On the relation between likelihood ratios and p-values for testing success probabilities of Bernoulli trials
Year: 2024
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Kager, Wouter, Meester, Ronald
Institution: Vrije Universiteit Amsterdam
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4402699207