Change the range not the language on confidence intervals

[R_cubed]

@f2harrell

If you poll consumers of such work and ask them to interpret this, their level of understanding will approach zero.

Until I started visiting this forum, my intuition regarding these elementary frequentist concepts was less than zero. But going through your posts and references, along with the writing of @Sander has helped greatly. I don’t think I’m alone in this.

Looking back, it would have been easier for me to understand the obscure frequentist notion of “confidence” that is distinct from probability if it were linked to the likelihood concept. The likelihood function draws frequentist and Bayesian inference much closer.

Sander pointed out in this old thread:

@Sander

The full graphs behind such numbers [ie. p values, s values, likelihood ratios, confidence intervals] are very important for teaching and classroom data analysis, however, because we need to instill everyone with the idea that the numbers are merely road signs indicating where things are located on a much more detailed map of results.

The most compatible value with the data within a confidence interval

R-cubed: “If one wishes to condition on the data (ie treat data as given), why wouldn’t he/she simply use relative measures of evidence (ie. likelihoods)?” ?: At the end did you mean “(e.g. likelihood ratios [LRs])”? There are other relative measures including posterior odds (POs) which are LRs only under near-flat priors. That aside, I’m fine with relative measures as part of a toolkit that also includes absolute measures. As an editor I’d have no rigid requirements other than using reasonabl…

[f2harrell]

The simplest answer to your question is that it doesn’t extend well to the multi parameter or multiple outcome cases. For example you’d have trouble quantifying evidence for a treatment reducing mortality by any amount or reducing blood pressure by > 10 mmHg (Bayes has no trouble with this).

[kiwiskiNZ]

@s_doi

a range of uncertainty in our estimate of the population parameter

Now you are talking my original language - I was once a physicist and my first ever undergraduate physics lecture was all about uncertainty (though perhaps not meant quite the same way). Though I expect it would take a generation to change the language in the medical literature unless we can get at the editors.
ps. given the hypothesis we care about is often only one sided in medicine, could we not say, eg. if a 97.5% interval was 2 to infinity then any test hypothesis between 2 and infinity will return a fail-to-reject P-value of ˃ (1 – 0.975)?

[f2harrell]

This is getting away from what researchers need. In the classical statistics world, one specifies a “coverage” probability and the procedure returns two limits. In practice it is much more common to desire the probability that the true unknown effect is within a researcher-specified interval that defines a clinically meaningful range.

[karlamoPA]

The resource you provided is very good for the layperson interested in learning the basic concepts in statistics - thank you.

For the broader public, it can be even more concise I feel, such as: the wide range in the CI indicates that additional study is needed to gain confidence that the results in this study predicts the possibility of benefit / risk of harm in other patients. (If I have it right.)