/*****************************************************************************************************************

SAS file name: Descriptive_Statistics.sas
File location: 
_________________________________________________________________________________________________________________

Purpose: To Demonstrate how the different descriptive statistics in PROC MEANS and PROC UNIVARIATE
         are calculated using the IML language.
Author: Peter Clemmensen
Creation Date: 01/03/2017

This Program support the "Descriptive Statistics in SAS/IML" Example on SASnrd.com

*****************************************************************************************************************/

/* Request different descriptive statistics of Height using PROC MEANS */
proc means data = sashelp.class n max min range Mean Std stderr t prt maxdec=2;
   var Height;
run;

/* Calculate the same quantities "Manually" in SAS/IML */
proc iml;

use sashelp.class;                                    /* Open dataset for reading              */                                 
   read all var {Height};                             /* Read variable Height into vector      */
close sashelp.class;                                  /* Close dataset                         */  

mu0      = 60;                                        /* Hypothesised mean                     */
N        = nrow(Height);                              /* Number of observations                */
min      = min(Height);                               /* Minimum Value                         */
max      = max(Height);                               /* Maximum Value                         */
range    = max - min;                                 /* The difference between min and max    */

Mean     = 1/n * sum(Height);                         /* Population mean value                 */
Std      = sqrt(1/(n-1) * sum((Height - Mean)##2));   /* Standard Deviation                    */
Std_Err  = Std / sqrt(n);                             /* Standard error of the mean            */
t_stat   = (Mean - mu0) / Std_Err;                    /* T statistic                           */
p_value  = (1-cdf('t',abs(t_stat),n-1))*2;            /* P value associated with t-statistic   */

print N max min range Mean Std Std_Err t_stat         /* Print selected descriptive statistics */
      p_value;          
quit;