Week 3/4 [06+ Sept.] Class Activities. File: week sep07.doc Directory: \\Muserver2\USERS\B\\baileraj\Classes\sta402\handouts

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1 Week 3/4 [06+ Sept.] Class Activities File: week sep07.doc Directory: \\Muserver2\USERS\B\\baileraj\Classes\sta402\handouts Week 3 Topic -- REPORT WRITING * Introduce the Output Delivery System (ODS) for customizing procedure output * PROC TABULATE for producing nicely-formatted tables Week 4 Topic INTRODUCTION TO MODELING PROCS * REG and GLM primarily Bonus Material conversational UNIX ODS References Gupta, S. (2003) Quick Results with the Output Delivery System. SAS Institute Inc., Cary, NC USA. Delwiche LD and Slaughter SJ. (2003) The Little SAS Book: A Primer, 3rd edition. SAS Institute. Cary, NC, USA. [pages ] Haworth LE (2001) Output Delivery System: The Basics. SAS Institute Inc. Cary, NC USA. ODS Basics What is ODS? * method of delivering output in a variety of formats (other than the default listing format ) * options available include HTML, Rich Text Format (RTF), PS, PDF, SAS data sets Basic ODS Terminology destinations locations to which ODS routes output (e.g. LISTING, HTML, RTF, PRINTER, PDF, OUTPUT new data set) objects output entities created by ODS to store the formatted results styles font/color/other attributes of a report Basic syntax of ODS statements * identify output objects; ODS TRACE ON </options>;

2 * open output destination; ODS destination <FILE=filename>; * create SAS data set with output object; ODS OUTPUT output-object-name=sas-data-set-name; * [optional] select particular objects for inclusion; ODS <destination> SELECT output-object-name; PROC PROC PROC ODS <destination> CLOSE; ODS TRACE OFF; ODS to different file types A familiar example proc format; value totfmt 0='none' 1-HIGH='some' ; data d1; infile "\\Muserver2\USERS\B\BAILERAJ\public.www\classes\sta402\SASprograms\ch2-dat.txt" firstobs=16 expandtabs missover pad ; * infile 'M:\public.www\classes\sta402\SAS-programs\ch2-dat.txt' firstobs=16 expandtabs missover pad ; animal conc brood1 brood2 brood3 total 2.; cbrood3 = brood3; format cbrood3 totfmt.; label animal = animal ID number; label conc = Nitrofen concentration; label brood1 = number of young in first brood; label brood2 = number of young in 2nd brood; label brood3 = number of young in 3rd brood; label total = total young produced in three broods; proc print;

3 where conc=0; /* aside: ODS LISTING open as a default. You can have multiple destinations open simultaneously. If you want to close the LISTING destination before generating output then type ODS LISTING CLOSE; before issuing the PROC for which output is desired. */ /* generate HTML files with objects from 3 PROCs */ ODS TRACE ON; * ODS HTML file='m:\public.www\classes\sta402\sas-programs\day6- example.html ; ODS HTML file="\\muserver2\users\b\baileraj\public.www\classes\sta402\sasprograms\ods-html-example.html ; proc plot; plot total*conc=cbrood3 / vaxis=0 to 40 by 2; proc freq; table conc*cbrood3 / nopct nocol chisq trend exact; proc univariate plot; by conc; var total; ODS HTML CLOSE; ODS TRACE OFF; /* now generate HTML files with additional linkage info */ ODS TRACE ON; ODS HTML path='\\muserver2\users\b\baileraj\public.www\classes\sta402\sasprograms body = day6-example2.html /* Output objects */ contents = day6-example2-toc.html /* Table of contents */ frame = day6-example2-frame.html /* organizes display */ newfile = NONE; /* all results to one file*/ /* old code where M drive referenced vs. specification of the full path ODS HTML path='m:\public.www\classes\sta402\sas-programs body = day6-example2.html /* Output objects */ contents = day6-example2-toc.html /* Table of contents */ frame = day6-example2-frame.html /* organizes display */ newfile = NONE; /* all results to one file*/ */ /* comment: by default, opens a new body file for each part of output so the

