/****************************************************************
* * Assessing Normality assumption: Univariate and Multivariate      *
*****************************************************************/
DM "output;clear;log;clear";
Options pagesize=45 linesize=80 PageNo=1 NoDate;
OPTIONS FORMCHAR="|----|+|---+=|-/\<>*";
    *To make your document display correctly without SAS Monospace font;
Title1 "Example 4.12 & 4.13";
ODS HTML body=    "norm-body.html"
         contents="norm-contents.html"
         frame=   "norm-frame.html"
         page=    "norm-page.html"
         headtext="<title>Assessing Normality Assumption</title>"
         anchor="norm";
    * HTML files are to be saved in, for example, C:\Program Files\SAS\SAS 9.1;
title "Normal Assessement";
Proc IML;
N=100;
Mu={1 2 3 4};
Cov={3 2 1 1, 2 5 3 2, 1 3 2 1, 1 2 1 3};
Call VNORMAL(mymat, Mu, Cov, N, 1234);
Create mydata1 from mymat (|colname={X1 X2 X3 X4}|);
Append from mymat;
run; quit;

Proc IML;
    Use mydata1;
    Read ALL into X; N=NROW(X);
    One=SHAPE(1,N,1);
    MeanVec=(One`*X)/N;         *Calculate Mean Vector;
    M=REPEAT(MeanVec,N,1);
    Sigma=(X-M)`*(X-M)/(N-1);   *Calculate Cov Matrix;
    Dis=VECDIAG((X-M)*INV(Sigma)*(X-M)`); *Calculate stat distance;
    print MeanVec;
    print Sigma;
    print Dis;

    CREATE D2 FROM Dis;
    APPEND FROM Dis;
run;
Data mydata2; merge mydata1 D2(RENAME=(COL1=D2)); run;

Proc Sort data=mydata2 out=sort_d2;
     by D2;
run;
Title "Distances, normal quantiles, and chi-sq quantiles";
Data norm_p; set sort_d2; N=100;
    NN=(_N_-.5)/N;
    Z=PROBIT(NN);       *Calculate Normal quantiles;
    Xsq=CINV(NN,2);     *Calculate Chi-sq quantiles;
    drop obs NN X1 X2 X3 X4;
Proc print data=norm_p;run;
Proc GPLOT data=norm_p;
    title 'Normal Probability Plot';
    Plot D2*Z / HAXIS=AXIS1 VAXIS=AXIS2 VREF=0;
        AXIS1 Label=('Standard Normal') ORDER=-2 to 2 by 1;
        AXIS2 Label=('Squared Distance');
        Footnote J=L 'Data Prob. 1.4'; run;
Proc GPLOT data=norm_p;
    title 'Chi-sq Probability Plot';
    Plot D2*Xsq / HAXIS=AXIS1 VAXIS=AXIS2 VREF=0;
        AXIS1 Label=('Chi-square') ORDER=0 to 7 by 1;
        AXIS2 Label=('Squared Distance');
        Footnote J=L 'Data Prob. 1.4';
run;

ODS HTML Close;
/****************************************************************
* Chapter 4 Example 4.12, 4.13 in Johnson and Wichern 5th ed    *
* Assessing Normality assumption: Univariate and Bivariate      *
*****************************************************************/
DM "output;clear;log;clear";
Options pagesize=45 linesize=80 PageNo=1 NoDate;
OPTIONS FORMCHAR="|----|+|---+=|-/\<>*";
        *To make your document display correctly without SAS Monospace font;

ODS HTML body=    "norm-body.html"
         contents="norm-contents.html"
         frame=   "norm-frame.html"
         page=    "norm-page.html"
         headtext="<title>Assessing Normality Assumption</title>"
         anchor="norm";
        * HTML files are to be saved in, for example, C:\Program Files\SAS\SAS 9.1;
title "Normal Assessment";
Proc IML;
N=100;
Mu={1 2 3 4};
Cov={3 2 1 1, 2 5 3 2, 1 3 2 1, 1 2 1 3};
Call VNORMAL(mymat, Mu, Cov, N, 1234);
Create mydata1 from mymat (|colname={X1 X2 X3 X4}|);
Append from mymat;
run; quit;

Proc IML;
        Use mydata1;
        Read ALL into X; N=NROW(X);
        One=SHAPE(1,N,1);
        MeanVec=(One`*X)/N;                     *Calculate Mean Vector;
        M=REPEAT(MeanVec,N,1);
        Sigma=(X-M)`*(X-M)/(N-1);       *Calculate Cov Matrix;
        Dis=VECDIAG((X-M)*INV(Sigma)*(X-M)`); *Calculate stat distance;
        print MeanVec;
        print Sigma;
        print Dis;

        CREATE D2 FROM Dis;
        APPEND FROM Dis;
run; quit;
Data mydata2; merge mydata1 D2(RENAME=(COL1=D2)); run;

Proc Sort data=mydata2 out=sort_d2;
         by D2;
run;
Title "Distances, normal quantiles, and chi-sq quantiles";
Data norm_p; set sort_d2; N=100;
        NN=(_N_-.5)/N;
        Z=PROBIT(NN);           *Calculate Normal quantiles;
        Xsq=CINV(NN,2);         *Calculate Chi-sq quantiles;
        drop obs NN X1 X2 X3 X4;
Proc print data=norm_p;run;
Proc GPLOT data=norm_p;
        title 'Normal Probability Plot';
        Plot D2*Z / HAXIS=AXIS1 VAXIS=AXIS2 VREF=0;
                AXIS1 Label=('Standard Normal') ORDER=-2 to 2 by 1;
                AXIS2 Label=('Squared Distance');
                Footnote J=L 'random sample from N4'; run;
Proc GPLOT data=norm_p;
        title 'Chi-sq Probability Plot';
        Plot D2*Xsq / HAXIS=AXIS1 VAXIS=AXIS2 VREF=0;
                AXIS1 Label=('Chi-square') ORDER=0 to 7 by 1;
                AXIS2 Label=('Squared Distance');
                Footnote J=L 'random sample from N4';
run;

ODS HTML Close;