Posts Tagged With: Statistical hypothesis testing

Egon Pearson’s Heresy

E.S. Pearson: 11 Aug 1895-12 June 1980.

Here’s one last entry in honor of Egon Pearson’s birthday: “Statistical Concepts in Their Relation to Reality” (Pearson 1955). I’ve posted it several times over the years (6!), but always find a new gem or two, despite its being so short. E. Pearson rejected some of the familiar tenets that have come to be associated with Neyman and Pearson (N-P) statistical tests, notably the idea that the essential justification for tests resides in a long-run control of rates of erroneous interpretations–what he termed the “behavioral” rationale of tests. In an unpublished letter E. Pearson wrote to Birnbaum (1974), he talks about N-P theory admitting of two interpretations: behavioral and evidential:

“I think you will pick up here and there in my own papers signs of evidentiality, and you can say now that we or I should have stated clearly the difference between the behavioral and evidential interpretations. Certainly we have suffered since in the way the people have concentrated (to an absurd extent often) on behavioral interpretations”.

(Nowadays, some people concentrate to an absurd extent on “science-wise error rates in dichotomous screening”.) Continue reading

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

Egon Pearson’s Heresy

E.S. Pearson: 11 Aug 1895-12 June 1980.

Today is Egon Pearson’s birthday: 11 August 1895-12 June, 1980.
E. Pearson rejected some of the familiar tenets that have come to be associated with Neyman and Pearson (N-P) statistical tests, notably the idea that the essential justification for tests resides in a long-run control of rates of erroneous interpretations–what he termed the “behavioral” rationale of tests. In an unpublished letter E. Pearson wrote to Birnbaum (1974), he talks about N-P theory admitting of two interpretations: behavioral and evidential:

“I think you will pick up here and there in my own papers signs of evidentiality, and you can say now that we or I should have stated clearly the difference between the behavioral and evidential interpretations. Certainly we have suffered since in the way the people have concentrated (to an absurd extent often) on behavioral interpretations”.

(Nowadays, some people concentrate to an absurd extent on “science-wise error rates in dichotomous screening”.)

When Erich Lehmann, in his review of my “Error and the Growth of Experimental Knowledge” (EGEK 1996), called Pearson “the hero of Mayo’s story,” it was because I found in E.S.P.’s work, if only in brief discussions, hints, and examples, the key elements for an “inferential” or “evidential” interpretation of N-P statistics. Granted, these “evidential” attitudes and practices have never been explicitly codified to guide the interpretation of N-P tests. If they had been, I would not be on about providing an inferential philosophy all these years.[i] Nevertheless, “Pearson and Pearson” statistics (both Egon, not Karl) would have looked very different from Neyman and Pearson statistics, I suspect. One of the few sources of E.S. Pearson’s statistical philosophy is his (1955) “Statistical Concepts in Their Relation to Reality”. It begins like this: Continue reading

Categories: phil/history of stat, Philosophy of Statistics, Statistics | Tags: , | 2 Comments

E.S. Pearson: “Ideas came into my head as I sat on a gate overlooking an experimental blackcurrant plot”

E.S.Pearson on Gate

E.S.Pearson on a Gate,             Mayo sketch

Today is Egon Pearson’s birthday (11 Aug., 1895-12 June, 1980); and here you see my scruffy sketch of him, at the start of my book, “Error and the Growth of Experimental Knowledge” (EGEK 1996). As Erich Lehmann put it in his EGEK review, Pearson is “the hero of Mayo’s story” because I found in his work, if only in brief discussions, hints, and examples, the key elements for an “inferential” or “evidential” interpretation of Neyman-Pearson theory of statistics.  “Pearson and Pearson” statistics (both Egon, not Karl) would have looked very different from Neyman and Pearson statistics, I suspect. One of the few sources of E.S. Pearson’s statistical philosophy is his (1955) “Statistical Concepts in Their Relation to Reality”. It begins like this:

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!…
Indeed, to dispel the picture of the Russian technological bogey, I might recall how certain early ideas came into my head as I sat on a gate overlooking an experimental blackcurrant plot…!

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

See also Aris Spanos: “Egon Pearson’s Neglected Contributions to Statistics“.

Happy Birthday E.S. Pearson!

Categories: phil/history of stat, Philosophy of Statistics, Statistics | Tags: , | 4 Comments

Matching Numbers Across Philosophies

The search for an agreement on numbers across different statistical philosophies is an understandable pastime in foundations of statistics. Perhaps identifying matching or unified numbers, apart from what they might mean, would offer a glimpse as to shared underlying goals? Jim Berger (2003) assures us there is no sacrilege in agreeing on methodology without philosophy, claiming “while the debate over interpretation can be strident, statistical practice is little affected as long as the reported numbers are the same” (Berger, 2003, p. 1).

Do readers agree?

Neyman and Pearson (or perhaps it was mostly Neyman) set out to determine when tests of statistical hypotheses may be considered “independent of probabilities a priori” ([p. 201). In such cases, frequentist and Bayesian may agree on a critical or rejection region.

The agreement between “default” Bayesians and frequentists in the case of one-sided Normal (IID) testing (known σ) is very familiar.   As noted in Ghosh, Delampady, and Samanta (2006, p. 35), if we wish to reject a null value when “the posterior odds against it are 19:1 or more, i.e., if posterior probability of H0 is < .05” then the rejection region matches that of the corresponding test of H0, (at the .05 level) if that were the null hypothesis. By contrast, they go on to note the also familiar fact that there would be disagreement between the frequentist and Bayesian if one were instead testing the two sided: H0: μ=μ0 vs. H1: μ≠μ0 with known σ. In fact, the same outcome that would be regarded as evidence against the null in the one-sided test (for the default Bayesian and frequentist) can result in statistically significant results being construed as no evidence against the null —for the Bayesian– or even evidence for it (due to a spiked prior).[i] Continue reading

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Guest Blogger. STEPHEN SENN: Fisher’s alternative to the alternative

By: Stephen Senn

This year marks 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 in1990 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

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E.S. PEARSON: Statistical Concepts in Their Relation to Reality

by E.S. PEARSON (1955)

SUMMARY: This paper contains a reply to some criticisms made by Sir Ronald Fisher in his recent article on “Scientific Methods and Scientific Induction”.

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), it is impossible to leave him altogether unanswered.

Continue reading

Categories: Statistics | Tags: , , , , , , | 2 Comments

R.A.FISHER: Statistical Methods and Scientific Inference

In honor of R.A. Fisher’s birthday this week (Feb 17), in a year that will mark 50 years since his death, we will post the “Triad” exchange between  Fisher, Pearson and Neyman, and other guest contributions*

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 R. A. FISHER’S  PAPER, CLICK HERE.

*If you wish to contribute something in connection to Fisher, send to error@vt.edu

Categories: Statistics | Tags: , , , , , , | 5 Comments

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