4 newfile=none directs all output to the same body file newfile=page creates new body file for each page of output */ proc plot; plot total*conc=cbrood3 / vaxis=0 to 40 by 2; proc freq; table conc*cbrood3 / nopct nocol chisq trend exact; proc univariate plot; by conc; var total; ODS HTML CLOSE; ODS TRACE OFF; /* select on one of the output objects for inclusion */ *ODS HTML file='m:\public.www\classes\sta402\sas-programs\day6- example3.html ; ODS HTML file= \\Muserver2\USERS\B\BAILERAJ\public.www\classes\sta402\SASprograms\day6-example3.html ; ODS HTML SELECT SSPLOTS; ODS HTML SHOW; /* write details to SASLOG confirming object sel. */ proc univariate plot; by conc; var total; ODS HTML CLOSE; /* select different destinations */ options orientation=landscape nocenter nodate; ODS ESCAPECHAR= ^ ; /* for fancy formatting later */ /* old program with M drive reference ODS RTF file='m:\public.www\classes\sta402\sas-programs\day6-example.rtf ; ODS PDF file='m:\public.www\classes\sta402\sas-programs\day6-example.pdf ;

5 ODS PS file='m:\public.www\classes\sta402\sas-programs\day6-example.ps ; */ ODS RTF file='\\muserver2\users\b\baileraj\public.www\classes\sta402\sasprograms\day6-example.rtf ; ODS PDF file='\\muserver2\users\b\baileraj\public.www\classes\sta402\sasprograms\day6-example.pdf ; ODS PS file='\\muserver2\users\b\baileraj\public.www\classes\sta402\sasprograms\day6-example.ps ; Title Plot of number of young vs. Nitrofen concentration^{super a} ; Footnote1 ^{super a}s=some young produced in Brood 3, n= no young produced in Brood 3 ; proc plot; plot total*conc=cbrood3 / vaxis=0 to 40 by 2; ODS RTF CLOSE; ODS PDF CLOSE; ODS PS CLOSE; ODS to create output data sets proc sort data=d1; by conc; ODS TRACE ON; /* see what ODS objects are created by univariate */ proc univariate data=d1; by conc; var total; ODS TRACE OFF; ODS OUTPUT Quantiles=data_quant; /* extract quantiles */ proc univariate data=d1; by conc; var total; ODS OUTPUT CLOSE; proc print data=data_quant; Var Obs conc Name Quantile Estimate 1 0 total 100% Max total 99% total 95% total 90% total 75% Q total 50% Median total 25% Q total 10% total 5% total 1% total 0% Min edited output total 100% Max total 99% total 95% total 90% total 75% Q3 6.0

6 total 50% Median total 25% Q total 10% total 5% total 1% total 0% Min 0.0 /* can also create multiple data sets */ ODS OUTPUT Quantiles(MATCH_ALL=conc_name_macro)=data_quant; proc univariate data=d1; by conc; var total; ODS OUTPUT CLOSE; proc print data=data_quant; from the SAS LOG file NOTE: The data set WORK.DATA_QUANT has 11 observations and 4 variables. NOTE: The above message was for the following by-group: Nitrofen concentration=0 NOTE: The data set WORK.DATA_QUANT1 has 11 observations and 4 variables. NOTE: The above message was for the following by-group: Nitrofen concentration=80 NOTE: The data set WORK.DATA_QUANT2 has 11 observations and 4 variables. NOTE: The above message was for the following by-group: Nitrofen concentration=160 NOTE: The data set WORK.DATA_QUANT3 has 11 observations and 4 variables. NOTE: The above message was for the following by-group: Nitrofen concentration=235 NOTE: The data set WORK.DATA_QUANT4 has 11 observations and 4 variables. NOTE: The above message was for the following by-group: Nitrofen concentration=310 /* write the data set names to the SAS LOG */ %put The conc_name_macro variables contains the following data sets &conc_name_macro; 76 %put The conc_name_macro variables contains the following data sets &conc_name_macro; The conc_name_macro variables contains the following data sets DATA_QUANT DATA_QUANT1 DATA_QUANT2 DATA_QUANT3 DATA_QUANT4&conc_name_macro; /* merge the concentration summary files to create single table */ data c0; set DATA_QUANT; rename Estimate=C0_Est; key=_n_; drop VarName conc; data c80; set DATA_QUANT1; rename Estimate=C80_Est; key=_n_; drop VarName conc; data c160; set DATA_QUANT2; rename Estimate=C160_Est; key=_n_; drop VarName conc; data c235; set DATA_QUANT3; rename Estimate=C235_Est; key=_n_; drop VarName conc; data c310; set DATA_QUANT4; rename Estimate=C310_Est; key=_n_; drop VarName conc; data all; merge c0 c80 c160 c235 c310; by key; drop key; proc print data=all; Obs Quantile C0_Est C80_Est C160_Est C235_Est C310_Est

