pglpm<p><span class="h-card" translate="no"><a href="https://lgbtqia.space/@AeonCypher" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@<span>AeonCypher</span></a></span> <span class="h-card" translate="no"><a href="https://mastodon.world/@paninid" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@<span>paninid</span></a></span> </p><p>"A p-value is an <a href="https://c.im/tags/estimate" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>estimate</span></a> of p(Data | Null Hypothesis). " – not correct. A p-value is an estimate of</p><p>p(Data or other imagined data | Null Hypothesis)</p><p>so not even just of the actual data you have. Which is why p-values depend on your stopping rule (and do not satisfy the "likelihood principle"). In this regard, see Jeffreys's quote below.</p><p>Imagine you design an experiment this way: "I'll test 10 subjects, and in the meantime I apply for a grant. At the time the 10th subject is tested, I'll know my application's outcome. If the outcome is positive, I'll test 10 more subjects; if it isn't, I'll stop". Not an unrealistic situation.</p><p>With this stopping rule, your p-value will depend on the probability that you get the grant. This is not a joke.</p><p>"*What the use of P implies, therefore, is that a hypothesis that may be true may be rejected because it has not predicted observable results that have not occurred.* This seems a remarkable procedure. On the face of it the fact that such results have not occurred might more reasonably be taken as evidence for the law, not against it." – H. Jeffreys, "Theory of Probability" § VII.7.2 (emphasis in the original) <<a href="https://doi.org/10.1093/oso/9780198503682.001.0001" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">doi.org/10.1093/oso/9780198503</span><span class="invisible">682.001.0001</span></a>>.</p><p><a href="https://c.im/tags/bayesian" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>bayesian</span></a> <a href="https://c.im/tags/bayes" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>bayes</span></a> <a href="https://c.im/tags/statistics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>statistics</span></a></p>