In a oneway analysis of variance (ANOVA), the alternative hypothesis is
that the means across the levels of
a factor variable
are not equal. In the situation where the factor variable has a natural
ordering, this alternative hypothesis may not be the exact hypothesis that one wishes to
test. An
alternative hypothesis is that the responses systematically increase or decrease
over the levels of the factor variable. In Stata,
the nptrend command performs a non-parametric test of trend for the
ranks of across ordered groups. The test is an extension of the Wilcoxon
rank-sum test.

For a quick example, we are going to see if there is a trend of ranks of
math score over the levels of socio-economic status (ses)
using the hsb2 dataset.

NOTE:  This syntax works for Stata 17 and later.

use https://stats.idre.ucla.edu/stat/stata/notes/hsb2, clear
(high school and beyond (200 cases))

nptrend math, group(ses) cuzick

Cuzick's test with rank scores

   Number of observations =      200
         Number of groups =        3
Number of response levels =       40

--------------------------------------------------------
             |                        Mean
             |                    response        Number
       Group |   Group score         score        of obs
-------------+------------------------------------------
         ses |
        low  |             1      49.17021            47
     middle  |             2      52.21053            95
       high  |             3      56.17241            58
--------------------------------------------------------

                Statistic =    12.18
                Std. err. = 2.954912
                        z =    4.122
               Prob > |z| =   0.0000

From the test, there appears to be a trend in math scores across
the ordered levels of ses.

The syntax for the nptrend command changed in Stata version 17. The code above works with Stata 17; for earlier versions of Stata, the code below will work.

nptrend math, by(ses)

           ses        score          obs   sum of ranks  
           low            1           47         3637.5  
        middle            2           95         9283.5  
          high            3           58           7179  

          z  =  4.12
  Prob > |z| = 0.000