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arXiv · 2408.12905

On the relation between likelihood ratios and p-values for testing success probabilities of Bernoulli trials

Wouter Kager·Ronald Meester
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Abstract

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.

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Wouter Kager, Ronald Meester. 2024-08-23. On the relation between likelihood ratios and p-values for testing success probabilities of Bernoulli trials. https://arxiv.org/abs/2408.12905

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