7 1 100% Max % % % % Q % Median % Q % % % % Min /* extract the rows-observations corresponding to the 5 number summary */ data fivenum; set all; if _n_=1 or _n_=5 or _n_=6 or _n_=7 or _n_=11; proc print; Obs Quantile C0_Est C80_Est C160_Est C235_Est C310_Est 1 100% Max % Q % Median % Q % Min Using ODS OUTPUT to create dataset in a simulation /* Extracting coefficients from simple linear regression simulation */ options formdlim="-" nodate; /* generate simulation data sets Y ~ N(mu(x)= 3+2x, sigma=2) */ data sims; do dataset=1 to 1000; do x=1 to 10; y = 3 + 2*x + 2*rannor(0); output; end; end; /* DEBUG: print to check generated data */ proc print data=sims; /* SORT for data set */ proc sort data=sims; by dataset;

8 /* USE OUTEST to extract the estimated coefficients */ proc reg data=sims outest=myparms; by dataset; model y=x; proc print data=myparms; /* HISTOGRAM for estimated slope */ proc gchart data=work.myparms; vbar x; /* Re-do this with ODS */ *ods trace on; * determine what output objects are constructed; ods output ParameterEstimates=reg_coefs; proc reg data=sims; by dataset; model y=x; proc print data=reg_coefs; ods output close; *ods trace off; proc print data=reg_coefs; proc contents data=reg_coefs; data slopes; set reg_coefs; if Variable="x"; slope=estimate; keep dataset slope; data intercepts; set reg_coefs; if Variable="Intercept"; Intercept = Estimate; keep dataset intercept; data both; merge slopes intercepts; by dataset;

9 proc gplot data=both; title "Plot of estimated slope vs. estimated intercept"; plot slope*intercept; proc gchart data=both; title "Sampling distribution of the estimated slope"; vbar slope; proc gchart data=both title "Sampling distribution of the estimated intercept"; vbar intercept; proc print data=slopes; PROC TABULATE (producing fancier results tables in SAS) PROC TABULATE <option(s)>; CLASS variable(s) </ options>; * identify non-numeric vars; FREQ variable; * identify variable containing frequency of observation; TABLE <<page-expression,> row-expression,> column-expression</ table-option(s)>; VAR analysis-variable(s)</ options>; * identify analysis vars; WEIGHT variable; * identify variable name e.g. sampling wts; * FORMATTING related subcommands CLASSLEV variable(s) / STYLE=<style-element-name PARENT> <[style-attribute-specification(s)] >; KEYLABEL keyword-1='description-1' <...keyword-n='description-n'>; KEYWORD keyword(s) / STYLE=<style-element-name PARENT> <[style-attribute-specification(s)] >;

10 [* check out results of search for Tabulate syntax on SAS doc] Comments: * concatenation (blank) operator * crossing (*) operator * format modifiers * grouping elements (parentheses) operator * ALL class variable data d1; infile 'M:\public.www\classes\sta402\SAS-programs\ch2-dat.txt' firstobs=16 expandtabs missover pad ; animal conc brood1 brood2 brood3 total 2.; proc tabulate data=d1; class conc; var brood1 brood2 brood3 total; table (brood1 brood2 brood3 total)*conc, min q1 median q3 max; proc tabulate data=d1; class conc; var total; table conc= Nitrofen Concentration all, total (mean var);

11 Week 04+/- [12+ Sept.] Class Activities AN INTRODUCTION TO STATISTICAL MODELING * PROC REG for linear modeling (a very basic introduction) * PROC GLM for anova models Other normal response modeling ANOVA balanced anova models Non-normal response modeling GENMOD generalized linear models LOGISTIC [grouped] binary regression PROBIT [grouped] binary regression (INVERSECL) CATMOD categorical data modeling Failure time modeling LIFEREG accelerated failure time models PHREG Cox s PH model And more REGRESSION using PROC REG Basic Model: Y i = X i + i [ simple linear regression ] = X i1 + 2 X i2 + 3 X i3 + 4 X i4 + 5 X i5 + ij [ multiple linear regression ] Error Assumption: ij ~ indep. N(0, 2 ) i=1,2,,n [observations]

