options ls=78;
title "Confidence Intervals - Women's Nutrition Data";

 /* %let allows the p variable to be used throughout the code below
  * After reading in the nutrient data, where each variable is
  * originally in its own column, the next statements stack the data
  * so that all variable names are in one column called 'variable',
  * and all response values are in another column called 'x'.
  * This format is used for the calculations that follow.
  */

%let p=5;
data nutrient;
  infile "D:\Statistics\STAT 505\data\nutrient.csv" firstobs=2 delimiter=',';
  input id calcium iron protein a c;
  variable="calcium"; x=calcium; output;
  variable="iron";    x=iron;    output;
  variable="protein"; x=protein; output;
  variable="vit a";   x=a;       output;
  variable="vit c";   x=c;       output;
  keep 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 'a' for use in the final step below.
  * /

proc means noprint;
  by variable;
  var x;
  output out=a n=n mean=xbar var=s2;
  run;

 /* The data step here is used to calculate the confidence interval
  * limits from the statistics calculated in the data set 'a'.
  * The values 't1', 'tb', and 'f' are the critical values used in the 
  * one-at-a-time, Bonferroni, and F intervals, respectively.
  * /

data b;
  set a;
  t1=tinv(1-0.025,n-1);
  tb=tinv(1-0.025/&p,n-1);
  f=finv(0.95,&p,n-&p);
  loone=xbar-t1*sqrt(s2/n);
  upone=xbar+t1*sqrt(s2/n);
  losim=xbar-sqrt(&p*(n-1)*f*s2/(n-&p)/n);
  upsim=xbar+sqrt(&p*(n-1)*f*s2/(n-&p)/n);
  lobon=xbar-tb*sqrt(s2/n);
  upbon=xbar+tb*sqrt(s2/n);
  run;

proc print data=b;
  run;