Timeline for When is it important for a practitioner to understand CIs?
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8 events
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| Apr 16, 2024 at 8:02 | comment | added | Dikran Marsupial | @MichaelLew It is indeed a contrived example, but it is intended to make a point clearly. The fact that you can contrive such an example shows that the misinterpretation of confidence intervals is a misinterpretation. I found it a very useful example in clarifying the distinction between a confidence interval and a credible interval, which makes me appreciate confidence intervals more. Nobody is saying that confidence intervals "fall apart", that is only if you insist on interpreting them as a direct answer to a question they are not intended to answer directly. | |
| Apr 15, 2024 at 21:06 | comment | added | COOLSerdash | This paper by Greenland et al. is more pertinent to the point made here, I think. The one currently linked to is also fantastic. | |
| Apr 15, 2024 at 20:42 | comment | added | Michael Lew | @Harvey Your response begs the question of whether there would be circumstances where it would be important that a practitioner might interpret a compatibility interval as being a confidence interval? | |
| Apr 15, 2024 at 20:38 | comment | added | Michael Lew | @DikranMarsupial Does the Jaynes example have a minimal dataset? From my reading I would say that it is relatively common for seeming counter-examples to consist of severely contrived conditions and less data than parameters. They do not in any way show that methods fall apart in more conventional circumstances. See here for an important example: arxiv.org/pdf/1507.08394.pdf | |
| Apr 15, 2024 at 13:45 | comment | added | Dikran Marsupial | @TasosPapastylianou I think "sufficiently compatible with the atypical data" would make "compatibility intervals" even more misleading than "confidence" interval. It seems easier just to understand what a confidence interval actually answers. | |
| Apr 15, 2024 at 13:12 | comment | added | Tasos Papastylianou | @DikranMarsupial Not OP, but what you say isn't contradictory. If the data obtained happens to be 'atypical' with respect to the population, then the CI will correctly give the range of models that are sufficiently compatible with the atypical data, but this will likely not contain the true population value. I think your main concern here is the phrase "with the data" used to imply the population, without taking into account the fact that, data obtained from a population can in fact be atypical (albeit with low probability). | |
| Apr 15, 2024 at 12:27 | comment | added | Dikran Marsupial | E.T. Jaynes gave an example of a correctly constructed confidence interval that is certain not to contain the true value (I think it is the paper mentioned here: stats.stackexchange.com/questions/2356/… ), so I'm not sure "highly compatible with the data" is any better. I quite like "confidence interval" - the fact that frequentist terminology avoids mentioning probabilities is itself a statement. | |
| Apr 15, 2024 at 1:46 | history | answered | Harvey Motulsky | CC BY-SA 4.0 |