12 /* example sas program that does simple linear regression */ options ls=75; data example1; input year nboats manatees; cards; ; /* WARNING: ODS RTF will place TITLE information along With SAS date/time/page number as part of a header in the RTP document. Check out Print Preview or view the header. */ ODS RTF file='d:\baileraj\classes\fall 2003\sta402\SAS-programs\linregoutput.rtf ; proc reg; title Number of Manatees killed regressed on the number of boats registered in Florida ; model manatees = nboats / p r cli clm; plot manatees*nboats= o p.*nboats= + / overlay; plot r.*nboats r.*p.; ODS RTF CLOSE;

13 Source DF Analysis of Variance Sum of Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total Root MSE R-Square Dependent Mean Adj R-Sq Coeff Var Variable DF Parameter Estimates Parameter Estimate Standard Error t Value Pr > t Intercept nboats <.0001

14 Obs Dep Var manatees Predicted Value Output Statistics Std Error Mean Predict 95% CL Mean 95% CL Predict Residual Std Error Residual Student Residual Output Statistics Obs ** 3 ** 4 ** 5 6 * 7 **** 8 ** 9 Cook's D

15 Output Statistics Obs * * 14 Cook's D Sum of Residuals 0 Sum of Squared Residuals Predicted Residual SS (PRESS) Multiple Regression with indicator variables Log(Brain Weight) i = Log(Body Weight) i + i Log(Brain Weight) i = Log(Body Weight) i + 2 I dinoi + i Log(Brain Weight) i = Log(Body Weight) i + 2 I dinoi + 3 I dinoi Log(Body Weight) i + i data mrexample; * Lunneborg (1994); * body weight brain example; input species $ bodywt logbody = log10(bodywt); logbrain = log10(brainwt); idino = 0; if (species="diplodoc" or species="tricerat" or species="brachios") then idino=1; idinobod = idino*logbody; cards; beaver cow wolf goat guipig diplodocus asielephant donkey horse potarmonkey cat giraffe gorilla human afrelephant triceratops rhemonkey kangaroo hamster mouse rabbit sheep jaguar chimp brachiosaurus rat mole pig

16 ; ODS RTF file='d:\baileraj\classes\fall 2003\sta402\SAS-programs\mregoutput.rtf ; proc print; title brain wt - body wt data ; proc univariate; var bodywt brainwt; id species; proc reg; title2 allometric scaling - brain and body wt. ; title3 [All Species combined] ; model logbrain=logbody; plot logbrain*logbody="o" p.*logbody="+" / overlay; plot r.*logbody; proc reg; title2 Dinosaurs fitted with potentially different line ; model logbrain=logbody idino idinobod; plot logbrain*logbody="o" p.*logbody="+" / overlay; plot r.*logbody; proc reg; title2 Dinosaurs fitted with potentially different INTERCEPTS ; model logbrain=logbody idino; plot logbrain*logbody="o" p.*logbody="+" / overlay; plot r.*logbody; ODS RTF CLOSE; Obs species bodywt brainwt logbody logbrain idino idinobod 1 beaver cow wolf goat guipig diplodoc asieleph donkey horse

17 Obs species bodywt brainwt logbody logbrain idino idinobod 10 potarmon cat giraffe gorilla human afreleph tricerat rhemonke kangaroo hamster mouse rabbit sheep jaguar chimp brachios rat mole pig

18 brain wt - body wt data The UNIVARIATE Procedure Variable: bodywt BODY WEIGHT Moments N 28 Sum Weights 28 Mean Sum Observations Std Deviation Variance Skewness Kurtosis Uncorrected SS Corrected SS Coeff Variation Std Error Mean Basic Statistical Measures Location Variability Mean Std Deviation Median Variance Mode. Range Interquartile Range Tests for Location: Mu0=0 Test Statistic p Value Student's t t Pr > t Sign M 14 Pr >= M <.0001 Signed Rank S 203 Pr >= S <.0001 Quantiles (Definition 5) Quantile Estimate 100% Max % % % % Q % Median % Q % % 0.120

