Neyman: Distinguishing tests of statistical hypotheses and tests of significance might have been a lapse of someone’s pen

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Neyman, drawn by ?

Tests of Statistical Hypotheses and Their Use in Studies of Natural Phenomena” by Jerzy Neyman

ABSTRACT. Contrary to ideas suggested by the title of the conference at which the present paper was presented, the author is not aware of a conceptual difference between a “test of a statistical hypothesis” and a “test of significance” and uses these terms interchangeably. A study of any serious substantive problem involves a sequence of incidents at which one is forced to pause and consider what to do next. In an effort to reduce the frequency of misdirected activities one uses statistical tests. The procedure is illustrated on two examples: (i) Le Cam’s (and associates’) study of immunotherapy of cancer and (ii) a socio-economic experiment relating to low-income homeownership problems.

I hadn’t posted this paper of Neyman’s before, so here’s something for your weekend reading:  “Tests of Statistical Hypotheses and Their Use in Studies of Natural Phenomena.”  I recommend, especially, the example on home ownership. Here are two snippets:

1. INTRODUCTION

The title of the present session involves an element that appears mysterious to me. This element is the apparent distinction between tests of statistical hypotheses, on the one hand, and tests of significance, on the other. If this is not a lapse of someone’s pen, then I hope to learn the conceptual distinction. Continue reading

Categories: Error Statistics, Neyman, Statistics | Tags: | 18 Comments

A. Spanos: Jerzy Neyman and his Enduring Legacy

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A Statistical Model as a Chance Mechanism
Aris Spanos 

Today is the birthday of Jerzy Neyman (April 16, 1894 – August 5, 1981). Neyman was a Polish/American statistician[i] who spent most of his professional career at the University of California, Berkeley. Neyman is best known in statistics for his pioneering contributions in framing the Neyman-Pearson (N-P) optimal theory of hypothesis testing and his theory of Confidence Intervals. (This article was first posted here.)

Neyman: 16 April

Neyman: 16 April 1894 – 5 Aug 1981

One of Neyman’s most remarkable, but least recognized, achievements was his adapting of Fisher’s (1922) notion of a statistical model to render it pertinent for  non-random samples. Fisher’s original parametric statistical model Mθ(x) was based on the idea of ‘a hypothetical infinite population’, chosen so as to ensure that the observed data x0:=(x1,x2,…,xn) can be viewed as a ‘truly representative sample’ from that ‘population’:

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Fisher and Neyman

“The postulate of randomness thus resolves itself into the question, Of what population is this a random sample? (ibid., p. 313), underscoring that: the adequacy of our choice may be tested a posteriori.’’ (p. 314)

In cases where data x0 come from sample surveys or it can be viewed as a typical realization of a random sample X:=(X1,X2,…,Xn), i.e. Independent and Identically Distributed (IID) random variables, the ‘population’ metaphor can be helpful in adding some intuitive appeal to the inductive dimension of statistical inference, because one can imagine using a subset of a population (the sample) to draw inferences pertaining to the whole population. Continue reading

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

Philosophy of Statistics Comes to the Big Apple! APS 2015 Annual Convention — NYC

Start Spreading the News…..

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 The Philosophy of Statistics: Bayesianism, Frequentism and the Nature of Inference,
2015 APS Annual Convention
Saturday, May 23  
2:00 PM- 3:50 PM in Wilder

(Marriott Marquis 1535 B’way)

 

 

gelman5

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Andrew Gelman

Professor of Statistics & Political Science
Columbia University

SENN FEB

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Stephen Senn

Head of Competence Center
for Methodology and Statistics (CCMS)

Luxembourg Institute of Health

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Slide1

D. Mayo headshot

D.G. Mayo, Philosopher


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Richard Morey, Session Chair & Discussant

Senior Lecturer
School of Psychology
Cardiff University
Categories: Announcement, Bayesian/frequentist, Statistics | 8 Comments

Heads I win, tails you lose? Meehl and many Popperians get this wrong (about severe tests)!

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bending of starlight.

[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, CR, [p. 36))

 

Popper lauds Einstein’s General Theory of Relativity (GTR) as sticking its neck out, bravely being ready to admit its falsity were the deflection effect not found. The truth is that even if no deflection effect had been found in the 1919 experiments it would have been blamed on the sheer difficulty in discerning so small an effect (the results that were found were quite imprecise.) This would have been entirely correct! Yet many Popperians, perhaps Popper himself, get this wrong.[i] Listen to Popperian Paul Meehl (with whom I generally agree).

