Information Class Levels Values RATION 3 a1 a2 a3 SEX 2 F M PEN 5 1 2 3 4 5 Dimensions Covariance Parameters 2 Columns in X 12 Columns in Z 5 Subjects 1 Max Obs Per Subject 30 Observations Used 30 Observations Not Used 0 Total Observations 30 Iteration History Iteration Evaluations -2 Res Log Like Criterion 0 1 63.35598278 1 1 60.98295712 0.00000000 Convergence criteria met. Covariance Parameter Estimates Cov Parm Estimate PEN 0.1329 Residual 0.4157 Fit Statistics -2 Res Log Likelihood 61.0 AIC (smaller is better) 65.0 AICC (smaller is better) 65.6 BIC (smaller is better) 64.2 Type 1 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F RATION 2 20 2.73 0.0896 SEX 1 20 1.04 0.3189 RATION*SEX 2 20 0.57 0.5730 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F RATION 2 20 2.73 0.0896 SEX 1 20 1.04 0.3189 RATION*SEX 2 20 0.57 0.5730EXST7015 : Statistical Techniques II Geaghan ANOVA – Design Analysis of Covariance (revisited) Page 3 25d-AnCova&Design.doc Analysis of Covariance example from Steel & Torrie, 1980 Analysis of Covariance Example Design done in PROC MIXED without a covariable Effect=RATION Method=Tukey-Kramer(P<.05) Comparison Group=1 Standard Letter MinSig MaxSig AvgSig Obs RATION SEX Estimate Error Group Diff Diff Diff 1 a1 9.6490 0.2610 A 0.72951 0.72951 0.72951 2 a2 9.2880 0.2610 A 0.72951 0.72951 0.72951 3 a3 8.9760