### Stata FAQ

How can I test for a trend across a categorical variable?

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 http://www.ats.ucla.edu/stat/stata/notes/hsb2, clear**
(highschool and beyond (200 cases))
**nptrend math, by(ses)**
ses score obs sum of ranks
1 1 47 3637.5
2 2 95 9283.5
3 3 58 7179
z = 4.12
Prob > |z| = 0.000

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

**ses. **
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