The stipulation beforehand that one will be pleased about substantive theory T when the numerical results come out as forecast, but will not necessarily abandon it when they do not, seems on the face of it to be about as blatant a violation of the Popperian commandment as you could commit. For the investigator, in a way, is doing…what astrologers and Marxists and psychoanalysts allegedly do, playing heads I win, tails you lose.” (Meehl 1978, 821)

No, there is a confusion of logic. A successful result may rightly be taken as evidence for a real effect H, even though failing to find the effect need not be taken to refute the effect, or even as evidence as against H. This makes perfect sense if one keeps in mind that a test might have had little chance to detect the effect, even if it existed. The point really reflects the asymmetry of falsification and corroboration. Popperian Alan Chalmers wrote an appendix to a chapter of his book, What is this Thing Called Science? (1999)(which at first had criticized severity for this) once I made my case. [i] Continue reading

Categories: fallacy of non-significance, philosophy of science, Popper, Severity, Statistics | Tags: | 2 Comments

Joan Clarke, Turing, I.J. Good, and “that after-dinner comedy hour…”

I finally saw The Imitation Game about Alan Turing and code-breaking at Bletchley Park during WWII. This short clip of Joan Clarke, who was engaged to Turing, includes my late colleague I.J. Good at the end (he’s not second as the clip lists him). Good used to talk a great deal about Bletchley Park and his code-breaking feats while asleep there (see note[a]), but I never imagined Turing’s code-breaking machine (which, by the way, was called the Bombe and not Christopher as in the movie) was so clunky. The movie itself has two tiny scenes including Good. Below I reblog: “Who is Allowed to Cheat?”—one of the topics he and I debated over the years. Links to the full “Savage Forum” (1962) may be found at the end (creaky, but better than nothing.)

[a]”Some sensitive or important Enigma messages were enciphered twice, once in a special variation cipher and again in the normal cipher. …Good dreamed one night that the process had been reversed: normal cipher first, special cipher second. When he woke up he tried his theory on an unbroken message – and promptly broke it.” This, and further examples may be found in this obituary

[b] Pictures comparing the movie cast and the real people may be found here. Continue reading

Categories: Bayesian/frequentist, optional stopping, Statistics, strong likelihood principle | 6 Comments

Are scientists really ready for ‘retraction offsets’ to advance ‘aggregate reproducibility’? (let alone ‘precautionary withdrawals’)

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Given recent evidence of the irreproducibility of a surprising number of published scientific findings, the White House’s Office of Science and Technology Policy (OSTP) sought ideas for “leveraging its role as a significant funder of scientific research to most effectively address the problem”, and announced funding for projects to “reset the self-corrective process of scientific inquiry”. (first noted in this post.)ostp

I was sent some information this morning with a rather long description of the project that received the top government award thus far (and it’s in the millions). I haven’t had time to read the proposal*, which I’ll link to shortly, but for a clear and quick description, you can read the excerpt of an interview of the OSTP representative by the editor of the Newsletter for Innovation in Science Journals (Working Group), Jim Stein, who took the lead in writing the author check list for Nature.

Stein’s queries are in burgundy, OSTP’s are in blue. Occasional comments from me are in black, which I’ll update once I study the fine print of the proposal itself. Continue reading

Categories: junk science, reproducibility, science communication, Statistics | 9 Comments

Your (very own) personalized genomic prediction varies depending on who else was around?

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personalized medicine roulette

As if I wasn’t skeptical enough about personalized predictions based on genomic signatures, Jeff Leek recently had a surprising post about a “A surprisingly tricky issue when using genomic signatures for personalized medicine“.  Leek (on his blog Simply Statistics) writes:

My student Prasad Patil has a really nice paper that just came out in Bioinformatics (preprint in case paywalled). The paper is about a surprisingly tricky normalization issue with genomic signatures. Genomic signatures are basically statistical/machine learning functions applied to the measurements for a set of genes to predict how long patients will survive, or how they will respond to therapy. The issue is that usually when building and applying these signatures, people normalize across samples in the training and testing set.

….it turns out that this one simple normalization problem can dramatically change the results of the predictions. In particular, we show that the predictions for the same patient, with the exact same data, can change dramatically if you just change the subpopulations of patients within the testing set.

