In Recognition of Fisher’s birthday (Feb 17), I reblog his contribution to the “Triad”–an exchange between Fisher, Neyman and Pearson 20 years after the Fisher-Neyman break-up. The other two are below. My favorite is the reply by E.S. Pearson, but all are chock full of gems for different reasons. They are each very short and are worth your rereading. Continue reading

# Fisher

## R.A. Fisher: “Statistical methods and Scientific Induction” with replies by Neyman and E.S. Pearson

## R. A. Fisher: How an Outsider Revolutionized Statistics (Aris Spanos)

This is a belated birthday post for R.A. Fisher (17 February, 1890-29 July, 1962)–it’s a guest post from earlier on this blog by Aris Spanos that has gotten the highest number of hits over the years.

**Happy belated birthday to R.A. Fisher!**

**‘R. A. Fisher: How an Outsider Revolutionized Statistics’**

by **Aris Spanos**

Few statisticians will dispute that R. A. Fisher **(February 17, 1890 – July 29, 1962)** is the father of modern statistics; see Savage (1976), Rao (1992). Inspired by William Gosset’s (1908) paper on the Student’s t finite sampling distribution, he recast statistics into the modern model-based induction in a series of papers in the early 1920s. He put forward a theory of *optimal estimation* based on the method of maximum likelihood that has changed only marginally over the last century. His significance testing, spearheaded by the p-value, provided the basis for the Neyman-Pearson theory of *optimal testing* in the early 1930s. According to Hald (1998) Continue reading

## R. A. Fisher: How an Outsider Revolutionized Statistics (Aris Spanos)

This is a belated birthday post for R.A. Fisher (17 February, 1890-29 July, 1962)–it’s a guest post from earlier on this blog by Aris Spanos.

**Happy belated birthday to R.A. Fisher!**

**‘R. A. Fisher: How an Outsider Revolutionized Statistics’**

by **Aris Spanos**

Few statisticians will dispute that R. A. Fisher **(February 17, 1890 – July 29, 1962)** is the father of modern statistics; see Savage (1976), Rao (1992). Inspired by William Gosset’s (1908) paper on the Student’s t finite sampling distribution, he recast statistics into the modern model-based induction in a series of papers in the early 1920s. He put forward a theory of *optimal estimation* based on the method of maximum likelihood that has changed only marginally over the last century. His significance testing, spearheaded by the p-value, provided the basis for the Neyman-Pearson theory of *optimal testing* in the early 1930s. According to Hald (1998) Continue reading

## S. Senn: “Error point: The importance of knowing how much you don’t know” (guest post)

**Stephen Senn**

*Consultant Statistician*

*Edinburgh*

‘The term “point estimation” made Fisher nervous, because he associated it with estimation without regard to accuracy, which he regarded as ridiculous.’ Jimmy Savage [1, p. 453]

## First things second

The classic text by David Cox and David Hinkley, *Theoretical Statistics *(1974), has two extremely interesting features as regards estimation. The first is in the form of an indirect, implicit, message and the second explicit and both teach that point estimation is far from being an obvious goal of statistical inference. The indirect message is that the chapter on point estimation (chapter 8) comes *after* that on interval estimation (chapter 7). This may puzzle the reader, who may anticipate that the complications of interval estimation would be handled after the apparently simpler point estimation rather than before. However, with the start of chapter 8, the reasoning is made clear. Cox and Hinkley state: Continue reading

## Deconstructing the Fisher-Neyman conflict wearing fiducial glasses + Excerpt 5.8 from SIST

This continues my previous post: “Can’t take the fiducial out of Fisher…” in recognition of Fisher’s birthday, February 17. These 2 posts reflect my working out of these ideas in writing Section 5.8 of *Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars* (SIST, CUP 2018).* *Here’s all of Section 5.8 (“Neyman’s Performance and Fisher’s Fiducial Probability”) for your Saturday night reading.*

Move up 20 years to the famous 1955/56 exchange between Fisher and Neyman. Fisher clearly connects Neyman’s adoption of a behavioristic-performance formulation to his denying the soundness of fiducial inference. When “Neyman denies the existence of inductive reasoning, he is merely expressing a verbal preference. For him ‘reasoning’ means what ‘deductive reasoning’ means to others.” (Fisher 1955, p. 74). Continue reading

## Can’t Take the Fiducial Out of Fisher (if you want to understand the N-P performance philosophy) [i]

Continuing with posts in recognition of R.A. Fisher’s birthday, I post one from a few years ago on a topic that had previously not been discussed on this blog: Fisher’s* fiducial probability*.

