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