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  "path": "/t/change-the-range-not-the-language-on-confidence-intervals/27740?page=2#post_31",
  "publishedAt": "2026-02-26T19:21:35.000Z",
  "site": "https://discourse.datamethods.org",
  "textContent": "As I explained in the 2019 exchange with Andrew Gelman in the BMJ, and many places elsewhere, **“uncertainty measures” is not justified and is even misleading in descriptions of P-values and interval estimates whenever there are uncontrolled or mismodeled sources of uncertainty** , such as the nonrandom variation inherent in observational studies of treatments. And in ordinary English usage, ‘compatibility’ is a much weaker descriptor than ‘certainty’ or ‘support’: Observing p=1 for a model or hypothesis only says that the divergence measure used to compute the P-value did not deviate from what the model or hypothesis predicted. It does not say say the data leaves no uncertainty about the correct model, or that the model is supported by the data. That can be seen from the fact that any saturated model (e.g., a regression model filled with every possible product term of every order) will have p=1, even when the model is contextually absurd.\n\nI view the continued push to interpret statistics like P-values as intrinsically measuring uncertainty or support as a blend of wishful thinking and of overselling of what formal statistics can provide us. Every situation in which one can justify inferential interpretations of P-values and interval estimates (such as “uncertainty”, “confidence”, and “credibility” applied to intervals) arises from successful design actions such as treatment randomization and masking. Statements about uncertainty, confidence, and posterior probability should be derived from such contextual features, including the documented mechanics of data generation. To use such evocative terms to describe what are only statistical relations of data to model predictions (such as P-values or interval estimates) is to slip into statistical descriptions assumptions that often have no justification in reality. In my view this evocation is a bane of accurate research reporting, one that sadly continues to be encouraged by some statisticians and researchers (who often have a clear investment in overinterpreting their data).",
  "title": "Change the range not the language on confidence intervals"
}