[Neyman and Pearson] “began an influential collaboration initially designed primarily, it would seem to clarify Fisher’s writing. This led to their theory of testing hypotheses and to Neyman’s development of confidence intervals, aiming to clarify Fisher’s idea of fiducial intervals (D.R.Cox, 2006, p. 195).

The entire episode of fiducial probability is fraught with minefields. Many say it was Fisher’s biggest blunder; others suggest it still hasn’t been understood. The majority of discussions omit the side trip to the Fiducial Forest altogether, finding the surrounding brambles too thorny to penetrate. Besides, a fascinating narrative about the Fisher-Neyman-Pearson divide has managed to bloom and grow while steering clear of fiducial probability–never mind that it remained a centerpiece of Fisher’s statistical philosophy. I now think that this is a mistake. It was thought, following Lehmann (1993) and others, that we could take the fiducial out of Fisher and still understand the core of the Neyman-Pearson vs Fisher (or Neyman vs Fisher) disagreements. We can’t. Quite aside from the intrinsic interest in correcting the “he said/he said” of these statisticians, the issue is intimately bound up with the current (flawed) consensus view of frequentist error statistics. Continue reading

## Guest Blog: R. A. Fisher: How an Outsider Revolutionized Statistics (Aris Spanos)

In recognition of R.A. Fisher’s birthday on February 17…a week of Fisher posts!

**‘R. A. Fisher: How an Outsider Revolutionized Statistics’**

by **Aris Spanos**

Few statisticians will dispute that R. A. Fisher **(February 17, 1890 – July 29, 1962)** is the father of modern statistics; see Savage (1976), Rao (1992). Inspired by William Gosset’s (1908) paper on the Student’s t finite sampling distribution, he recast statistics into the modern model-based induction in a series of papers in the early 1920s. He put forward a theory of *optimal estimation* based on the method of maximum likelihood that has changed only marginally over the last century. His significance testing, spearheaded by the p-value, provided the basis for the Neyman-Pearson theory of *optimal testing* in the early 1930s. According to Hald (1998)

“Fisher was a genius who almost single-handedly created the foundations for modern statistical science, without detailed study of his predecessors. When young he was ignorant not only of the Continental contributions but even of contemporary publications in English.” (p. 738)

What is not so well known is that Fisher was the *ultimate outsider* when he brought about this change of paradigms in statistical science. As an undergraduate, he studied mathematics at Cambridge, and then did graduate work in statistical mechanics and quantum theory. His meager knowledge of statistics came from his study of astronomy; see Box (1978). That, however did not stop him from publishing his first paper in statistics in 1912 (still an undergraduate) on “curve fitting”, questioning Karl Pearson’s method of moments and proposing a new method that was eventually to become the likelihood method in his 1921 paper. Continue reading

## R.A. Fisher: “Statistical methods and Scientific Induction”

In Recognition of Fisher’s birthday (Feb 17), I reblog his contribution to the “Triad”–an exchange between Fisher, Neyman and Pearson 20 years after the Fisher-Neyman break-up. The other two are below. They are each very short and are worth your rereading.

*“Statistical Methods and Scientific Induction“*

*by Sir Ronald Fisher (1955)
*

**SUMMARY**

The attempt to reinterpret the common tests of significance used in scientific research as though they constituted some kind of acceptance procedure and led to “decisions” in Wald’s sense, originated in several misapprehensions and has led, apparently, to several more.

The three phrases examined here, with a view to elucidating they fallacies they embody, are:

- “Repeated sampling from the same population”,
- Errors of the “second kind”,
- “Inductive behavior”.

Mathematicians without personal contact with the Natural Sciences have often been misled by such phrases. The errors to which they lead are not only numerical.

To continue reading Fisher’s paper.

