2025 leisurely cruise

67 Years of Cox’s (1958) Chestnut: Excerpt from Excursion 3 Tour II

Posted on December 29, 2025 by Mayo

2025-26 Cruise

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We’re stopping to consider one of the “chestnuts” in the exhibits of “chestnuts and howlers” in Excursion 3 (Tour II) of Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (SIST 2018). It is now 67 years since Cox gave his famous weighing machine example in Sir David Cox (1958)[1]. It will play a vital role in our discussion of the (strong) Likelihood Principle later this week. The excerpt is from SIST (pp. 170-173).

Exhibit (vi): Two Measuring Instruments of Different Precisions. Did you hear about the frequentist who, knowing she used a scale that’s right only half the time, claimed her method of weighing is right 75% of the time? 

She says, “I flipped a coin to decide whether to use a scale that’s right 100% of the time, or one that’s right only half the time, so, overall, I’m right 75% of the time.” (She wants credit because she could have used a better scale, even knowing she used a lousy one.)

Basis for the joke: An N-P test bases error probability on all possible outcomes or measurements that could have occurred in repetitions, but did not. Continue reading →

Categories: 2025 leisurely cruise, Birnbaum, Likelihood Principle | Leave a comment

(DEC #2) December Leisurely Tour Meeting 3: SIST Excursion 3 Tour III

Posted on December 19, 2025 by Mayo

2025-26 Cruise

We are now at the second stop on our December leisurely cruise through SIST: Excursion 3 Tour III. I am pasting the slides and video from this session during the LSE Research Seminars in 2020 (from which this cruise derives). (Remember it was early pandemic, and we weren’t so adept with zooming.)  The Higgs discussion clarifies (and defends) a somewhat controversial interpretation of p-values. (If you’re interested in the Higgs discovery, there’s a lot more on this blog you can find with the search. I am not sure if I would include the section on “capability and severity” were I to write a second edition, though I would keep the duality of tests and CIs. My goal was to expose a fallacy that is even more common nowadays, but I would have placed a revised version later in the book. Share your remarks in the comments.

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III. Deeper Concepts: Confidence Intervals and Tests: Higgs’ Discovery: Continue reading →

Categories: 2025 leisurely cruise, confidence intervals and tests | Leave a comment

December leisurely cruise “It’s the Methods, Stupid!” Excursion 3 Tour II (3.4-3.6)

Posted on December 14, 2025 by Mayo

2025-26 Cruise

Welcome to the December leisurely cruise:
Wherever we are sailing, assume that it’s warm, warm, warm (not like today in NYC). This is an overview of our first set of readings for December from my Statistical Inference as Severe Testing: How to get beyond the statistics wars (CUP 2018): [SIST]–Excursion 3 Tour II. This leisurely cruise, participants know, is intended to take a whole month to cover one week of readings from my 2020 LSE Seminars, except for December and January which double up. 

What do you think of  “3.6 Hocus-Pocus: P-values Are Not Error probabilities, Are Not Even Frequentist”? This section refers to Jim Berger’s famous attempted unification of Jeffreys, Neyman and Fisher in 2003. The unification considers testing 2 simple hypotheses using a random sample from a Normal distribution, computing their two P-values, rejecting whichever gets a smaller P-value, and then computing its posterior probability, assuming each gets a prior of .5. This becomes what he calls the “Bayesian error probability” upon which he defines “the frequentist principle”. On Berger’s reading of an important paper* by Neyman (1977), Neyman criticized p-values for violating the frequentist principle (SIST p. 186). *The paper is “frequentist probability and frequentist statistics”. Remember that links to readings outside SIST are at the Captains biblio on the top left of the blog. Share your thoughts in the comments.

Some snapshots from Excursion 3 tour II.

Continue reading →

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First Look at N-P Methods as Severe Tests: Water plant accident [Exhibit (i) from Excursion 3]

Posted on November 28, 2025 by Mayo

November Cruise

The example I use here to illustrate formal severity comes in for criticism  in a paper to which I reply in a 2025 BJPS paper linked to here. Use the comments for queries.

