Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.12905 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910060886622208 |
|---|---|
| author | Kager, Wouter Meester, Ronald |
| author_facet | Kager, Wouter Meester, Ronald |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12905 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the relation between likelihood ratios and p-values for testing success probabilities of Bernoulli trials Kager, Wouter Meester, Ronald Statistics Theory 62A01, 62H15 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. |
| title | On the relation between likelihood ratios and p-values for testing success probabilities of Bernoulli trials |
| topic | Statistics Theory 62A01, 62H15 |
| url | https://arxiv.org/abs/2408.12905 |