EXST7015 : Statistical Techniques II Geaghan Analysis of Variance Introductory SAS example Page 1 15d-Anova_Intro.doco 1 **EXAMPLE 1******************************************************; 2 *** Example of unbalanced CRD with experimental error ***; 3 *** From Snedecor & Cochran, 1967 (pg 278) ***; 4 *****************************************************************; 5 OPTIONS PS=256 LS=78 NOCENTER NODATE PAGENO=1; 6 dm 'log;clear;output;clear'; 7 DATA MICE onebyone; INFILE CARDS MISSOVER; 8 INPUT STRAIN $ 1-4 DAYS NUMBER; 9 TITLE1 'EXST7015: DAYS TO DEATH FOR MICE INOCULATED WITH 3 TYPHOID STRAINS'; 10 TITLE2 'UNEQUAL NUMBER OF MICE IN EACH TREATMENT'; 11 do i = 1 to number by 1; output onebyone; end; 12 output mice; 13 CARDS; NOTE: The data set WORK.MICE has 31 observations and 4 variables. NOTE: The data set WORK.ONEBYONE has 224 observations and 4 variables. NOTE: DATA statement used: real time 0.07 seconds cpu time 0.07 seconds 13 ! RUN; 45 ; 46 PROC PRINT data=mice; TITLE3 'RAW DATA LISTING'; RUN; NOTE: There were 31 observations read from the data set WORK.MICE. NOTE: The PROCEDURE PRINT printed page 1. NOTE: PROCEDURE PRINT used: real time 0.04 seconds cpu time 0.04 seconds EXST7015: DAYS TO DEATH FOR MICE INOCULATED WITH 3 TYPHOID STRAINS 1 UNEQUAL NUMBER OF MICE IN EACH TREATMENT RAW DATA LISTING Obs STRAIN DAYS NUMBER i 1 9D 2 6 7 2 9D 3 4 5 3 9D 4 9 10 4 9D 5 8 9 5 9D 6 3 4 6 9D 7 1 2 7 11C 2 1 2 8 11C 3 3 4 9 11C 4 3 4 10 11C 5 6 7 11 11C 6 6 7 12 11C 7 14 15 13 11C 8 11 12 14 11C 9 4 5 15 11C 10 6 7 16 11C 11 2 3 17 11C 12 3 4 18 11C 13 1 2 19 DSC1 2 3 4 20 DSC1 3 5 6 21 DSC1 4 5 6 22 DSC1 5 8 9 23 DSC1 6 19 20 24 DSC1 7 23 24 25 DSC1 8 22 23 26 DSC1 9 14 15 27 DSC1 10 14 15 28 DSC1 11 7 8 29 DSC1 12 8 9 30 DSC1 13 4 5 31 DSC1 14 1 2 47 PROC MIXED DATA=OnebyOne cl covtest; CLASSES STRAIN; 48 TITLE3 'ANALYSIS OF VARIANCE'; 49 MODEL DAYS = STRAIN / htype=3 DDFM=Satterthwaite outp=ResidDataP; 50 repeated / group=strain; 51 run; NOTE: Convergence criteria met. NOTE: The data set WORK.RESIDDATAP has 224 observations and 11 variables. NOTE: The PROCEDURE MIXED printed page 2. NOTE: PROCEDURE MIXED used: real time 0.14 seconds cpu time 0.13 secondsEXST7015 : Statistical Techniques II Geaghan Analysis of Variance Introductory SAS example Page 2 15d-Anova_Intro.doco EXST7015: DAYS TO DEATH FOR MICE INOCULATED WITH 3 TYPHOID STRAINS 2 UNEQUAL NUMBER OF MICE IN EACH TREATMENT ANALYSIS OF VARIANCE The Mixed Procedure Model Information Data Set WORK.ONEBYONE Dependent Variable DAYS Covariance Structure Variance Components Group Effect STRAIN Estimation Method REML Residual Variance Method None Fixed Effects SE Method Model-Based Degrees of Freedom Method Satterthwaite Class Level Information Class Levels Values STRAIN 3 11C 9D DSC1 Dimensions Covariance Parameters 3 Columns in X 4 Columns in Z 0 Subjects 224 Max Obs Per Subject 1 Observations Used 224 Observations Not Used 0 Total Observations 224 Iteration History Iteration Evaluations -2 Res Log Like Criterion 0 1 1027.49256195 1 1 1012.92789611 0.00000000 Convergence criteria met. Covariance Parameter Estimates Standard Z Cov Parm Group Estimate Error Value Pr Z Alpha Lower Upper Residual STRAIN 11C 5.8633 1.0795 5.43 <.0001 0.05 4.2127 8.7221 Residual STRAIN 9D 1.8989 0.4903 3.87 <.0001 0.05 1.2126 3.3928 Residual STRAIN DSC1 6.6327 0.8164 8.12 <.0001 0.05 5.2839 8.5761 Fit Statistics -2 Res Log Likelihood 1012.9 AIC (smaller is better) 1018.9 AICC (smaller is better) 1019.0 BIC (smaller is better) 1029.2 Null Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq 2 14.56 0.0007 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F STRAIN 2 114 70.10 <.0001EXST7015 : Statistical Techniques II Geaghan Analysis of Variance Introductory SAS example Page 3 15d-Anova_Intro.doco 53 PROC UNIVARIATE DATA=ResidDataP PLOT NORMAL; VAR resid; RUN; NOTE: The PROCEDURE UNIVARIATE printed page 3. NOTE: PROCEDURE UNIVARIATE used: real time 0.02 seconds cpu time 0.02 seconds 53 ! QUIT; EXST7015: DAYS TO DEATH FOR MICE INOCULATED WITH 3 TYPHOID STRAINS 3 UNEQUAL NUMBER OF MICE IN EACH TREATMENT ANALYSIS OF VARIANCE The UNIVARIATE Procedure Variable: Resid Moments N 224 Sum Weights 224 Mean 0 Sum Observations 0 Std Deviation 2.39433175 Variance 5.73282454 Skewness 0.06043085 Kurtosis -0.0153611 Uncorrected SS 1278.41987 Corrected SS 1278.41987 Coeff Variation . Std