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.

use https://stats.idre.ucla.edu/stat/stata/notes/hsb2, clear(highschool and beyond (200 cases))nptrend math, group(ses) cuzickCuzick'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