Here’s an extract from the paper,”Test set bias affects reproducibility of gene signatures“:

Test set bias is a failure of reproducibility of a genomic signature. In other words, the same patient, with the same data and classification algorithm, may be assigned to different clinical groups. A similar failing resulted in the cancellation of clinical trials that used an irreproducible genomic signature to make chemotherapy decisions (Letter (2011)).

This is a reference to the Anil Potti case:

Letter, T. C. (2011). Duke Accepts Potti Resignation; Retraction Process Initiated with Nature Medicine.

But far from the Potti case being some particularly problematic example (see here and here), at least with respect to test set bias, this article makes it appear that test set bias is a threat to be expected much more generally. Going back to the abstract of the paper: Continue reading

Categories: Anil Potti, personalized medicine, Statistics | 10 Comments

3 YEARS AGO (MARCH 2012): MEMORY LANE

3 years ago...

3 years ago…

MONTHLY MEMORY LANE: 3 years ago: March 2012. I mark in red three posts that seem most apt for general background on key issues in this blog. (Posts that are part of a “unit” or a group of “U-Phils” count as one.) This new feature, appearing the last week of each month, began at the blog’s 3-year anniversary in Sept, 2014.

Since the 3/14 and 3/18 posts on objectivity (part of a 5-part unit on objectivity) were recently reblogged, they are marked in burgundy, not bright red. The 3/18 comment on Barnard and Copas includes two items: A paper by Bernard and Copas, which happens to cite Stephen Senn twice, and a note by Aris Spanos pertaining to that paper.

March 2012

Categories: 3-year memory lane | Leave a comment

Objectivity in Statistics: “Arguments From Discretion and 3 Reactions”

dirty hands

We constantly hear that procedures of inference are inescapably subjective because of the latitude of human judgment as it bears on the collection, modeling, and interpretation of data. But this is seriously equivocal: Being the product of a human subject is hardly the same as being subjective, at least not in the sense we are speaking of—that is, as a threat to objective knowledge. Are all these arguments about the allegedly inevitable subjectivity of statistical methodology rooted in equivocations? I argue that they are! [This post combines this one and this one, as part of our monthly “3 years ago” memory lane.]

“Argument from Discretion” (dirty hands)

Insofar as humans conduct science and draw inferences, it is obvious that human judgments and human measurements are involved. True enough, but too trivial an observation to help us distinguish among the different ways judgments should enter, and how, nevertheless, to avoid introducing bias and unwarranted inferences. The issue is not that a human is doing the measuring, but whether we can reliably use the thing being measured to find out about the world.

Remember the dirty-hands argument? In the early days of this blog (e.g., October 13, 16), I deliberately took up this argument as it arises in evidence-based policy because it offered a certain clarity that I knew we would need to come back to in considering general “arguments from discretion”. To abbreviate:

  1. Numerous  human judgments go into specifying experiments, tests, and models.
  2. Because there is latitude and discretion in these specifications, they are “subjective.”
  3. Whether data are taken as evidence for a statistical hypothesis or model depends on these subjective methodological choices.
  4. Therefore, statistical inference and modeling is invariably subjective, if only in part.

We can spot the fallacy in the argument much as we did in the dirty hands argument about evidence-based policy. It is true, for example, that by employing a very insensitive test for detecting a positive discrepancy d’ from a 0 null, that the test has low probability of finding statistical significance even if a discrepancy as large as d’ exists. But that doesn’t prevent us from determining, objectively, that an insignificant difference from that test fails to warrant inferring evidence of a discrepancy less than d’.

Test specifications may well be a matter of  personal interest and bias, but, given the choices made, whether or not an inference is warranted is not a matter of personal interest and bias. Setting up a test with low power against d’ might be a product of your desire not to find an effect for economic reasons, of insufficient funds to collect a larger sample, or of the inadvertent choice of a bureaucrat. Or ethical concerns may have entered. But none of this precludes our critical evaluation of what the resulting data do and do not indicate (about the question of interest). The critical task need not itself be a matter of economics, ethics, or what have you. Critical scrutiny of evidence reflects an interest all right—an interest in not being misled, an interest in finding out what the case is, and others of an epistemic nature. Continue reading

Categories: Objectivity, Statistics | Tags: , | 6 Comments

Stephen Senn: The pathetic P-value (Guest Post)

S. Senn

S. Senn

Stephen Senn
Head of Competence Center for Methodology and Statistics (CCMS)
Luxembourg Institute of Health

The pathetic P-value

This is the way the story is now often told. RA Fisher is the villain. Scientists were virtuously treading the Bayesian path, when along came Fisher and gave them P-values, which they gladly accepted, because they could get ‘significance’ so much more easily. Nearly a century of corrupt science followed but now there are signs that there is a willingness to return to the path of virtue and having abandoned this horrible Fisherian complication:

We shall not cease from exploration
And the end of all our exploring
Will be to arrive where we started …

A condition of complete simplicity..

