Safe testing
We develop the theory of hypothesis testing based on the e-value, a notion of evidence that, unlike the p-value, allows for effortlessly combining results from several studies in the common scenario where the decision to perform a new study may depend on previous outcomes. Tests based on e-values ar...
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| Published in: | Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 86; no. 5; pp. 1091 - 1128 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
13.11.2024
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| ISSN: | 1369-7412, 1467-9868 |
| Online Access: | Get full text |
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| Summary: | We develop the theory of hypothesis testing based on the e-value, a notion of evidence that, unlike the p-value, allows for effortlessly combining results from several studies in the common scenario where the decision to perform a new study may depend on previous outcomes. Tests based on e-values are safe, i.e. they preserve type-I error guarantees, under such optional continuation. We define growth rate optimality (GRO) as an analogue of power in an optional continuation context, and we show how to construct GRO e-variables for general testing problems with composite null and alternative, emphasizing models with nuisance parameters. GRO e-values take the form of Bayes factors with special priors. We illustrate the theory using several classic examples including a 1-sample safe t-test and the 2×2 contingency table. Sharing Fisherian, Neymanian, and Jeffreys–Bayesian interpretations, e-values may provide a methodology acceptable to adherents of all three schools. |
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| ISSN: | 1369-7412 1467-9868 |
| DOI: | 10.1093/jrsssb/qkae011 |