Wilcoxon-Mann-Whitney or t-test? On assumptions for hypothesis tests and multiple interpretations of decision rules

In a mathematical approach to hypothesis tests, we start with a clearly defined set of hypotheses and choose the test with the best properties for those hypotheses. In practice, we often start with less precise hypotheses. For example, often a researcher wants to know which of two groups generally has the larger responses, and either a t-test or a Wilcoxon-Mann-Whitney (WMW) test could be acceptable. Although both t-tests and WMW tests are usually associated with quite different hypotheses, the decision rule and p-value from either test could be associated with many different sets of assumptions, which we call perspectives. It is useful to have many of the different perspectives to which a decision rule may be…