Spanos

Aris Spanos Guest Post: “On Frequentist Testing: revisiting widely held confusions and misinterpretations”

Posted on August 8, 2024 by Mayo

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Aris Spanos
Wilson Schmidt Professor of Economics
Department of Economics
Virginia Tech

The following guest post (link to PDF of this post) was written as a comment to Mayo’s recent post: “Abandon Statistical Significance and Bayesian Epistemology: some troubles in philosophy v3“.

On Frequentist Testing: revisiting widely held confusions and misinterpretations

After reading chapter 13.2 of the 2022 book Fundamentals of Bayesian Epistemology 2: Arguments, Challenges, Alternatives, by Michael G. Titelbaum, I decided to write a few comments relating to his discussion in an attempt to delineate certain key concepts in frequentist testing with a view to shed light on several long-standing confusions and misinterpretations of these testing procedures. The key concepts include ‘what is a frequentist test’, ‘what is a test statistic and how it is chosen’, and ‘how the hypotheses of interest are framed’. Continue reading →

Categories: abandon statistical significance, Spanos | 13 Comments

A. Spanos: Jerzy Neyman and his Enduring Legacy (guest post)

Posted on April 17, 2021 by Mayo

I am reblogging a guest post that Aris Spanos wrote for this blog on Neyman’s birthday some years ago.   

A. Spanos

A Statistical Model as a Chance Mechanism
Aris Spanos 

Jerzy Neyman (April 16, 1894 – August 5, 1981), 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.) Continue reading →

Categories: Neyman, Spanos | Leave a comment

Aris Spanos: Modeling vs. Inference in Frequentist Statistics (guest post)

Posted on February 25, 2021 by Mayo

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Aris Spanos
Wilson Schmidt Professor of Economics
Department of Economics
Virginia Tech

The following guest post (link to updated PDF) was written in response to C. Hennig’s presentation at our Phil Stat Wars Forum on 18 February, 2021: “Testing With Models That Are Not True”. Continue reading →

Categories: misspecification testing, Spanos, stat wars and their casualties | 11 Comments

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

Posted on February 18, 2021 by Mayo
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 | 2 Comments

A. Spanos:  Isaac Newton and his two years in quarantine:  how science could germinate in bewildering ways (Guest post)

Posted on April 3, 2020 by Mayo

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Aris Spanos
Wilson Schmidt Professor of Economics
Department of Economics
Virginia Tech

Beyond the plenitude of misery and suffering that pandemics bring down on humanity, occasionally they contribute to the betterment of humankind by (inadvertently) boosting creative activity that leads to knowledge, and not just in epidemiology. A case in point is that of Isaac Newton and the pandemic of 1665-6.  Continue reading →

Categories: quarantine, Spanos | 14 Comments

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

Posted on February 21, 2020 by Mayo
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 | 2 Comments

Aris Spanos Reviews Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars

Posted on January 11, 2020 by Mayo

A. Spanos

Aris Spanos was asked to review my Statistical Inference as Severe Testing: how to Get Beyond the Statistics Wars (CUP, 2018), but he was to combine it with a review of the re-issue of Ian Hacking’s classic  Logic of Statistical Inference. The journal is OEconomia: History, Methodology, Philosophy. Below are excerpts from his discussion of my book (pp. 843-860). I will jump past the Hacking review, and occasionally excerpt for length.To read his full article go to external journal pdf or stable internal blog pdf. Continue reading →

Categories: Spanos, Statistical Inference as Severe Testing | Leave a comment

A. Spanos: Jerzy Neyman and his Enduring Legacy

Posted on April 16, 2019 by Mayo

Today is Jerzy Neyman’s birthday. I’ll post various Neyman items this week in recognition of it, starting with a guest post by Aris Spanos. Happy Birthday Neyman!

A. Spanos

A Statistical Model as a Chance Mechanism
Aris Spanos 

Jerzy Neyman (April 16, 1894 – August 5, 1981), 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’: Continue reading →

Categories: Neyman, Spanos | Leave a comment

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

Posted on February 20, 2019 by Mayo
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 | 2 Comments

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

Posted on February 19, 2018 by Mayo
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 | 3 Comments

A. Spanos: Egon Pearson’s Neglected Contributions to Statistics

Posted on August 17, 2017 by Mayo

11 August 1895 – 12 June 1980

Continuing with my Egon Pearson posts in honor of his birthday, I reblog a post by Aris Spanos:  “Egon Pearson’s Neglected Contributions to Statistics“. 