19 brain wt - body wt data The UNIVARIATE Procedure Variable: bodywt Quantiles (Definition 5) Quantile Estimate 1% % Min Extreme Observations Lowest Highest Value species Obs Value species Obs mouse asieleph hamster afreleph mole tricerat rat diplodoc guipig brachios 25

20 brain wt - body wt data The UNIVARIATE Procedure Variable: brainwt BRAIN WEIGHT Moments N 28 Sum Weights 28 Mean Sum Observations Std Deviation Variance Skewness Kurtosis Uncorrected SS Corrected SS Coeff Variation Std Error Mean Basic Statistical Measures Location Variability Mean Std Deviation 1335 Median Variance Mode Range 5712 Interquartile Range Tests for Location: Mu0=0 Test Statistic p Value Student's t t Pr > t Sign M 14 Pr >= M <.0001 Signed Rank S 203 Pr >= S <.0001 Quantiles (Definition 5) Quantile Estimate 100% Max % % % % Q % Median % Q % % 1.00

21 brain wt - body wt data The UNIVARIATE Procedure Variable: brainwt Quantiles (Definition 5) Quantile Estimate 1% % Min 0.40 Extreme Observations Lowest Highest Value species Obs Value species Obs 0.4 mouse horse hamster giraffe rat human mole asieleph guipig afreleph 15

22 Source Analysis of Variance DF Sum of Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total Root MSE R-Square Dependent Mean Adj R-Sq Coeff Var Variable DF Parameter Estimates Parameter Estimate Standard Error t Value Pr > t Intercept <.0001 logbody <.0001

23 Source Analysis of Variance DF Sum of Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total Root MSE R-Square Dependent Mean Adj R-Sq Coeff Var Variable DF Parameter Estimates Parameter Estimate Standard Error t Value Pr > t Intercept <.0001 logbody <.0001 idino idinobod

24 Source Analysis of Variance DF Sum of Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total Root MSE R-Square Dependent Mean Adj R-Sq Coeff Var Variable DF Parameter Estimates Parameter Estimate Standard Error t Value Pr > t Intercept <.0001 logbody <.0001 idino <.0001 One-way ANOVA Basic Model: Y ij = μ i + ij [ cell means coding] = μ + i + ij [ effects coding] (constraint for estimation? 1 =0 or g =0 or i =0) Error Assumption: ij ~ indep. N(0, 2 ) i=1,2,,g [treatments or populations] j=1,2,,n i [replications] H 0 : μ 1 = = μ g or equivalently, H 0 : 1 = = g =0 /* Bacteria in meat under 4 different conditions */ options ls = 75; data meat;

25 input condition $ datalines; Plastic 7.66 Plastic 6.98 Plastic 7.80 Vacuum 5.26 Vacuum 5.44 Vacuum 5.80 Mixed 7.41 Mixed 7.33 Mixed 7.04 Co Co Co ; title bacteria growth under 4 packaging conditions; ODS RTF file='d:\baileraj\classes\fall 2003\sta402\SAS-programs\onewayoutput.rtf ; proc boxplot; plot logcount*condition; proc glm data=meat order=data; title2 fitting the one-way anova model via GLM; class condition; model logcount = condition; means condition / bon tukey scheffe cldiff lines; lsmeans condition / cl pdiff; contrast plastic vs. rest condition ; output out=new p=yhat r=resid stdr=eresid; proc plot data=new; title2 residual analyses; plot resid*yhat; proc univariate data=new plot; var resid; proc boxplot data=new; plot resid*condition; ODS RTF CLOSE;

26 bacteria growth under 4 packaging conditions fitting the one-way anova model via GLM The GLM Procedure Class condition Class Level Information Levels Values 4 Plastic Vacuum Mixed Co2 Number of observations 12

27 bacteria growth under 4 packaging conditions fitting the one-way anova model via GLM The GLM Procedure Dependent Variable: logcount Source DF Sum of Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total R-Square Coeff Var Root MSE logcount Mean Source DF Type I SS Mean Square F Value Pr > F condition <.0001 Source DF Type III SS Mean Square F Value Pr > F condition <.0001

