Error Statistics

American Phil Assoc Blog: The Stat Crisis of Science: Where are the Philosophers?

Ship StatInfasST

The Statistical Crisis of Science: Where are the Philosophers?

This was published today on the American Philosophical Association blog. 

“[C]onfusion about the foundations of the subject is responsible, in my opinion, for much of the misuse of the statistics that one meets in fields of application such as medicine, psychology, sociology, economics, and so forth.” (George Barnard 1985, p. 2)

“Relevant clarifications of the nature and roles of statistical evidence in scientific research may well be achieved by bringing to bear in systematic concert the scholarly methods of statisticians, philosophers and historians of science, and substantive scientists…” (Allan Birnbaum 1972, p. 861).

“In the training program for PhD students, the relevant basic principles of philosophy of science, methodology, ethics and statistics that enable the responsible practice of science must be covered.” (p. 57, Committee Investigating fraudulent research practices of social psychologist Diederik Stapel)

I was the lone philosophical observer at a special meeting convened by the American Statistical Association (ASA) in 2015 to construct a non-technical document to guide users of statistical significance tests–one of the most common methods used to distinguish genuine effects from chance variability across a landscape of social, physical and biological sciences.

It was, by the ASA Director’s own description, “historical”, but it was also highly philosophical, and its ramifications are only now being discussed and debated. Today, introspection on statistical methods is rather common due to the “statistical crisis in science”. What is it? In a nutshell: high powered computer methods make it easy to arrive at impressive-looking ‘findings’ that too often disappear when others try to replicate them when hypotheses and data analysis protocols are required to be fixed in advance.

How should scientific integrity be restored? Experts do not agree and the disagreement is intertwined with fundamental disagreements regarding the nature, interpretation, and justification of methods and models used to learn from incomplete and uncertain data. Today’s reformers, fraudbusters, and replication researchers increasingly call for more self-critical scrutiny on philosophical foundations. Philosophers should take this seriously. While philosophers of science are interested in helping to clarify, if not also to resolve, matters of evidence and inference, they are rarely consulted in practice for this end. The assumptions behind today’s competing evidence reforms–issues of what I will call evidence-policy–are largely hidden to those outside the loop of the philosophical foundations of statistics and data analysis, or Phil Stat. This is a crucial obstacle to scrutinizing the consequences to science policy, clinical trials, personalized medicine, and across a wide landscape of Big Data modeling.

Statistics has a fascinating and colorful history of philosophical debate, marked by unusual heights of passion, personality, and controversy for at least a century. Wars between frequentists and Bayesians have been so contentious that everyone wants to believe we are long past them: we now have unifications and reconciliations, and practitioners only care about what works. The truth is that both brand new and long-standing battles simmer below the surface in questions about scientific trustworthiness. They show up unannounced in the current problems of scientific integrity, questionable research practices, and in the swirl of methodological reforms and guidelines that spin their way down from journals and reports, the ASA Statement being just one. There isn’t even agreement as to what is to be meant by the method “works”. These are key themes in my Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (2018, CUP).

Many of the key problems in today’s evidence-policy disputes inherit the conceptual confusions of the underlying methods for evidence and inference. They are intertwined with philosophical terms that often remain vague, such as inference, reliability, testing, rationality, explanation, induction, confirmation, and falsification. This hampers communication among various stakeholders, making it difficult to even recognize and articulate where they agree. The philosopher’s penchant for laying bare presuppositions of claims and arguments would let us cut through the unclarity that blocked the experts at the ASA meeting from clearly pinpointing where and why they agree or disagree. (As a mere “observer”, I rarely intervened.) We should put philosophy to work on the popular memes: “All models are false”, “Everything is equally subjective and objective”, “P -values exaggerate evidence”, and “ most published research findings are false”.

So am I calling on my fellow philosophers (at least some of them) to learn formal statistics? That would be both too much and too little. Too much because it would be impractical; too little because despite technical sophistication, basic concepts of statistical testing and inference are more unsettled than ever. Debates about P-values–whether to redefine them, lower them, or ban them altogether–are all the subject of heated discussion and journalistic debates. Megateams of seventy or more authors array themselves on either side of the debate (e.g., Benjamin 2017, Lakens 2018), including some philosophers (I was a co-author in Lakens, arguing that redefining significance would not help with the problem of replication). The deepest problems underlying the replication crisis go beyond formal statistics–into measurement, experimental design, communication of uncertainty. Yet these rarely occupy center stage in all the brouhaha. By focusing just on the formal statistical issues, the debates give short shrift to the need to tie formal methods to substantive inferences, to a general account of collecting and learning from data, and to entirely non-statistical types of inference. The goal becomes: who can claim to offer the highest proportion of “true” effects among those outputted by a formal method?