    Egon Pearson (11 August 1895 – 12 June 1980), is widely known today for his contribution in recasting of Fisher’s significance testing into the Neyman-Pearson (1933) theory of hypothesis testing. Occasionally, he is also credited with contributions in promoting statistical methods in industry and in the history of modern statistics; see Bartlett (1981). What is rarely mentioned is Egon’s early pioneering work on:

(i) specification: the need to state explicitly the inductive premises of one’s inferences,

(ii) robustness: evaluating the ‘sensitivity’ of inferential procedures to departures from the Normality assumption, as well as

(iii) Mis-Specification (M-S) testing: probing for potential departures from the Normality  assumption.

Arguably, modern frequentist inference began with the development of various finite sample inference procedures, initially by William Gosset (1908) [of the Student’s t fame] and then Fisher (1915, 1921, 1922a-b). These inference procedures revolved around a particular statistical model, known today as the simple Normal model: Continue reading →

Categories: E.S. Pearson, phil/history of stat, Spanos, Testing Assumptions | 2 Comments

A. Spanos: Jerzy Neyman and his Enduring Legacy

Posted on April 16, 2017 by Mayo

Today is Jerzy Neyman’s birthday. I’ll post various Neyman items this week in honor of it, starting with a guest post by Aris Spanos. Happy Birthday Neyman!

A. Spanos

A Statistical Model as a Chance Mechanism
Aris Spanos 

Jerzy Neyman (April 16, 1894 – August 5, 1981), 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’:

“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) Continue reading →

Categories: Neyman, Spanos | Leave a comment

Guest Blog: ARIS SPANOS: The Enduring Legacy of R. A. Fisher

Posted on February 19, 2017 by Mayo

By Aris Spanos

One of R. A. Fisher’s (17 February 1890 — 29 July 1962) most re­markable, but least recognized, achievement was to initiate the recast­ing of statistical induction. Fisher (1922) pioneered modern frequentist statistics as a model-based approach to statistical induction anchored on the notion of a statistical model, formalized by:

Mθ(x)={f(x;θ); θ∈Θ}; x∈Rn ;Θ⊂Rm; m < n; (1)

where the distribution of the sample f(x;θ) ‘encapsulates’ the proba­bilistic information in the statistical model.

Before Fisher, the notion of a statistical model was vague and often implicit, and its role was primarily confined to the description of the distributional features of the data in hand using the histogram and the first few sample moments; implicitly imposing random (IID) samples. The problem was that statisticians at the time would use descriptive summaries of the data to claim generality beyond the data in hand x0:=(x1,x2,…,xn) As late as the 1920s, the problem of statistical induction was understood by Karl Pearson in terms of invoking (i) the ‘stability’ of empirical results for subsequent samples and (ii) a prior distribution for θ.

Fisher was able to recast statistical inference by turning Karl Pear­son’s approach, proceeding from data x0 in search of a frequency curve f(x;ϑ) to describe its histogram, on its head. He proposed to begin with a prespecified Mθ(x) (a ‘hypothetical infinite population’), and view x0 as a ‘typical’ realization thereof; see Spanos (1999). Continue reading →

Categories: Fisher, Spanos, Statistics | Tags: , , , , , , | Leave a comment

“Error statistical modeling and inference: Where methodology meets ontology” A. Spanos and D. Mayo

Posted on May 16, 2015 by Mayo
copy-cropped-ampersand-logo-blog1

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A new joint paper….

“Error statistical modeling and inference: Where methodology meets ontology”

Aris Spanos · Deborah G. Mayo

Abstract: In empirical modeling, an important desideratum for deeming theoretical entities and processes real is that they can be reproducible in a statistical sense. Current day crises regarding replicability in science intertwine with the question of how statistical methods link data to statistical and substantive theories and models. Different answers to this question have important methodological consequences for inference, which are intertwined with a contrast between the ontological commitments of the two types of models. The key to untangling them is the realization that behind every substantive model there is a statistical model that pertains exclusively to the probabilistic assumptions imposed on the data. It is not that the methodology determines whether to be a realist about entities and processes in a substantive field. It is rather that the substantive and statistical models refer to different entities and processes, and therefore call for different criteria of adequacy.

Keywords: Error statistics · Statistical vs. substantive models · Statistical ontology · Misspecification testing · Replicability of inference · Statistical adequacy

To read the full paper: “Error statistical modeling and inference: Where methodology meets ontology.”