28 bacteria growth under 4 packaging conditions fitting the one-way anova model via GLM The GLM Procedure Tukey's Studentized Range (HSD) Test for logcount NOTE: This test controls the Type I experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 8 Error Mean Square Critical Value of Studentized Range Minimum Significant Difference 0.89 Comparisons significant at the 0.05 level are indicated by ***. condition Comparison Difference Between Means Simultaneous 95% Confidence Limits Plastic - Mixed Plastic - Vacuum *** Plastic - Co *** Mixed - Plastic Mixed - Vacuum *** Mixed - Co *** Vacuum - Plastic *** Vacuum - Mixed *** Vacuum - Co *** Co2 - Plastic *** Co2 - Mixed *** Co2 - Vacuum ***

29 bacteria growth under 4 packaging conditions fitting the one-way anova model via GLM The GLM Procedure Bonferroni (Dunn) t Tests for logcount NOTE: This test controls the Type I experimentwise error rate, but it generally has a higher Type II error rate than Tukey's for all pairwise comparisons. Alpha 0.05 Error Degrees of Freedom 8 Error Mean Square Critical Value of t Minimum Significant Difference Comparisons significant at the 0.05 level are indicated by ***. condition Comparison Difference Between Means Simultaneous 95% Confidence Limits Plastic - Mixed Plastic - Vacuum *** Plastic - Co *** Mixed - Plastic Mixed - Vacuum *** Mixed - Co *** Vacuum - Plastic *** Vacuum - Mixed *** Vacuum - Co *** Co2 - Plastic *** Co2 - Mixed *** Co2 - Vacuum ***

30 bacteria growth under 4 packaging conditions fitting the one-way anova model via GLM The GLM Procedure Scheffe's Test for logcount NOTE: This test controls the Type I experimentwise error rate, but it generally has a higher Type II error rate than Tukey's for all pairwise comparisons. Alpha 0.05 Error Degrees of Freedom 8 Error Mean Square Critical Value of F Minimum Significant Difference Comparisons significant at the 0.05 level are indicated by ***. condition Comparison Difference Between Means Simultaneous 95% Confidence Limits Plastic - Mixed Plastic - Vacuum *** Plastic - Co *** Mixed - Plastic Mixed - Vacuum *** Mixed - Co *** Vacuum - Plastic *** Vacuum - Mixed *** Vacuum - Co *** Co2 - Plastic *** Co2 - Mixed *** Co2 - Vacuum ***

31 bacteria growth under 4 packaging conditions fitting the one-way anova model via GLM The GLM Procedure Tukey's Studentized Range (HSD) Test for logcount NOTE: This test controls the Type I experimentwise error rate, but it generally has a higher Type II error rate than REGWQ. Alpha 0.05 Error Degrees of Freedom 8 Error Mean Square Critical Value of Studentized Range Minimum Significant Difference 0.89 Means with the same letter are not significantly different. Tukey Grouping Mean N condition A Plastic A A Mixed B Vacuum C Co2

32 bacteria growth under 4 packaging conditions fitting the one-way anova model via GLM The GLM Procedure Bonferroni (Dunn) t Tests for logcount NOTE: This test controls the Type I experimentwise error rate, but it generally has a higher Type II error rate than REGWQ. Alpha 0.05 Error Degrees of Freedom 8 Error Mean Square Critical Value of t Minimum Significant Difference Means with the same letter are not significantly different. Bon Grouping Mean N condition A Plastic A A Mixed B Vacuum C Co2

33 bacteria growth under 4 packaging conditions fitting the one-way anova model via GLM The GLM Procedure Scheffe's Test for logcount NOTE: This test controls the Type I experimentwise error rate. Alpha 0.05 Error Degrees of Freedom 8 Error Mean Square Critical Value of F Minimum Significant Difference Means with the same letter are not significantly different. Scheffe Grouping Mean N condition A Plastic A A Mixed B Vacuum C Co2

34 bacteria growth under 4 packaging conditions fitting the one-way anova model via GLM The GLM Procedure Least Squares Means condition logcount LSMEAN LSMEAN Number Plastic Vacuum Mixed Co Least Squares Means for effect condition Pr > t for H0: LSMean(i)=LSMean(j) Dependent Variable: logcount i/j < < < < < <.0001 <.0001 <.0001 condition logcount LSMEAN 95% Confidence Limits Plastic Vacuum Mixed Co i Least Squares Means for Effect condition j Difference Between Means 95% Confidence Limits for LSMean(i)-LSMean(j) NOTE: To ensure overall protection level, only probabilities associated with pre-planned comparisons should be used.