**“Note on an Article by Sir Ronald Fisher“**

**by Jerzy Neyman (1956)**

**Summary**

(1) FISHER’S allegation that, contrary to some passages in the introduction and on the cover of the book by Wald, this book does not really deal with experimental design is unfounded. In actual fact, the book is permeated with problems of experimentation. (2) Without consideration of hypotheses alternative to the one under test and without the study of probabilities of the two kinds, no purely probabilistic theory of tests is possible. Continue reading

## Guest Post: STEPHEN SENN: ‘Fisher’s alternative to the alternative’

**As part of the week of posts on R.A.Fisher (February 17, 1890 – July 29, 1962), I reblog a guest post by Stephen Senn from 2012, and 2017. See especially the comments from Feb 2017. **

*‘Fisher’s alternative to the alternative’*

*By: Stephen Senn*

[2012 marked] the 50th anniversary of RA Fisher’s death. It is a good excuse, I think, to draw attention to an aspect of his philosophy of significance testing. In his extremely interesting essay on Fisher, Jimmie Savage drew attention to a problem in Fisher’s approach to testing. In describing Fisher’s aversion to power functions Savage writes, ‘Fisher says that some tests are *more sensitive* than others, and I cannot help suspecting that that comes to very much the same thing as thinking about the power function.’ (Savage 1976) (P473).

The modern statistician, however, has an advantage here denied to Savage. Savage’s essay was published posthumously in 1976 and the lecture on which it was based was given in Detroit on 29 December 1971 (P441). At that time Fisher’s scientific correspondence did not form part of his available oeuvre but in 1990 Henry Bennett’s magnificent edition of Fisher’s statistical correspondence (Bennett 1990) was published and this throws light on many aspects of Fisher’s thought including on significance tests. Continue reading

## Happy Birthday R.A. Fisher: ‘Two New Properties of Mathematical Likelihood’

*Today is R.A. Fisher’s birthday. I will post some Fisherian items this week in recognition of it*. This paper comes just before the conflicts with Neyman and Pearson erupted. Fisher links his tests and sufficiency, to the Neyman and Pearson lemma in terms of power. We may see them as ending up in a similar place while starting from different origins. I quote just the most relevant portions…the full article is linked below. Happy Birthday Fisher!*

“Two New Properties of Mathematical Likelihood“

by R.A. Fisher, F.R.S.

Proceedings of the Royal Society, Series A, 144: 285-307 (1934)

The property that where a sufficient statistic exists, the likelihood, apart from a factor independent of the parameter to be estimated, is a function only of the parameter and the sufficient statistic, explains the principle result obtained by Neyman and Pearson in discussing the efficacy of tests of significance. Neyman and Pearson introduce the notion that any chosen test of a hypothesis H_{0} is more powerful than any other equivalent test, with regard to an alternative hypothesis H_{1}, when it rejects H_{0} in a set of samples having an assigned aggregate frequency ε when H_{0} is true, and the greatest possible aggregate frequency when H_{1} is true. If any group of samples can be found within the region of rejection whose probability of occurrence on the hypothesis H_{1} is less than that of any other group of samples outside the region, but is not less on the hypothesis H_{0}, then the test can evidently be made more powerful by substituting the one group for the other. Continue reading

## Deconstructing the Fisher-Neyman conflict wearing fiducial glasses (continued)

**[An updated version with corrected links can be found here.]**

This continues my previous post: “Can’t take the fiducial out of Fisher…” in recognition of Fisher’s birthday, February 17. I supply a few more intriguing articles you may find enlightening to read and/or reread on a Saturday night

Move up 20 years to the famous 1955/56 exchange between Fisher and Neyman. Fisher clearly connects Neyman’s adoption of a behavioristic-performance formulation to his denying the soundness of fiducial inference. When “Neyman denies the existence of inductive reasoning, he is merely expressing a verbal preference. For him ‘reasoning’ means what ‘deductive reasoning’ means to others.” (Fisher 1955, p. 74). Continue reading

## Can’t Take the Fiducial Out of Fisher (if you want to understand the N-P performance philosophy) [i]

Continuing with posts in recognition of R.A. Fisher’s birthday, I post one from a couple of years ago on a topic that had previously not been discussed on this blog: Fisher’s* fiducial probability*.

