Isotonic regression and nonparametric trend test
There are two ways which tests if groups are ordered with respect to a single response given an assumed apriori ordering of the groups with respect to this response.
- Isotonic regression finds the best fitting model which has an unknown number of changepoints separating linear fits. An alternative nonparametric approach, Jonckheere-Terpstra test compares the ordering in the groups to that which would be expected by chance.
Both these tests may be fitted in R using code [http://www.stat.umn.edu/geyer/5601/examp/oneway.html here.] The more reent ISOREG procedure in R will also perform an isotonic regression. In each case a p-value is produced to assess whether the groups form an ordering with respect to the observed response. Jonckheere's trend test is also fitted in the analyse>nonparametric tests procedure in SPSS. Further details of Jonckheere's test, with an example, are also given [:FAQ/JonckheereTrendTest_Jonckheere%27s_Trend_Test: here.]