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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. $\bar{A}<\bar{B}<\bar{C}<\bar{D}$?

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  • $\begingroup$ 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? $\endgroup$ – kjetil b halvorsen May 1 '19 at 9:52
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What you need is called order restricted inference, there is books dedicated to the topic, one modern book is here.

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.

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