  This article outlines a broadly-applicable new method of statistical analysis
for situations involving two competing hypotheses. Hypotheses assessment is a
frequentist procedure designed to answer the question: Given the sample
evidence (and assumed model), what is the relative plausibility of each
hypothesis? Our aim is to determine frequentist confidences in the hypotheses
that are relevant to the data at hand and are as powerful as the particular
application allows. Hypotheses assessments complement significance 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 significance test and confidence
interval outcomes, and thus fill a gap in the statistician's toolkit.
