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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.12905 |
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Table of Contents:
- It is well known that there is no direct one-to-one relation between $p$-values and likelihood ratios or Bayes factors, since their relation crucially involves the sample size $n$. We investigate their (asymptotic) relation in a coin-tossing context where the hypotheses of interest address the success probability of the coin, and where detailed computations are possible. This leads to useful insights in the nature of $p$-values and likelihood ratios. Our results imply, for instance, that under mild conditions, a $p$-value of 0.05 cannot correspond to a likelihood ratio larger than 7.5, for any hypothesis versus a null hypothesis that the success probability has a specific value. We also show it is unlikely one can obtain a large likelihood ratio by tossing a fair coin until the number of heads deviates from the mean by several standard deviations.