"Outcome-counting'-Significance tests from incomplete predictions of order

Experiments testing models usually predict that some treatment effects will be greater than others, but they do not as a rule feel able to predict the exact ordering of treatment effects. A useful significance test for such incomplete order predictions can be obtained by comparing the number of possible outcomes (orderings) with the number that satisfy the predictions. The difficulty is to count the outcomes satisfying the predictions, which can be a lengthy task if there are many treatments. A straightforward method of outcome-counting is derived from simple algebra and examples of its use are given.