And all shall be well and
All manner of thing shall be well

TS Eliot, Little Gidding

Consider, for example, distinguished scientist David Colquhoun citing the excellent scientific journalist Robert Matthews as follows

“There is an element of truth in the conclusion of a perspicacious journalist:

‘The plain fact is that 70 years ago Ronald Fisher gave scientists a mathematical machine for turning baloney into breakthroughs, and flukes into funding. It is time to pull the plug. ‘

Robert Matthews Sunday Telegraph, 13 September 1998.” [1]

However, this is not a plain fact but just plain wrong. Even if P-values were the guilty ‘mathematical machine’ they are portrayed to be, it is not RA Fisher’s fault. Putting the historical record right helps one to understand the issues better. As I shall argue, at the heart of this is not a disagreement between Bayesian and frequentist approaches but between two Bayesian approaches: it is a conflict to do with the choice of prior distributions[2].

Fisher did not persuade scientists to calculate P-values rather than Bayesian posterior probabilities; he persuaded them that the probabilities that they were already calculating and interpreting as posterior probabilities relied for this interpretation on a doubtful assumption. He proposed to replace this interpretation with one that did not rely on the assumption. Continue reading

Categories: P-values, S. Senn, statistical tests, Statistics | 147 Comments

All She Wrote (so far): Error Statistics Philosophy: 3.5 years on

 

metablog old fashion typewriter

D.G. Mayo with typewriter

Error Statistics Philosophy: Blog Contents (3.5 years)
By: D. G. Mayo [i]

September 2011

October 2011

Continue reading

Categories: blog contents, Metablog, Statistics | 1 Comment

A puzzle about the latest test ban (or ‘don’t ask, don’t tell’)

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A large number of people have sent me articles on the “test ban” of statistical hypotheses tests and confidence intervals at a journal called Basic and Applied Social Psychology (BASP)[i]. Enough. One person suggested that since it came so close to my recent satirical Task force post, that I either had advance knowledge or some kind of ESP. Oh please, no ESP required.None of this is the slightest bit surprising, and I’ve seen it before; I simply didn’t find it worth blogging about. Statistical tests are being banned, say the editors, because they purport to give probabilities of null hypotheses (really?) and do not, hence they are “invalid”.[ii] (Confidence intervals are thrown in the waste bin as well—also claimed “invalid”).“The state of the art remains uncertain” regarding inferential statistical procedures, say the editors.  I don’t know, maybe some good will come of all this.

Yet there’s a part of their proposal that brings up some interesting logical puzzles, and logical puzzles are my thing. In fact, I think there is a mistake the editors should remedy, lest authors be led into disingenuous stances, and strange tangles ensue. I refer to their rule that authors be allowed to submit papers whose conclusions are based on allegedly invalid methods so long as, once accepted, they remove any vestiges of them!

Question 1. Will manuscripts with p-values be desk rejected automatically?

Answer to Question 1. No. If manuscripts pass the preliminary inspection, they will be sent out for review. But prior to publication, authors will have to remove all vestiges of the NHSTP (p-values, t-values, F-values, statements about “significant” differences or lack thereof, and so on).”

Now if these measures are alleged to be irrelevant and invalid instruments for statistical inference, then why should they be included in the peer review process at all? Will reviewers be told to ignore them? That would only seem fair: papers should not be judged by criteria alleged to be invalid, but how will reviewers blind themselves to them? It would seem the measures should be excluded from the get-go. If they are included in the review, why shouldn’t the readers see what the reviewers saw when they recommended acceptance?

But here’s where the puzzle really sets in. If the authors must free their final papers from such encumbrances as sampling distributions and error probabilities, what will be the basis presented for their conclusions in the published paper? Presumably, from the notice, they are allowed only mere descriptive statistics or non-objective Bayesian reports (added: actually can’t tell which kind of Bayesianism they allow, given the Fisher reference which doesn’t fit*). Won’t this be tantamount to requiring authors support their research in a way that is either (actually) invalid, or has little to do with the error statistical properties that were actually reported and on which the acceptance was based?[ii] Continue reading

Categories: P-values, reforming the reformers, Statistics | 72 Comments

“Probabilism as an Obstacle to Statistical Fraud-Busting”

Boston Colloquium 2013-2014

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“Is the Philosophy of Probabilism an Obstacle to Statistical Fraud Busting?” was my presentation at the 2014 Boston Colloquium for the Philosophy of Science):“Revisiting the Foundations of Statistics in the Era of Big Data: Scaling Up to Meet the Challenge.”  

