Confidences in Hypotheses

This article introduces a broadly-applicable new method of statistical analysis called hypotheses assessment. The method uses sample data to directly measure the truthfulness of competing hypotheses. Our aim is to determine frequentist non-misleading confidences in the hypotheses that are as powerful as the particular application allows. Hypotheses assessments complement hypothesis tests because providing confidences in the hypotheses in addition to test results can better inform applied researchers about the strength of evidence provided by the data. For simple hypotheses, the method produces minimum and maximum confidences in each hypothesis. The composite case is more complex, and we introduce two conventions to aid with understanding the strength of evidence. Assessments are qualitatively different from hypothesis testing and confidence interval outcomes, and thus fill a gap in the statistician's toolkit.