[Neyman and Pearson] “began an influential collaboration initially designed primarily, it would seem to clarify Fisher’s writing. This led to their theory of testing hypotheses and to Neyman’s development of confidence intervals, aiming to clarify Fisher’s idea of fiducial intervals (D.R.Cox, 2006, p. 195).

The entire episode of fiducial probability is fraught with minefields. Many say it was Fisher’s biggest blunder; others suggest it still hasn’t been understood. The majority of discussions omit the side trip to the Fiducial Forest altogether, finding the surrounding brambles too thorny to penetrate. Besides, a fascinating narrative about the Fisher-Neyman-Pearson divide has managed to bloom and grow while steering clear of fiducial probability–never mind that it remained a centerpiece of Fisher’s statistical philosophy. I now think that this is a mistake. It was thought, following Lehman (1993) and others, that we could take the fiducial out of Fisher and still understand the core of the Neyman-Pearson vs Fisher (or Neyman vs Fisher) disagreements. We can’t. Quite aside from the intrinsic interest in correcting the “he said/he said” of these statisticians, the issue is intimately bound up with the current (flawed) consensus view of frequentist error statistics.

So what’s *fiducial inference*? I follow Cox (2006), adapting for the case of the lower limit: Continue reading

## R.A. Fisher: “Statistical methods and Scientific Induction”

I continue a week of Fisherian posts begun on his birthday (Feb 17). This is his contribution to the “Triad”–an exchange between Fisher, Neyman and Pearson 20 years after the Fisher-Neyman break-up. The other two are below. They are each very short and are worth your rereading.

*“Statistical Methods and Scientific Induction”*

*by Sir Ronald Fisher (1955)
*

**SUMMARY**

The attempt to reinterpret the common tests of significance used in scientific research as though they constituted some kind of acceptance procedure and led to “decisions” in Wald’s sense, originated in several misapprehensions and has led, apparently, to several more.

The three phrases examined here, with a view to elucidating they fallacies they embody, are:

- “Repeated sampling from the same population”,
- Errors of the “second kind”,
- “Inductive behavior”.

Mathematicians without personal contact with the Natural Sciences have often been misled by such phrases. The errors to which they lead are not only numerical.

To continue reading Fisher’s paper.

**“Note on an Article by Sir Ronald Fisher“**

**by Jerzy Neyman (1956)**

**Summary**

(1) FISHER’S allegation that, contrary to some passages in the introduction and on the cover of the book by Wald, this book does not really deal with experimental design is unfounded. In actual fact, the book is permeated with problems of experimentation. (2) Without consideration of hypotheses alternative to the one under test and without the study of probabilities of the two kinds, no purely probabilistic theory of tests is possible. (3) The conceptual fallacy of the notion of fiducial distribution rests upon the lack of recognition that valid probability statements about random variables usually cease to be valid if the random variables are replaced by their particular values. The notorious multitude of “paradoxes” of fiducial theory is a consequence of this oversight. (4) The idea of a “cost function for faulty judgments” appears to be due to Laplace, followed by Gauss.

“**Statistical Concepts in Their Relation to Reality“.**

**by E.S. Pearson (1955)**

Controversies in the field of mathematical statistics seem largely to have arisen because statisticians have been unable to agree upon how theory is to provide, in terms of probability statements, the numerical measures most helpful to those who have to draw conclusions from observational data. We are concerned here with the ways in which mathematical theory may be put, as it were, into gear with the common processes of rational thought, and there seems no reason to suppose that there is one best way in which this can be done. If, therefore, Sir Ronald Fisher recapitulates and enlarges on his views upon statistical methods and scientific induction we can all only be grateful, but when he takes this opportunity to criticize the work of others through misapprehension of their views as he has done in his recent contribution to this *Journal* (Fisher 1955 “Scientific Methods and Scientific Induction” ), it is impossible to leave him altogether unanswered.

