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JDK's avatar

You didn't cite any papers in this thread. Maybe you were replying to someone else?

But there are at least 3 generations of poorly trained physicians. (statistically illiterate, see eg (Odette Wegwarth 2013))

Yes, 2 sigma is NOT much evidence, but we are stuck in a paradigm where medicine generally thinks it is enough. And it verges on scientism!

Ok 5 sigma for Physics, I mistated. But I am not advocating for that in medicine, 3 sigma would be sufficient.

But I would note that Shewhart and then Deming, were pretty explicit that their approach was not probabilistic. It was empirically based on the best place to minimize (but not eliminate) Type I and Type II errors.

I will keep an open mind about "degree of surprise" (Shackle, I presume) and further contemplate. Is starting with Derbyshire (1977), a good place?

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Sander Greenland's avatar

I don't know Derbyshire. Some history of what I was describing is cited in a few of the articles below. Shannon (1948) is the earliest cite I have that settled on and proved theorems about measuring the information in seeing an event of probability p as s = -log_b(p), where the base b of the logs determines the scale of information units. For use with P-values, I cited the following in my first post on this page this morning, and I ask you to read that post as well as:

Greenland, S., Senn, S.J., Rothman, K.J., Carlin, J.C., Poole, C., Goodman, S.N., Altman, D.G. (2016). Statistical tests, confidence intervals, and power: A guide to misinterpretations. The American Statistician, 70, online supplement 1 at https://amstat.tandfonline.com/doi/suppl/10.1080/00031305.2016.1154108/suppl_file/utas_a_1154108_sm5368.pdf, https://www.jstor.org/stable/44851769

Rafi, Z., Greenland, S. (2020). Semantic and cognitive tools to aid statistical science: Replace confidence and significance by compatibility and surprise. BMC Medical Research Methodology https://bmcmedresmethodol.biomedcentral.com/articles/10.1186/s12874-020-01105-9

Greenland, S., Mansournia, M., and Joffe, M. (2022). To curb research misreporting, replace significance and confidence by compatibility. Preventive Medicine, 164, https://www.sciencedirect.com/science/article/pii/S0091743522001761

- Those are very basic however, and you might prefer these treatments: (next post as this is getting cut off)

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JDK's avatar

I thought Surprise Theory is G. L. S. Shackle beginning in the 30s.

https://www.sciencedirect.com/science/article/pii/S0040162516300671

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Sander Greenland's avatar

Thanks for the cite but I am discussing surprisals as found in information theory, not surprise theory - see my post below for "more sophisticated treatments" of surprisal interpretations for P-values and CIs.

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Sander Greenland's avatar

More sophisticated treatments:

Greenland, S. (2019). Some misleading criticisms of P-values and their resolution with S-values. The American Statistician, 73, supplement 1, 106-114, open access at www.tandfonline.com/doi/pdf/10.1080/00031305.2018.1529625

Greenland, S., Rafi, Z. (2020). Technical issues in the interpretation of S-values and their relation to other information measures. Supplement to Rafi & Greenland at https://arxiv.org/abs/2008.

Greenland, S. (2023). Divergence vs. decision P-values: A distinction worth making in theory and keeping in practice. Scandinavian Journal of Statistics, 50(1), 1-35, free preprint at https://arxiv.org/ftp/arxiv/papers/2301/2301.02478.pdf. Discussion and Rejoinder appear in issue 3 of vol. 50.

Amrhein, V., and Greenland, S. (2022). Discuss practical importance of results based on interval estimates and p-value functions, not only on point estimates and null p-values. Journal of Information Technology, 37(3), 316-320, https://journals.sagepub.com/doi/full/10.1177/02683962221105904

Here is some motivating background for these approaches:

Greenland, S. (2017). The need for cognitive science in methodology. American Journal of Epidemiology, 186, 639-645, https://academic.oup.com/aje/article/186/6/639/3886035.

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