Ken Rice, Professor in the Department of Biostatistics at the University of Washington, will present:
“Knowing the Signs: Testing Made Simple and Coherent”
Abstract: Testing remains a controversial area of statistics, in which default frequentist and Bayesian methods disagree. Moreover, some basic and widely-used testing methods are so widely-misunderstood that retiring them has been publicly promoted by experts in our field – and also publicly disavowed by others. In this talk we present an alternative derivation of two-sided tests, intended to clear up some of this mess.
We develop two-sided tests as decisions on (only) the sign of an underlying parameter, where we can conclude that the parameter is positive, negative, or simply say nothing either way. Unusually, we consider the whole set of possible utility functions available, and hence show how close analogs of familiar two-sided tests are the inevitable answers to the question thus posed. We argue that this simplicity could aid non-experts’ understanding and use of tests – and help them think critically about whether or not tests are appropriate for answering their scientific questions. Extending the sign-decision framework gives methods for post hoc test assessment, multiple testing corrections, Bayes Factors and p-values. In this talk we focus on how it resolves an embarrassing failure of UMPU tests, which for interval null hypotheses in straightforward Normal location problems lead to nonsensical results.
This is joint work with Chloe Krakauer, Tyler Bonnett, and Spencer Hansen
All are welcome.