Syntax

STDMED

where is the sample size.

Description

The STDMED function gives the standard deviation of the median of a normally distributed sample with a mean of 0 and a variance of 1. This function gives the standard error used to determine the width of the control limits for charts produced by the MCHART and MRCHART statements in PROC SHEWHART.

Let represent the sample size and represent the th order statistic. Then, when is odd, the STDMED function calculates , where

where B and is the gamma function, is the standard normal cumulative distribution function, and is the corresponding density function.

If is even, the function calculates the square root of the following:

where

For more details, refer to David (1981), Kendall and Stuart; 1977, p. 252, and Sarhan and Greenberg (1962).

Examples

These statements use a loop to calculate the standard deviation of the median for sample sizes from 6 to 12:

data;
   do n=6 to 12;
      s=stdmed(n);
      put s;
      output;
   end;
run;

The statements produce these values:

0.4634033519
0.4587448763
0.410098592
0.4075552495
0.3719226208
0.3703544701
0.3428063408