= 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.]