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1 dm'log;clear;output;clear'; options ps=512 ls=99 nocenter nodate nonumber nolabel FORMCHAR=" = -/\<>*"; ODS LISTING; *** Table 23.2 ********************************************; *** Moore, David S. Essential Statistics, 1st Ed. 2010, ***; *** W. H. Freeman & Co. NY, NY ***; *** in Borneo ***; ***********************************************************; TITLE1 'Analysis of Variance (One-way ANOVA)'; data Rainforest; infile cards missover; infile 'Rainforest logging.csv' missover DSD dlm="," firstobs=2; TITLE2 ''; LABEL group = '1=Never harvested, 2=1 year ago, 3=8 years ago' trees = 'Number of trees' Species = 'Number of species represented' Richness = 'Number of species / number of trees'; input Obs Group Trees Species Richness; datalines; ; ODS PDF style=minimal body='rainforest logging boxplot.pdf' ; proc sort data=rainforest; by group; proc boxplot data=rainforest; plot Richness * group; ods PDF close; ODS HTML style=minimal body='rainforest logging ANOVA CRD.html' ; proc print data=rainforest; var group Richness; TITLE3 'Raw data list (unsorted)'; proc mixed data=rainforest order=data; class group; TITLE3 'ANOVA with PROC MIXED'; model Richness = group / DDFM = KR; repeated / group = group; quit; proc mixed data=rainforest order=data; class group; TITLE3 'ANOVA with PROC MIXED - separate variances'; model Richness = group / DDFM=KR outp=resids; lsmeans group / adjust=tukey pdiff; ods output diffs=ppp lsmeans=mmm; *ods listing exclude diffs lsmeans; * this line is inactive; TITLE4 'Post hoc adjustment with macro by Arnold Saxton'; * SAS Macro by Arnold Saxton: Saxton, A.M A macro for ; * converting mean separation output to letter groupings in Proc Mixed. ; * In Proc. 23rd SAS Users Group Intl., SAS Institute, Cary, NC, pp ; %include 'C:\pdmix800.sas'; %pdmix800(ppp,mmm,alpha=0.05,sort=yes); proc univariate data=resids normal plot; var resid; TITLE4 'Univariate analysis of residuals'; TITLE5 'Test of normality and plots only'; ods exclude Moments BasicMeasures ExtremeObs ExtremeValues Modes MissingValues Quantiles TestsForLocation; histogram resid / normal;
2 proc GlimMix data=rainforest order=data; class group; TITLE3 'ANOVA with SAS PROC GlimMix with Poisson distribution'; model species = group / dist=poisson; proc GlimMix data=rainforest order=data; class group; TITLE3 'ANOVA with SAS PROC GlimMix with negative binomial distribution'; TITLE4 'with post hoc tests'; model species = group / dist=negb; LSmeans group / adjust=tukey lines; LSmeans group / adjust=dunnett diff=control('1'); quit; ods html close; quit; Analysis of Variance (One-way ANOVA) Raw data list (unsorted) Obs group Richness
3 Richness group
4 ANOVA with PROC MIXED The Mixed Procedure Model Information Data Set Dependent Variable Covariance Structure Group Effect Estimation Method Residual Variance Method Fixed Effects SE Method Degrees of Freedom Method WORK.RAINFOREST Richness Variance Components group REML None Kenward-Roger Kenward-Roger Class Level Information Class Levels Values group Dimensions Covariance Parameters 3 Columns in X 4 Columns in Z 0 Subjects 33 Max Obs Per Subject 1 Number of Observations Number of Observations Read 33 Number of Observations Used 33 Number of Observations Not Used 0 Iteration History Iteration Evaluations -2 Res Log Like Criterion Convergence criteria met. Covariance Parameter Estimates Cov Parm Group Estimate Residual group Residual group Residual group FitStatistics -2 Res Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) Null Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F group
5 ANOVA with PROC MIXED - separate variances 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.RAINFOREST Richness Diagonal REML Profile Model-Based Residual Class Level Information Class Levels Values group Dimensions Covariance Parameters 1 Columns in X 4 Columns in Z 0 Subjects 1 Max Obs Per Subject 33 Number of Observations Number of Observations Read 33 Number of Observations Used 33 Number of Observations Not Used 0 Covariance Parameter Estimates Cov Parm Estimate Residual FitStatistics -2 Res Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F group Least Squares Means Effect group Estimate Error DF t Value Pr > t group <.0001 group <.0001 group <.0001 Differences ofleast Squares Means Effect group _group Estimate Error DF t Value Pr > t Adjustment Adj P group Tukey-Kramer group Tukey-Kramer group Tukey-Kramer
