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Significance Testing with No Alternative Hypothesis: A Measure of Surprise

J. V. Howard
Erkenntnis (1975-)
Vol. 70, No. 2, Conditionals (Mar., 2009), pp. 253-270
Published by: Springer
Stable URL: http://www.jstor.org/stable/40267421
Page Count: 18
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Significance Testing with No Alternative Hypothesis: A Measure of Surprise
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Abstract

A pure significance test would check the agreement of a statistical model with the observed data even when no alternative model was available. The paper proposes the use of a modified p-value to make such a test. The model will be rejected if something surprising is observed (relative to what else might have been observed). It is shown that the relation between this measure of surprise (the s-value) and the surprise indices of Weaver and Good is similar to the relationship between a p-value, a corresponding odds-ratio, and a logit or log-odds statistic. The s-value is always larger than the corresponding p-value, and is not uniformly distributed. Difficulties with the whole approach are discussed.

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