8 - Assumptions and Hypothesis Tests

Summary

This short chapter formally defines hypothesis tests in terms of decision rules paired with assumptions. It defines when one set of assumptions is more restrictive than another set. It further defines a multiple perspective decision rule, where one decision rule (and hence its p-value function) can be applied under different sets of assumptions, called perspectives.For example, the one sample t-test p-value may be interpreted as testing a mean restricted to the class of normal distributions, but that same p-value is asymptotically valid under an expanded class of distributions that does not require the normality assumption. This multiple perspective decision rule formulation may allow an appropriate interpretation the t-test p-value even when the data are clearly not normally distributed. Another example is presented, giving the Wilcoxon–Mann–Whitney decision rule under two different perspectives.