In the first place it seems unfortunate that much of Fisher’s criticism of Neyman and Pearson’s approach to the testing of statistical hypotheses should be built upon a “penetrating observation” ascribed to Professor G.A. Barnard, the assumption involved in which happens to be historically incorrect. There was no question of a difference in point of view having “originated” when Neyman “reinterpreted” Fisher’s early work on tests of significance “in terms of that technological and commercial apparatus which is known as an acceptance procedure”. There was no sudden descent upon British soil of Russian ideas regarding the function of science in relation to technology and to five-year plans. It was really much simpler–or worse. *The original heresy, as we shall see, was a Pearson one!…*

To continue reading, “Statistical Concepts in Their Relation to Reality” click HERE

## R. A. Fisher: How an Outsider Revolutionized Statistics (Aris Spanos)

In recognition of R.A. Fisher’s birthday on February 17….

**‘R. A. Fisher: How an Outsider Revolutionized Statistics’**

by **Aris Spanos**

Few statisticians will dispute that R. A. Fisher **(February 17, 1890 – July 29, 1962)** is the father of modern statistics; see Savage (1976), Rao (1992). Inspired by William Gosset’s (1908) paper on the Student’s t finite sampling distribution, he recast statistics into the modern model-based induction in a series of papers in the early 1920s. He put forward a theory of *optimal estimation* based on the method of maximum likelihood that has changed only marginally over the last century. His significance testing, spearheaded by the p-value, provided the basis for the Neyman-Pearson theory of *optimal testing* in the early 1930s. According to Hald (1998)

“Fisher was a genius who almost single-handedly created the foundations for modern statistical science, without detailed study of his predecessors. When young he was ignorant not only of the Continental contributions but even of contemporary publications in English.” (p. 738)

What is not so well known is that Fisher was the *ultimate outsider* when he brought about this change of paradigms in statistical science. As an undergraduate, he studied mathematics at Cambridge, and then did graduate work in statistical mechanics and quantum theory. His meager knowledge of statistics came from his study of astronomy; see Box (1978). That, however did not stop him from publishing his first paper in statistics in 1912 (still an undergraduate) on “curve fitting”, questioning Karl Pearson’s method of moments and proposing a new method that was eventually to become the likelihood method in his 1921 paper. Continue reading

## Guest Blog: STEPHEN SENN: ‘Fisher’s alternative to the alternative’

**As part of the week of recognizing R.A.Fisher (February 17, 1890 – July 29, 1962), I reblog a guest post by Stephen Senn from 2012/2017. The comments from 2017 lead to a troubling issue that I will bring up in the comments today.**

*‘Fisher’s alternative to the alternative’*

*By: Stephen Senn*

[2012 marked] the 50th anniversary of RA Fisher’s death. It is a good excuse, I think, to draw attention to an aspect of his philosophy of significance testing. In his extremely interesting essay on Fisher, Jimmie Savage drew attention to a problem in Fisher’s approach to testing. In describing Fisher’s aversion to power functions Savage writes, ‘Fisher says that some tests are *more sensitive* than others, and I cannot help suspecting that that comes to very much the same thing as thinking about the power function.’ (Savage 1976) (P473).

The modern statistician, however, has an advantage here denied to Savage. Savage’s essay was published posthumously in 1976 and the lecture on which it was based was given in Detroit on 29 December 1971 (P441). At that time Fisher’s scientific correspondence did not form part of his available oeuvre but in 1990 Henry Bennett’s magnificent edition of Fisher’s statistical correspondence (Bennett 1990) was published and this throws light on many aspects of Fisher’s thought including on significance tests. Continue reading

## Happy Birthday R.A. Fisher: ‘Two New Properties of Mathematical Likelihood’

*Today is R.A. Fisher’s birthday. I’ll post some Fisherian items this week in honor of it. This paper comes just before the conflicts with Neyman and Pearson erupted. Fisher links his tests and sufficiency, to the Neyman and Pearson lemma in terms of power. It’s as if we may see them as ending up in a similar place while starting from different origins. I quote just the most relevant portions…the full article is linked below. Happy Birthday Fisher!*

“Two New Properties of Mathematical Likelihood“

by R.A. Fisher, F.R.S.