You might say my project is only relevant for philosophers of science, logic, formal epistemology and the like. While they are the obvious suspects, it goes further. Despite the burgeoning of discussions of ethics in research and in data science, the work is generally done by practitioners apart from philosophy, or by philosophers apart from the nitty-gritty details of the data sciences themselves. Without grasping the basic statistics, informed by understanding contrasting views of the nature and goals of using probability in learning, it’s impossible to see where the formal issues leave off and informal, value-laden issues arise or intersect. Philosophers in research ethics can wind up building arguments that forfeit a stronger stance that a critical assessment of the methods would afford (e.g., arguing for a precautionary stance, when there is evidence of genuine risk increase in the data, despite non-significant results.) Interest in experimental philosophy is another area that underscores the importance of a critical assessment of the statistical methods on which it is based. Formal methods, logic and probability are staples of philosophy, why not methods of inference based on probabilistic methods? That’s what statistics is.

Not only is PhilStat relevant to addressing some long-standing philosophical problems of evidence, inference and knowledge, it offers a superb avenue for philosophers to genuinely impact scientific practice and policy. Even a sufficient understanding of the inference methods together with a platform for raising questions about fallacies and pitfalls could be extremely effective. What is at stake is a critical standpoint that we may be in danger of losing. Without it, we forfeit the ability to communicate with, and hold accountable, the “experts,” the agencies, the quants, and all those data handlers increasingly exerting power over our lives. It goes beyond philosophical outreach–as important as that is–to becoming citizen scholars and citizen scientists.

I have been pondering how to overcome these obstacles, and am keen to engage fellow philosophers in the project. I am going to take one step toward exploring and meeting this goal, together with a colleague, Aris Spanos, in economics. We are running a two-week immersive seminar on PhilStat for philosophy faculty and post-docs who wish to acquire or strengthen their background in PhilStat as it relates to philosophical problems of evidence and inference, to today’s statistical crisis of replication, and to associated evidence-policy debates. The logistics are modeled on the NEH Summer Seminars for college faculty that I directed in 1999 (on Philosophy of Experiment: Induction, Reliability, and Error). The content reflects Mayo (2018), which is written as a series of Excursions and Tours in a “Philosophical Voyage” to illuminate statistical inference. Consider joining me. In the meantime, I would like to hear from philosophers interested or already involved in this arena. Do you have references to existing efforts in this direction? Please share them.

 

Barnard, G. (1985). A Coherent View of Statistical Inference, Statistics Technical Report Series. Department of Statistics & Actuarial Science, University of Waterloo, Canada.

Benjamin, D. et al (2017). Redefine Statistical Significance, Nature Human Behaviour 2, 6-10.

Birnbaum, A. (1972). More on concepts of statistical evidence. J. Amer. Statist. Assoc. 67 858–861. MR0365793

Lakens et al (2018). Justify Your Alpha Nature Human Behaviour 2, 168-71.

Levelt Committee, Noort Committee, Drenth Committee (2012). Flawed Science: The Fraudulent Research Practices of Social Psychologist Diederik Stapel (www.commissielevelt.nl/).

Mayo, D. (2018). Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (CUP). (The first chapter [Excursion 1 Tour I ] is here.)

Wasserstein & Lazar (2016). The ASA’s Statement on P-values: Context, Process and Purpose, (and supplemental materials), The American Statistician 70(2), 129–33.

 

Credit for the ‘statistical cruise ship’ artwork goes to Mickey Mayo of Mayo Studios, Inc.

 

Deborah Mayo is Professor Emerita in the Department of Philosophy at 

Virginia Tech. She’s the author of Error and the Growth of Experimental Knowledge (1996, Chicago), which won the 1998 Lakatos Prize awarded to the most outstanding contribution to the philosophy of science during the previous six years. She co-edited, with Aris Spanos, Error and Inference: Recent Exchanges on Experimental Reasoning, Reliability, and the Objectivity and Rationality of Science(2010, CUP), and co-edited, with Rochelle Hollander, Acceptable Evidence: Science and Values in Risk Management (1991, Oxford). Other publications are available here.

many thanks to Nathan Oserloff for inviting me to submit this blogpost to the APA blog.
Categories: Error Statistics, Philosophy of Statistics, Summer Seminar in PhilStat | 1 Comment

Little Bit of Logic (5 mini problems for the reader)

Little bit of logic (5 little problems for you)[i]

Deductively valid arguments can readily have false conclusions! Yes, deductively valid arguments allow drawing their conclusions with 100% reliability but only if all their premises are true. For an argument to be deductively valid means simply that if the premises of the argument are all true, then the conclusion is true. For a valid argument to entail  the truth of its conclusion, all of its premises must be true.  In that case the argument is said to be (deductively) sound.

