How can I test for equality of distribution? | SAS FAQ

This page is done using SAS 9.2. In a simple example, we’ll see if the distribution of writing test scores across gender are equal using the High-School and Beyond 2000 data set, hsb2. We will conduct the Kolmogorov-Smirnov test for equality of distribution functions using proc npar1way.  We’ll first do a kernel density plot of writing scores by gender.

ods graphics on;
proc univariate data = hsb2 normal;
  class female;
  var write;
  histogram /normal kernel;
run;

proc npar1way data = hsb2;
class female;
var write;
run;

The NPAR1WAY Procedure

    Kolmogorov-Smirnov Test for Variable write
           Classified by Variable female

                      EDF at    Deviation from Mean
female       N       Maximum        at Maximum
___________________________________________________
0           91      0.494505          1.283101
1          109      0.247706         -1.172379
Total      200      0.360000

   Maximum Deviation Occurred at Observation 89
         Value of write at Maximum = 49.0

Kolmogorov-Smirnov Two-Sample Test (Asymptotic)
KS   0.122899    D         0.246799
KSa  1.738051    Pr > KSa  0.0048

[remaining of output omitted]

From the test, it is apparent that the writing scores across gender do not have the same distribution function.