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options ls=78;
title "Confidence Intervals - Swiss Bank Notes";

 /* %let allows the p variable to be used throughout the code below
  */

%let p=6;

data swiss;
  infile "D:\Statistics\STAT 505\data\swiss3.csv" firstobs=2 delimiter=','
  input type $ length left right bottom top diag;
  run;

 /* A new data set named 'real' is created, consisting 
  * of only the real notes. This is used for calculation 
  * of the statistics needed for the last step.
  * Also, where each variable is originally in its own column, 
  * these commands stack the data so that all variable names 
  * are in one column called 'variable', and all response values 
  * are in another column called 'x'.
  */

data real;
  set swiss;
  if type="real";
  variable="length";   x=length; output;
  variable="left";     x=left;   output;
  variable="right";    x=right;  output;
  variable="bottom";   x=bottom; output;
  variable="top";      x=top;    output;
  variable="diagonal"; x=diag;   output;
  keep type variable x;
  run;

proc sort;
  by variable;
  run;

 /* The means procedure calculates and saves the sample size,
  * mean, and variance for each variable. It then saves these results 
  * in a new data set 'pop1', corresponding to the real notes.
  * /

proc means data=real noprint;
  by variable;
  id type;
  var x;
  output out=pop1 n=n1 mean=xbar1 var=s21;

 /* A new data set named 'fake' is created, consisting 
  * of only the fake notes. This is used for calculation 
  * of the statistics needed for the last step.
  * Also, where each variable is originally in its own column, 
  * these commands stack the data so that all variable names 
  * are in one column called 'variable', and all response values 
  * are in another column called 'x'.
  */

data fake;
  set swiss;
  if type="fake";
  variable="length";   x=length; output;
  variable="left";     x=left;   output;
  variable="right";    x=right;  output;
  variable="bottom";   x=bottom; output;
  variable="top";      x=top;    output;
  variable="diagonal"; x=diag;   output;
  keep type variable x;
  run;

proc sort;
  by variable;
  run;

 /* The means procedure calculates and saves the sample size,
  * mean, and variance for each variable. It then saves these results 
  * in a new data set 'pop2', corresponding to the fake notes.
  * /

proc means data=fake noprint;
  by variable;
  id type;
  var x;
  output out=pop2 n=n2 mean=xbar2 var=s22;


 /* This last step combines the two separate data sets to one
  * and computes the 95% simultaneous confidence interval limits 
  * from the statistics calculated previously. 
  * The variances are pooled from both the real and the fake samples.
  */

data combine;
  merge pop1 pop2;
  by variable;
  f=finv(0.95,&p,n1+n2-&p-1);
  t=tinv(1-0.025/&p,n1+n2-2);
  sp=((n1-1)*s21+(n2-1)*s22)/(n1+n2-2);
  losim=xbar1-xbar2-sqrt(&p*(n1+n2-2)*f*(1/n1+1/n2)*sp/(n1+n2-&p-1));
  upsim=xbar1-xbar2+sqrt(&p*(n1+n2-2)*f*(1/n1+1/n2)*sp/(n1+n2-&p-1));
  lobon=xbar1-xbar2-t*sqrt((1/n1+1/n2)*sp);
  upbon=xbar1-xbar2+t*sqrt((1/n1+1/n2)*sp);
  run;

proc print data=combine;
  run;