Proceedings of the Royal Society, Series A, 144: 285-307 (1934)

The property that where a sufficient statistic exists, the likelihood, apart from a factor independent of the parameter to be estimated, is a function only of the parameter and the sufficient statistic, explains the principle result obtained by Neyman and Pearson in discussing the efficacy of tests of significance. Neyman and Pearson introduce the notion that any chosen test of a hypothesis H_{0} is more powerful than any other equivalent test, with regard to an alternative hypothesis H_{1}, when it rejects H_{0} in a set of samples having an assigned aggregate frequency ε when H_{0} is true, and the greatest possible aggregate frequency when H_{1} is true. If any group of samples can be found within the region of rejection whose probability of occurrence on the hypothesis H_{1} is less than that of any other group of samples outside the region, but is not less on the hypothesis H_{0}, then the test can evidently be made more powerful by substituting the one group for the other. Continue reading

## Erich Lehmann’s 100 Birthday: Neyman Pearson vs Fisher on P-values

**Erich Lehmann was born 100 years ago today! (20 November 1917 – 12 September 2009).** Lehmann was Neyman’s first student at Berkeley (Ph.D 1942), and his framing of Neyman-Pearson (NP) methods has had an enormous influence on the way we typically view them.*

I got to know Erich in 1997, shortly after publication of EGEK (1996). One day, I received a bulging, six-page, handwritten letter from him in tiny, extremely neat scrawl (and many more after that). He began by telling me that he was sitting in a very large room at an ASA (American Statistical Association) meeting where they were shutting down the conference book display (or maybe they were setting it up), and on a very long, wood table sat just one book, all alone, shiny red.

He said ” I wonder if it might be of interest to me!” So he walked up to it…. It turned out to be my *Error and the Growth of Experimental Knowledge* (1996, Chicago), which he reviewed soon after[0]. (What are the chances?) Some related posts on Lehmann’s letter are here and here.

## S. Senn: Fishing for fakes with Fisher (Guest Post)

**Stephen Senn**

* Head of Competence Center *

*for Methodology and Statistics (CCMS)
Luxembourg Institute of Health
Twitter @stephensenn*

**Fishing for fakes with Fisher**

### Stephen Senn

The essential fact governing our analysis is that the errors due to soil heterogeneity will be divided by a good experiment into two portions. The first, which is to be made as large as possible, will be completely eliminated, by the arrangement of the experiment, from the experimental comparisons, and will be as carefully eliminated in the statistical laboratory from the estimate of error. As to the remainder, which cannot be treated in this way, no attempt will be made to eliminate it in the field, but, on the contrary, it will be carefully randomised so as to provide a valid estimate of the errors to which the experiment is in fact liable. R. A. Fisher,

The Design of Experiments,(Fisher 1990) section 28.

## Fraudian analysis?

John Carlisle must be a man endowed with exceptional energy and determination. A recent paper of his is entitled, ‘Data fabrication and other reasons for non-random sampling in 5087 randomised, controlled trials in anaesthetic and general medical journals,’ (Carlisle 2017) and has created quite a stir. The journals examined include the *Journal of the American Medical Association *and the *New England Journal of Medicine*. What Carlisle did was examine 29,789 variables using 72,261 means to see if they were ‘consistent with random sampling’ (by which, I suppose, he means ‘randomisation’). The papers chosen had to report either standard deviations or standard errors of the mean. P-values as measures of balance or lack of it were then calculated using each of three methods and the method that gave the value closest to 0.5 was chosen. For a given trial the P-values chosen were then back-converted to z-scores combined by summing them and then re-converted back to P-values using a method that assumes the summed Z-scores to be independent. As Carlisle writes, ‘All p values were one-sided and inverted, such that dissimilar means generated p values near 1’. Continue reading

## “Fusion-Confusion?” My Discussion of Nancy Reid: “BFF Four- Are we Converging?”

Here are the slides from my discussion of Nancy Reid today at BFF4: The Fourth Bayesian, Fiducial, and Frequentist Workshop: May 1-3, 2017 (hosted by Harvard University)

## Slides from the Boston Colloquium for Philosophy of Science: “Severe Testing: The Key to Error Correction”

Slides from my March 17 presentation on “Severe Testing: The Key to Error Correction” given at the Boston Colloquium for Philosophy of Science Alfred I.Taub forum on “Understanding Reproducibility and Error Correction in Science.”