# The most compatible value with the data within a confidence interval

**URL:** <https://discourse.datamethods.org/t/the-most-compatible-value-with-the-data-within-a-confidence-interval/4281>\
**Category:** data analysis\
**Tags:** confidence-interval, bayes\
**Created:** [April 13, 2021, 5:23pm UTC](https://discourse.datamethods.org/t/the-most-compatible-value-with-the-data-within-a-confidence-interval/4281 "2021-04-13T17:23:54Z")\
**Posts on this page:** 1\
**Showing post:** 13

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**Author:** ![R\_cubed](https://discourse.datamethods.org/user_avatar/discourse.datamethods.org/r_cubed/32/1518_2.png) [@R\_cubed](https://discourse.datamethods.org/u/R_cubed)\
**Post date:** [April 15, 2021, 9:41pm UTC](https://discourse.datamethods.org/t/the-most-compatible-value-with-the-data-within-a-confidence-interval/4281/13 "2021-04-15T21:41:25Z")

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> Blockquote  
> 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 was precisely what I meant. I own a copy of Richard Royall’s monograph _Statistical Evidence: A Likelihood Paradigm_ and he had convinced me that a distinction between questions of belief revision, choosing a course of action, and summarizing information from experiments (broadly defined to include observational studies) is useful.

I wanted your opinion on data reporting, as I agree with Royall that questions of “what the data say” should not, in principle, depend on the prior of the experimenter. I’d prefer reports that permit me to substitute my own prior or \alpha.

I don’t want to burden you any further as you have been very generous in giving your time and expertise in this thread until I have some time to think more about what you have posted.

For context, I’ve been thinking about this comment by Herman Chernoff on Bradley Efron’s paper “Why Isn’t Everyone Bayesian” I posted in another thread:

> Blockquote  
> With the help of theory, I have developed insights and intuitions that prevent me from giving weight to data dredging and other forms of statistical heresy. This feeling of freedom and ease does not exist until I have a decision theoretic, Bayesian view of the problem … I am a Bayesian decision theorist in spite of my use of Fisherian tools.

> [@Frequentist vs Bayesian debate applied to real-world data analysis: any philosophical insights?](https://discourse.datamethods.org/t/frequentist-vs-bayesian-debate-applied-to-real-world-data-analysis-any-philosophical-insights/1695/7):
>
> I think we need to keep in mind the important distinction between correct frequentist statistics, and simply bad statistics. @Sander posted a link to a youtube video (I’ve also posted it here in a few different threads) on p-values, confidence intervals, and their common, but incorrect interpretations. [[Digging Deeper Into p-values: NISS Webinar Follow-up with Three Authors - November, 2020] ](https://www.youtube.com/watch?v=_p0MRqSlYec) It was mentioned in passing in the video that Jeffries and Fisher would pose statistical p…

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