The related conference.

Mayo & Spanos spotlight

Reference: Spanos, A. & Mayo, D. G. (2015). “Error statistical modeling and inference: Where methodology meets ontology.” Synthese (online May 13, 2015), pp. 1-23.

Categories: Error Statistics, misspecification testing, O & M conference, reproducibility, Severity, Spanos | 2 Comments

Spurious Correlations: Death by getting tangled in bedsheets and the consumption of cheese! (Aris Spanos)

Posted on May 4, 2015 by Mayo
Spanos

Spanos

These days, there are so many dubious assertions about alleged correlations between two variables that an entire website: Spurious Correlation (Tyler Vigen) is devoted to exposing (and creating*) them! A classic problem is that the means of variables X and Y may both be trending in the order data are observed, invalidating the assumption that their means are constant. In my initial study with Aris Spanos on misspecification testing, the X and Y means were trending in much the same way I imagine a lot of the examples on this site are––like the one on the number of people who die by becoming tangled in their bedsheets and the per capita consumption of cheese in the U.S.

The annual data for 2000-2009 are: xt: per capita consumption of cheese (U.S.) : x = (29.8, 30.1, 30.5, 30.6, 31.3, 31.7, 32.6, 33.1, 32.7, 32.8); yt: Number of people who died by becoming tangled in their bedsheets: y = (327, 456, 509, 497, 596, 573, 661, 741, 809, 717)

I asked Aris Spanos to have a look, and it took him no time to identify the main problem. He was good enough to write up a short note which I’ve pasted as slides.

spurious-correlation-updated-4-1024

Aris Spanos

Wilson E. Schmidt Professor of Economics
Department of Economics, Virginia Tech

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*The site says that the server attempts to generate a new correlation every 60 seconds.

Categories: misspecification testing, Spanos, Statistics, Testing Assumptions | 14 Comments

A. Spanos: Jerzy Neyman and his Enduring Legacy

Posted on April 16, 2015 by Mayo

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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’:

photoSmall

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

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

Posted on February 17, 2015 by Mayo
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

Erich Lehmann: Statistician and Poet

Posted on November 20, 2014 by Mayo
Erich Lehmann 20 November 1917 – 12 September 2009

Erich Lehmann                       20 November 1917 –              12 September 2009

Memory Lane 1 Year (with update): Today is Erich Lehmann’s birthday. The last time I saw him was at the Second Lehmann conference in 2004, at which I organized a session on philosophical foundations of statistics (including David Freedman and D.R. Cox).

I got to know Lehmann, Neyman’s first student, in 1997.  One day, I received a bulging, six-page, handwritten letter from him in tiny, extremely neat scrawl (and many more after that).  He told me he was sitting in a very large room at an ASA meeting where they were shutting down the conference book display (or maybe they were setting it up), and on a very long, dark table sat just one book, all alone, shiny red.  He said he wondered if it might be of interest to him!  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. Some related posts on Lehmann’s letter are here and here.

That same year I remember having a last-minute phone call with Erich to ask how best to respond to a “funny Bayesian example” raised by Colin Howson. It is essentially the case of Mary’s positive result for a disease, where Mary is selected randomly from a population where the disease is very rare. See for example here. (It’s just like the case of our high school student Isaac). His recommendations were extremely illuminating, and with them he sent me a poem he’d written (which you can read in my published response here*). Aside from being a leading statistician, Erich had a (serious) literary bent. Continue reading →

Categories: highly probable vs highly probed, phil/history of stat, Sir David Cox, Spanos, Statistics | Tags: , | Leave a comment

A. Spanos: Jerzy Neyman and his Enduring Legacy

Posted on April 16, 2014 by Mayo

A Statistical Model as a Chance Mechanism
Aris Spanos 

Jerzy Neyman (April 16, 1894 – August 5, 1981), 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. Continue reading →

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

Phil 6334: March 26, philosophy of misspecification testing (Day #9 slides)

Posted on March 30, 2014 by Mayo

 

may-4-8-aris-spanos-e2809contology-methodology-in-statistical-modelinge2809d“Probability/Statistics Lecture Notes 6: An Introduction to Mis-Specification (M-S) Testing” (Aris Spanos)

 

[Other slides from Day 9 by guest, John Byrd, can be found here.]

Categories: misspecification testing, Phil 6334 class material, Spanos, Statistics | Leave a comment

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