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.

interval null hypothesis, one-sided test, p-value, Schervish phenomenon, two-sided test.

Received: May 5, 2024; Accepted: June 20, 2024; Published: June 25, 2024

How to cite this article: Michael P. Cohen, Interval null hypotheses when different intervals are considered, Far East Journal of Theoretical Statistics 68(2) (2024), 263-269. https://doi.org/10.17654/0972086324016

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:
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[2] Thomas S. Ferguson. Mathematical Statistics: A Decision Theoretic Approach, Academic Press, New York, 1967.
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[6] Mark J. Schervish, P values: what they are and what they are not, Amer. Statist. 50 (1996), 203-206.