 As often happens, I never put these slides into a stand alone paper. But I have incorporated them into my book (in progress*), “How to Tell What’s True About Statistical Inference”. Background and slides were posted last year.

Slides (draft from Feb 21, 2014) 

Download the 54th Annual Program

Cosponsored by the Department of Mathematics & Statistics at Boston University.

Friday, February 21, 2014
10 a.m. – 5:30 p.m.
Photonics Center, 9th Floor Colloquium Room (Rm 906)
8 St. Mary’s Street

*Seeing a light at the end of tunnel, finally.
Categories: P-values, significance tests, Statistical fraudbusting, Statistics | 7 Comments

Big Data Is The New Phrenology?

Mayo:

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It happens I’ve been reading a lot lately about the assumption in social psychology and psychology in general that what they’re studying is measurable, quantifiable. Addressing the problem has been shelved to the back burner for decades thanks to some redefinitions of what it is to “measure” in psych (anything for which there’s a rule to pop out a number says Stevens–an operationalist in the naive positivist spirit). This at any rate is what I’m reading, thanks to papers sent by a colleague of Meehl’s (N. Waller).  (Here’s one by Mitchell.) I think it’s time to reopen the question.The measures I see of “severity of moral judgment”, “degree of self-esteem” and much else in psychology appear to fall into this behavior in a very non-self critical manner. No statistical window-dressing (nor banning of statistical inference) can help them become more scientific. So when I saw this on Math Babe’s twitter I decided to try the “reblog” function and see what happened. Here it is (with her F word included). The article to which she alludes is “Recruiting Better Talent Through Brain Games” )

Originally posted on mathbabe:

Have you ever heard of phrenology? It was, once upon a time, the “science” of measuring someone’s skull to understand their intellectual capabilities.

This sounds totally idiotic but was a huge fucking deal in the mid-1800’s, and really didn’t stop getting some credit until much later. I know that because I happen to own the 1911 edition of the Encyclopedia Britannica, which was written by the top scholars of the time but is now horribly and fascinatingly outdated.

For example, the entry for “Negro” is famously racist. Wikipedia has an excerpt: “Mentally the negro is inferior to the white… the arrest or even deterioration of mental development [after adolescence] is no doubt very largely due to the fact that after puberty sexual matters take the first place in the negro’s life and thoughts.”

But really that one line doesn’t tell the whole story. Here’s the whole thing…

View original 351 more words

Categories: msc kvetch, scientism, Statistics | 3 Comments

3 YEARS AGO: (FEBRUARY 2012) MEMORY LANE

3 years ago...

3 years ago…

MONTHLY MEMORY LANE: 3 years ago: February 2012. I am to mark in red three posts (or units) that seem most apt for general background on key issues in this blog. Given our Fisher reblogs, we’ve already seen many this month. So, I’m marking in red (1) The Triad, and (2) the Unit on Spanos’ misspecification tests. Plase see those posts for their discussion. The two posts from 2/8 are apt if you are interested in a famous case involving statistics at the Supreme Court. Beyond that it’s just my funny theatre of the absurd piece with Barnard. (Gelman’s is just a link to his blog.)

 

February 2012

TRIAD:

  • (2/11) R.A. Fisher: Statistical Methods and Scientific Inference
  • (2/11)  JERZY NEYMAN: Note on an Article by Sir Ronald Fisher
  • (2/12) E.S. Pearson: Statistical Concepts in Their Relation to Reality

REBLOGGED LAST WEEK

 

M-S TESTING UNIT

 

This new, once-a-month, feature began at the blog’s 3-year anniversary in Sept, 2014.

Previous 3 YEAR MEMORY LANES:

Jan. 2012

Dec. 2011

Nov. 2011

Oct. 2011

Sept. 2011 (Within “All She Wrote (so far))

Categories: 3-year memory lane, Statistics | 1 Comment

Sir Harold Jeffreys’ (tail area) one-liner: Saturday night comedy (b)

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This headliner appeared before, but to a sparse audience, so Management’s giving him another chance… His joke relates to both Senn’s post (about alternatives), and to my recent post about using (1 – β)/α as a likelihood ratio--but for very different reasons. (I’ve explained at the bottom of this “(b) draft”.)

