# Hypothesis test testing for monotonic group mean change

I wonder if there is a statistical hypothesis test testing whether group average monotonically increases across groups?

For example, I have four treatment groups, A, B, C and D. I would like to test the hypothesis if the averages increase monotonically, i.e. $$\bar{A}<\bar{B}<\bar{C}<\bar{D}$$?

• Can you tell us some more about your data? For instance, is these normal distributed or not? If not, any idea of how they are distributed? Sample sizes? – kjetil b halvorsen May 1 '19 at 9:52

See the post Why bother looking at an omnibus ANOVA when I have a priori hypotheses about group differences? for some examples and other references. There is also some R packages on CRAN, and here is the home page of a project developing relevant software in R.