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INTERVAL NULL HYPOTHESES WHEN DIFFERENT INTERVALS ARE CONSIDERED
Keywords:
interval null hypothesis, one-sided test, p-value, Schervish phenomenon, two-sided testDOI:
https://doi.org/10.17654/0972086324016Abstract
We study interval null hypotheses when more than one interval is being considered. For one-sided tests, the behavior corresponds to what one might expect. But for two-sided testing, Schervish [6] shows that it is possible for the p-value for a particular null hypothesis interval to be smaller than the p-value for a second null hypothesis interval that is a subset of the first interval. This result contradicts the initial expectation that it should be harder to reject the first interval. We examine this situation in detail and shed light on what is going on.
Received: May 5, 2024
Accepted: June 20, 2024
References
Michael P. Cohen, Why not an interval null hypothesis? Journal of Data Science 17(2) (2019), 363-390.
Thomas S. Ferguson. Mathematical Statistics: A Decision Theoretic Approach, Academic Press, New York, 1967.
S. Hansen and K. Rice, Coherent tests for interval null hypotheses, Amer. Statist. 77 (2023), 20-28.
J. H. Kim and A. P. Robinson, Interval-based hypothesis testing and its applications to economics and finance, Econometrics 7(2) (2019), 1-22.
E. L. Lehmann and J. P. Romano, Testing Statistical Hypotheses, Springer, New York, 3rd ed., 2005.
Mark J. Schervish, P values: what they are and what they are not, Amer. Statist. 50 (1996), 203-206.
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