Exhibit (i) N-P Methods as Severe Tests: First Look (Water Plant Accident) 

There’s been an accident at a water plant where our ship is docked, and the cooling system had to be repaired.  It is meant to ensure that the mean temperature of discharged water stays below the temperature that threatens the ecosystem, perhaps not much beyond 150 degrees Fahrenheit. There were 100 water measurements taken at randomly selected times and the sample mean x computed, each with a known standard deviation σ = 10.  When the cooling system is effective, each measurement is like observing X ~ N(150, 102). Because of this variability, we expect different 100-fold water samples to lead to different values of X, but we can deduce its distribution. If each X ~N(μ = 150, 102) then X is also Normal with μ = 150, but the standard deviation of X is only σ/√n = 10/√100 = 1. So X ~ N(μ = 150, 1). Continue reading →

Categories: 2025 leisurely cruise, severe tests, severity function, water plant accident | Leave a comment

Where Are Fisher, Neyman, Pearson in 1919? Opening of Excursion 3, snippets from 3.1

Posted on November 13, 2025 by Mayo

November Cruise

This second excerpt for November is really just the preface to 3.1. Remember, our abbreviated cruise this fall is based on my LSE Seminars in 2020, and since there are only 5, I had to cut. So those seminars skipped 3.1 on the eclipse tests of GTR. But I want to share snippets from 3.1 with current readers, along with reflections in the comments.

Excursion 3 Statistical Tests and Scientific Inference

Tour I Ingenious and Severe Tests

[T]he impressive thing about [the 1919 tests of Einstein’s theory of gravity] is the risk involved in a prediction of this kind. If observation shows that the predicted effect is definitely absent, then the theory is simply refuted.The theory is incompatible with certain possible results of observation – in fact with results which everybody before Einstein would have expected. This is quite different from the situation I have previously described, [where] . . . it was practically impossible to describe any human behavior that might not be claimed to be a verification of these [psychological] theories. (Popper 1962, p. 36)

Continue reading →

Categories: 2025 leisurely cruise, SIST, Statistical Inference as Severe Testing | 2 Comments

November: The leisurely tour of SIST continues

Posted on November 7, 2025 by Mayo

2025 Cruise

We continue our leisurely tour of Statistical Inference as Severe Testing [SIST] (Mayo 2018, CUP) with Excursion 3. This is based on my 5 seminars at the London School of Economics in 2020; I include slides and video for those who are interested. (use the comments for questions) Continue reading →

Categories: 2025 leisurely cruise, significance tests, Statistical Inference as Severe Testing | 1 Comment

Excursion 1 Tour I (3rd stop): The Current State of Play in Statistical Foundations: A View From a Hot-Air Balloon (1.3)

Posted on October 26, 2025 by Mayo

Third Stop

Readers: With this third stop we’ve covered Tour 1 of Excursion 1.  My slides from the first LSE meeting in 2020 which dealt with elements of Excursion 1 can be found at the end of this post. There’s also a video giving an overall intro to SIST, Excursion 1. It’s noteworthy to consider just how much things seem to have changed in just the past few years. Or have they? What would the view from the hot-air balloon look like now?  Share your thoughts in the comments.

ZOOM: I propose a zoom meeting for Sunday Nov. 15, Sunday, November 16 at 11 am or Friday, November 21 at 11am, New York time. (An equal # prefer Fri & Sun.) The link will be available to those who register/registered with Dr. Miller*.

The Current State of Play in Statistical Foundations: A View From a Hot-Air Balloon (1.3)

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How can a discipline, central to science and to critical thinking, have two methodologies, two logics, two approaches that frequently give substantively different answers to the same problems? … Is complacency in the face of contradiction acceptable for a central discipline of science? (Donald Fraser 2011, p. 329)

We [statisticians] are not blameless … we have not made a concerted professional effort to provide the scientific world with a unified testing methodology. (J. Berger 2003, p. 4)

Continue reading →

Categories: 2025 leisurely cruise, Statistical Inference as Severe Testing | Leave a comment

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