Yet you didnât respond to his statement of the Bayesian alternative, namely, reporting likelihoods. Reporting likelihoods addresses all of your complaints (because it doesnât rely on a prior at all). You can use arbitrary likelihood-ratio cutoffs in essentially the same way that youâd use arbitrary p-value cutoffs.
Some advantages of likelihoods over p-values:
You are encouraged to explicitly contrast hypotheses against each other, rather than pretending that thereâs a privileged ânull hypothesisâ to contrast against. This somewhat helps avoid the failure mode of rejecting a fake null hypothesis that no one actually believed, and calling that a significant result.
If you do have a prior, itâs super easy to update on likelihoods (or even better, likelihood ratios).
p-values are almost likelihoods anyway, they just add the weird âx or greaterâ trick, which makes it harder to translate into likelihood ratios.
In other words: why mess up the nice elegant math of likelihoods with the weird alterations for p-values? Since likelihoods meet all the criteria youâve stated in your post, and more besides, there should be some additional motivation for using p-values instead; some advantage over likelihoods which is worth the cost.
Iâm pretty sure Iâve missed something, given that the number of papers giving yet-another-argument-against-p-values is approximately infinite, but thatâs what I can come up with.
Eliezerâs tweet is what prompted me to write this. đ
Yet you didnât respond to his statement of the Bayesian alternative, namely, reporting likelihoods. Reporting likelihoods addresses all of your complaints (because it doesnât rely on a prior at all). You can use arbitrary likelihood-ratio cutoffs in essentially the same way that youâd use arbitrary p-value cutoffs.
Some advantages of likelihoods over p-values:
You are encouraged to explicitly contrast hypotheses against each other, rather than pretending that thereâs a privileged ânull hypothesisâ to contrast against. This somewhat helps avoid the failure mode of rejecting a fake null hypothesis that no one actually believed, and calling that a significant result.
If you do have a prior, itâs super easy to update on likelihoods (or even better, likelihood ratios).
p-values are almost likelihoods anyway, they just add the weird âx or greaterâ trick, which makes it harder to translate into likelihood ratios.
In other words: why mess up the nice elegant math of likelihoods with the weird alterations for p-values? Since likelihoods meet all the criteria youâve stated in your post, and more besides, there should be some additional motivation for using p-values instead; some advantage over likelihoods which is worth the cost.
Iâm pretty sure Iâve missed something, given that the number of papers giving yet-another-argument-against-p-values is approximately infinite, but thatâs what I can come up with.