35 bacteria growth under 4 packaging conditions fitting the one-way anova model via GLM The GLM Procedure Dependent Variable: logcount Contrast DF Contrast SS Mean Square F Value Pr > F plastic vs. rest <.0001

36 bacteria growth under 4 packaging conditions residual analyses Plot of resid*yhat. Legend: A = 1 obs, B = 2 obs, etc. resid 0.4 ˆ A 0.3 ˆ A A 0.2 ˆ A A A 0.1 ˆ A 0.0 ˆ A -0.1 ˆ -0.2 ˆ A A -0.3 ˆ -0.4 ˆ A -0.5 ˆ A ƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒƒˆ ƒƒƒƒƒƒƒƒƒˆƒ yhat

37 bacteria growth under 4 packaging conditions residual analyses The UNIVARIATE Procedure Variable: resid Moments N 12 Sum Weights 12 Mean 0 Sum Observations 0 Std Deviation Variance Skewness Kurtosis Uncorrected SS Corrected SS Coeff Variation. Std Error Mean Basic Statistical Measures Location Variability Mean Std Deviation Median Variance Mode Range Interquartile Range Tests for Location: Mu0=0 Test Statistic p Value Student's t t 0 Pr > t Sign M 1 Pr >= M Signed Rank S 2 Pr >= S Quantiles (Definition 5) Quantile Estimate 100% Max % % % % Q % Median % Q % % -0.50

38 bacteria growth under 4 packaging conditions residual analyses The UNIVARIATE Procedure Variable: resid Quantiles (Definition 5) Quantile Estimate 1% % Min Extreme Observations Lowest Highest Value Obs Value Obs Stem Leaf # Boxplot *-----* Multiply Stem.Leaf by 10**-1 Normal Probability Plot * *++ * ++++ * *+* *++++ * *+ * +++ +*++ *

39 Two-way ANOVA/ Factorial example 2 - interaction plots Patient Waiting Time data Factorial anova model Basic Model: Y ijk = μ ij + ijk [ cell means coding] = μ + i + j + ( ) ij + ijk [ effects coding] Error Assumption: ijk ~ indep. N(0, 2 ) i=1,2,,g [treatments or populations] j=1,2,,n i [replications] H 0 : all ( ) ij =0 [no interaction] H 0 : all i =0 [no A main effect] H 0 : all j =0 [no B main effect] ODS ESCAPECHAR= ^ ; /* for fancy formatting later */ ODS RTF file='d:\baileraj\classes\fall 2003\sta402\SAS-programs\twowayoutput.rtf ; title Two-way ANOVA/ Factorial example 2 - interaction plots; title2 Patient Waiting Time data; data cwait; input doctype $ practype $ cards; gen group 15 gen group 20 gen group 25 gen group 20 gen solo 20 gen solo 25 gen solo 30 gen solo 25 spec group 30 spec group 25 spec group 30 spec group 35 spec solo 25 spec solo 20 spec solo 30 spec solo 30 ; proc print; proc sort; by doctype practype; proc means noprint; by doctype practype; output out=factmean mean=timemean; proc plot data=factmean; plot timemean*doctype=practype / vaxis=0 to 35 by 5; proc glm data=cwait order=data; class doctype practype; model time=doctype practype; /* equivalent model statement

40 Two-way ANOVA/ Factorial example 2 - interaction plots Patient Waiting Time data model time=doctype practype doctype*practype; */ output out=new p=yhat r=resid; lsmeans doctype practype doctype*practype / stderr pdiff; means doctype practype doctype*practype / tukey; ODS RTF CLOSE; Obs doctype practype time 1 gen group 15 2 gen group 20 3 gen group 25 4 gen group 20 5 gen solo 20 6 gen solo 25 7 gen solo 30 8 gen solo 25 9 spec group spec group spec group spec group spec solo spec solo spec solo spec solo 30

41 Two-way ANOVA/ Factorial example 2 - interaction plots Patient Waiting Time data Plot of timemean*doctype. Symbol is value of practype. g s timemean 35 ˆ 30 ˆ 25 ˆ s 20 ˆ g 15 ˆ 10 ˆ 5 ˆ 0 ˆ ƒƒˆƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒˆƒƒ gen spec doctype