Significance Testing with No Alternative Hypothesis: A Measure of Surprise |
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Authors: | J V Howard |
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Institution: | (1) London School of Economics, Houghton Street, London, WC2A 2AE, UK |
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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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