2024/08/23 by Wouter Kager, Kager, Wouter, Ronald Meester +1
Mathematics · #62A01 #62H15 #Advanced Statistical Methods and Models #FOS: Mathematics #Statistical Methods in Clinical Trials #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2408.12905
openalex publication_date 2024/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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.