 ….If you look closely, you’ll see that it’s actually not Jay Leno who is standing up there at the mike, (especially as he’s no longer doing the Tonight Show) ….

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It’s Sir Harold Jeffreys himself! And his (very famous) joke, I admit, is funny. So, since it’s Saturday night, let’s listen in on Sir Harold’s howler joke* in criticizing the use of p-values.

“Did you hear the one about significance testers rejecting H0 because of outcomes H0 didn’t predict?

‘What’s unusual about that?’ you ask?

What’s unusual is that they do it when these unpredicted outcomes haven’t even occurred!”

Much laughter.

[The actual quote from Jeffreys: Using p-values implies that “An hypothesis that may be true is rejected because it has failed to predict observable results that have not occurred. This seems a remarkable procedure.” (Jeffreys 1939, 316)]

I say it’s funny, so to see why I’ll strive to give it a generous interpretation. Continue reading

Categories: Comedy, Discussion continued, Fisher, Jeffreys, P-values, Statistics, Stephen Senn | 5 Comments

Stephen Senn: Fisher’s Alternative to the Alternative

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As part of the week of recognizing R.A.Fisher (February 17, 1890 – July 29, 1962), I reblog Senn from 3 years ago.  

‘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.

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The key letter here is Fisher’s reply of 6 October 1938 to Chester Bliss’s letter of 13 September. Bliss himself had reported an issue that had been raised with him by Snedecor on 6 September. Snedecor had pointed out that an analysis using inverse sine transformations of some data that Bliss had worked on gave a different result to an analysis of the original values. Bliss had defended his (transformed) analysis on the grounds that a) if a transformation always gave the same result as an analysis of the original data there would be no point and b) an analysis on inverse sines was a sort of weighted analysis of percentages with the transformation more appropriately reflecting the weight of information in each sample. Bliss wanted to know what Fisher thought of his reply.

Fisher replies with a ‘shorter catechism’ on transformations which ends as follows: Continue reading

Categories: Fisher, Statistics, Stephen Senn | Tags: , , , | 59 Comments

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

A SPANOS

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In recognition of R.A. Fisher’s birthday….

‘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 | 6 Comments

R.A. Fisher: ‘Two New Properties of Mathematical Likelihood': Just before breaking up (with N-P)

17 February 1890–29 July 1962

In recognition of R.A. Fisher’s birthday tomorrow, I will post several entries on him. I find this (1934) paper to be intriguing –immediately before the conflicts with Neyman and Pearson erupted. It represents essentially the last time he could take their work at face value, without the professional animosities that almost entirely caused, rather than being caused by, the apparent philosophical disagreements and name-calling everyone focuses on. 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 very similar place (no pun intended) while starting from different origins. I quote just the most relevant portions…the full article is linked below. I’d blogged it earlier here.  You may find some gems in it.

‘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, Statistics | Tags: , , , | 3 Comments

Continuing the discussion on truncation, Bayesian convergence and testing of priors

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My post “What’s wrong with taking (1 – β)/α, as a likelihood ratio comparing H0 and H1?” gave rise to a set of comments that were mostly off topic but interesting in their own right. Being too long to follow, I put what appears to be the last group of comments here, starting with Matloff’s query. Please feel free to continue the discussion here; we may want to come back to the topic. Feb 17: Please note one additional voice at the end. (Check back to that post if you want to see the history)

matloff

I see the conversation is continuing. I have not had time to follow it, but I do have a related question, on which I’d be curious as to the response of the Bayesians in our midst here.

Say the analyst is sure that μ > c, and chooses a prior distribution with support on (c,∞). That guarantees that the resulting estimate is > c. But suppose the analyst is wrong, and μ is actually less than c. (I believe that some here conceded this could happen in some cases in whcih the analyst is “sure” μ > c.) Doesn’t this violate one of the most cherished (by Bayesians) features of the Bayesian method — that the effect of the prior washes out as the sample size n goes to infinity?

Alan

(to Matloff),

The short answer is that assuming information such as “mu is greater than c” which isn’t true screws up the analysis. It’s like a mathematician starting a proof of by saying “assume 3 is an even number”. If it were possible to consistently get good results from false assumptions, there would be no need to ever get our assumptions right. Continue reading

Categories: Discussion continued, Statistics | 60 Comments

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