6 ANOVA with PROC MIXED - separate variances Post hoc adjustment with macro by Arnold Saxton Effect=group ADJUSTMENT=Tukey-Kramer(P<0.05) bygroup=1 Obs group Estimate StdErr MSGROUP A AB B Analysis of Variance (One-way ANOVA) ANOVA with PROC MIXED - separate variances Univariate analysis of residuals Test of normality and plots only The UNIVARIATE Procedure Variable: Resid Tests for Normality Test --Statistic p Value Shapiro-Wilk W Pr < W Kolmogorov-Smirnov D Pr > D < Cramer-von Mises W-Sq Pr > W-Sq < Anderson-Darling A-Sq Pr > A-Sq < Stem Leaf Boxplot *--+--* Multiply Stem.Leaf by 10**-1 Normal Probability Plot * ** * * ****** * *******+ * +++ ** ***++ * * ++++ * *
7 ANOVA with PROC MIXED - separate variances Univariate analysis of residuals Test of normality and plots only The UNIVARIATE Procedure Fitted Normal Distribution for Resid Parameters for Normal Distribution Parameter Symbol Estimate Mean Mu 0 Std Dev Sigma Goodness-of-Fit Tests for Normal Distribution Test ----Statistic p Value Kolmogorov-Smirnov D Pr > D <0.010 Cramer-von Mises W-Sq Pr > W-Sq <0.005 Anderson-Darling A-Sq Pr > A-Sq <0.005 Quantiles for Normal Distribution Quantile Percent Observed Estimated
8 ANOVA with SAS PROC GlimMix with Poisson distribution The GLIMMIX Procedure Model Information Data Set Response Variable Response Distribution Link Function Variance Function Variance Matrix Estimation Technique Degrees of Freedom Method WORK.RAINFOREST Species Poisson Log Default Diagonal Maximum Likelihood Residual Class Level Information Class Levels Values group Number of Observations Read 33 Number of Observations Used 33 Dimensions Columns in X 4 Columns in Z 0 Subjects (Blocks in V) 1 Max Obs per Subject 33 Optimization Information Optimization Technique Newton-Raphson Parameters in Optimization 3 Lower Boundaries 0 Upper Boundaries 0 Fixed Effects Not Profiled Iteration History Objective Max Iteration Restarts Evaluations Function Change Gradient E-10 Convergence criterion (GCONV=1E-8) satisfied. FitStatistics -2 Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) CAIC (smaller is better) HQIC (smaller is better) Pearson Chi-Square Pearson Chi-Square / DF 1.25 Type III Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F group
9 ANOVA with SAS PROC GlimMix with negative binomial distribution with post hoc tests The GLIMMIX Procedure Model Information Data Set Response Variable Response Distribution Link Function Variance Function Variance Matrix Estimation Technique Degrees of Freedom Method WORK.RAINFOREST Species Negative Binomial Log Default Diagonal Maximum Likelihood Residual Class Level Information Class Levels Values group Number of Observations Read 33 Number of Observations Used 33 Dimensions Covariance Parameters 1 Columns in X 4 Columns in Z 0 Subjects (Blocks in V) 1 Max Obs per Subject 33 Optimization Information Optimization Technique Newton-Raphson Parameters in Optimization 4 Lower Boundaries 1 Upper Boundaries 0 Fixed Effects Not Profiled Iteration History Objective Max Iteration Restarts Evaluations Function Change Gradient E-7 Convergence criterion (GCONV=1E-8) satisfied. FitStatistics -2 Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) CAIC (smaller is better) HQIC (smaller is better) Pearson Chi-Square Pearson Chi-Square / DF 1.14
10 Type III Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F group group Least Squares Means group Estimate Error DF t Value Pr > t < < <.0001 Differences of group Least Squares Means Adjustment for Multiple Comparisons: Tukey-Kramer group _group Estimate Error DF t Value Pr > t Adj P Tukey-Kramer Grouping for group Least Squares Means (Alpha=0.05) LS-means with the same letter are not significantly different. group Estimate A A B A B B Group Least Squares Means group Estimate Error DF t Value Pr > t < < <.0001 Differences of group Least Squares Means Adjustment for Multiple Comparisons: Dunnett group _group Estimate Error DF t Value Pr > t Adj P
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