Fisher

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

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R.A. Fisher: February 17, 1890 – July 29, 1962

Continuing with posts in recognition of R.A. Fisher’s birthday, I reblog (with a few new comments) 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).

Continue reading

Categories: fiducial probability, Fisher, Phil6334/ Econ 6614, Statistics | Leave a comment

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

17 Feb 1890-29 July 1962

In recognition of Fisher’s birthday (Feb 17), I reblog what I call the “Triad”–an exchange between  Fisher, Neyman and Pearson (N-P) a full 20 years after the Fisher-Neyman break-up–adding a few new introductory remarks here. While my favorite is still the reply by E.S. Pearson, which alone should have shattered Fisher’s allegations that N-P “reinterpret” tests of significance as “some kind of acceptance procedure”, they are all chock full of gems for different reasons. They are short and worth rereading. Neyman’s article pulls back the cover on what is really behind Fisher’s over-the-top polemics, what with Russian 5-year plans and commercialism in the U.S. Not only is Fisher jealous that N-P tests came to overshadow “his” tests, he is furious at Neyman for driving home the fact that Fisher’s fiducial approach had been shown to be inconsistent (by others). The flaw is glaring and is illustrated very simply by Neyman in his portion of the triad. Further details may be found in my book, SIST (2018) especially pp 388-392 linked to here. It speaks to a common fallacy seen every day in interpreting confidence intervals. As for Neyman’s “behaviorism”, Pearson’s last sentence is revealing. Continue reading

Categories: E.S. Pearson, Fisher, Neyman, phil/history of stat | Leave a comment

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

17 February 1890–29 July 1962

Today is R.A. Fisher’s birthday. I’ll reblog some Fisherian items this week with a few new remarks. This paper comes just before the conflicts with Neyman and Pearson (N-P) erupted.  Fisher links his tests and sufficiency, to the Neyman and Pearson lemma in terms of power. It’s as if we may see Fisher and N-P as ending up in a similar place while starting from different origins, as David Cox might say [1]. Unfortunately, the blow-up that occurred soon after is behind today’s misdirected war vs statistical significance tests.* I quote just the most relevant portions…the full article is linked below.** Happy Birthday Fisher! Continue reading

Categories: Fisher, phil/history of stat | Tags: , , , | Leave a comment

Bickel’s defense of significance testing on the basis of Bayesian model checking

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In my last post, I said I’d come back to a (2021) article by David Bickel, “Null Hypothesis Significance Testing Defended and Calibrated by Bayesian Model Checking” in The American Statistician. His abstract begins as follows:

 

Significance testing is often criticized because p-values can be low even though posterior probabilities of the null hypothesis are not low according to some Bayesian models. Those models, however, would assign low prior probabilities to the observation that the p-value is sufficiently low. That conflict between the models and the data may indicate that the models needs revision. Indeed, if the p-value is sufficiently small while the posterior probability according to a model is insufficiently small, then the model will fail a model check….(from Bickel 2021)

Continue reading

Categories: Bayesian/frequentist, D. Bickel, Fisher, P-values | 3 Comments

P-values disagree with posteriors? Problem is your priors, says R.A. Fisher

What goes around…

How often do you hear P-values criticized for “exaggerating” the evidence against a null hypothesis? If your experience is like mine, the answer is ‘all the time’, and in fact, the charge is often taken as one of the strongest cards in the anti-statistical significance playbook. The argument boils down to the fact that the P-value accorded to a point null H0 can be small while its Bayesian posterior probability high–provided a high enough prior is accorded to H0. But why suppose P-values should match Bayesian posteriors? And what justifies the high (or “spike”) prior to a point null? While I discuss this criticism at considerable length in Statistical Inference as Severe Testing: How to get beyond the statistics wars (CUP, 2018), I did not quote an intriguing response by R.A. Fisher to disagreements between P-values and posteriors’s (in Statistical Methods and Scientific Inference, Fisher 1956); namely, that such a prior probability assignment would itself be rejected by the observed small P-value–if the prior were itself regarded as a hypothesis to test. Or so he says. I did mention this response by Fisher in an encyclopedia article from way back in 2006 on “philosophy of statistics”: Continue reading

Categories: Bayesian/frequentist, Fisher, P-values | 7 Comments

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

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

Categories: E.S. Pearson, Fisher, Neyman, phil/history of stat

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

A SPANOS

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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

Categories: Fisher, phil/history of stat, Spanos

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

A SPANOS

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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

Categories: Fisher, phil/history of stat, Spanos

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

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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

Categories: Fisher, randomization, Stephen Senn | Tags:

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

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Fisher/ Neyman

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

Categories: fiducial probability, Fisher, Neyman, Statistics

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

imgres

R.A. Fisher: February 17, 1890 – July 29, 1962

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

Categories: fiducial probability, Fisher, Phil6334/ Econ 6614, Statistics

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

A SPANOS

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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

Categories: Fisher, phil/history of stat, Phil6334/ Econ 6614, Spanos, Statistics

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.

17 February 1890 — 29 July 1962

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:

  1. “Repeated sampling from the same population”,
  2. Errors of the “second kind”,
  3. “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)

Neyman

Neyman

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

Categories: E.S. Pearson, Fisher, Neyman, phil/history of stat

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

“You May Believe You Are a Bayesian But You Are Probably Wrong”

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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

Categories: Fisher, S. Senn, Statistics

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

17 February 1890–29 July 1962

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 H0 is more powerful than any other equivalent test, with regard to an alternative hypothesis H1, when it rejects H0 in a set of samples having an assigned aggregate frequency ε when H0 is true, and the greatest possible aggregate frequency when H1 is true. If any group of samples can be found within the region of rejection whose probability of occurrence on the hypothesis H1 is less than that of any other group of samples outside the region, but is not less on the hypothesis H0, then the test can evidently be made more powerful by substituting the one group for the other. Continue reading

Categories: Fisher, phil/history of stat, Phil6334/ Econ 6614, Statistics | Tags: , , ,

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

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Fisher/ Neyman

[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

Categories: fiducial probability, Fisher, Neyman, Statistics

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

imgres

R.A. Fisher: February 17, 1890 – July 29, 1962

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

Categories: fiducial probability, Fisher, Statistics

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.

17 February 1890 — 29 July 1962

“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:

  1. “Repeated sampling from the same population”,
  2. Errors of the “second kind”,
  3. “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)

Neyman

Neyman

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.

 

E.S. Pearson

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

Categories: E.S. Pearson, fiducial probability, Fisher, Neyman, phil/history of stat, Phil6334/ Econ 6614

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

A SPANOS

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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

Categories: Fisher, phil/history of stat, Spanos, Statistics

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

“You May Believe You Are a Bayesian But You Are Probably Wrong”

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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

Categories: Fisher, S. Senn, Statistics

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