Equivalently, using the definition of deductive validity that I prefer: A deductively valid argument is one where, the truth of all its premises together with the falsity of its conclusion, leads to a logical contradiction (A & ~A).

Show that an argument with the form of disjunctive syllogism can have a false conclusion. Such an argument take the form (where A, B are statements): Continue reading

Categories: Error Statistics | 22 Comments

Mayo-Spanos Summer Seminar PhilStat: July 28-Aug 11, 2019: Instructions for Applying Now Available

INSTRUCTIONS FOR APPLYING ARE NOW AVAILABLE

See the Blog at SummerSeminarPhilStat

Categories: Announcement, Error Statistics, Statistics | Leave a comment

You Should Be Binge Reading the (Strong) Likelihood Principle

 

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An essential component of inference based on familiar frequentist notions: p-values, significance and confidence levels, is the relevant sampling distribution (hence the term sampling theory, or my preferred error statistics, as we get error probabilities from the sampling distribution). This feature results in violations of a principle known as the strong likelihood principle (SLP). To state the SLP roughly, it asserts that all the evidential import in the data (for parametric inference within a model) resides in the likelihoods. If accepted, it would render error probabilities irrelevant post data.

SLP (We often drop the “strong” and just call it the LP. The “weak” LP just boils down to sufficiency)

For any two experiments E1 and E2 with different probability models f1, f2, but with the same unknown parameter θ, if outcomes x* and y* (from E1 and E2 respectively) determine the same (i.e., proportional) likelihood function (f1(x*; θ) = cf2(y*; θ) for all θ), then x* and y* are inferentially equivalent (for an inference about θ).

(What differentiates the weak and the strong LP is that the weak refers to a single experiment.)
Continue reading

Categories: Error Statistics, Statistics, strong likelihood principle | 1 Comment

Excerpt from Excursion 4 Tour I: The Myth of “The Myth of Objectivity” (Mayo 2018, CUP)

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Tour I The Myth of “The Myth of Objectivity”*

 

Objectivity in statistics, as in science more generally, is a matter of both aims and methods. Objective science, in our view, aims to find out what is the case as regards aspects of the world [that hold] independently of our beliefs, biases and interests; thus objective methods aim for the critical control of inferences and hypotheses, constraining them by evidence and checks of error. (Cox and Mayo 2010, p. 276)

Whenever you come up against blanket slogans such as “no methods are objective” or “all methods are equally objective and subjective” it is a good guess that the problem is being trivialized into oblivion. Yes, there are judgments, disagreements, and values in any human activity, which alone makes it too trivial an observation to distinguish among very different ways that threats of bias and unwarranted inferences may be controlled. Is the objectivity–subjectivity distinction really toothless, as many will have you believe? I say no. I know it’s a meme promulgated by statistical high priests, but you agreed, did you not, to use a bit of chutzpah on this excursion? Besides, cavalier attitudes toward objectivity are at odds with even more widely endorsed grass roots movements to promote replication, reproducibility, and to come clean on a number of sources behind illicit results: multiple testing, cherry picking, failed assumptions, researcher latitude, publication bias and so on. The moves to take back science are rooted in the supposition that we can more objectively scrutinize results – even if it’s only to point out those that are BENT. The fact that these terms are used equivocally should not be taken as grounds to oust them but rather to engage in the difficult work of identifying what there is in “objectivity” that we won’t give up, and shouldn’t. Continue reading

Categories: Error Statistics, SIST, Statistical Inference as Severe Testing | 4 Comments

Summer Seminar PhilStat: July 28-Aug 11, 2019 (ii)

First draft of PhilStat Announcement

 

Categories: Announcement, Error Statistics | 5 Comments

It’s the Methods, Stupid: Excerpt from Excursion 3 Tour II (Mayo 2018, CUP)

Tour II It’s the Methods, Stupid

There is perhaps in current literature a tendency to speak of the Neyman–Pearson contributions as some static system, rather than as part of the historical process of development of thought on statistical theory which is and will always go on. (Pearson 1962, 276)

This goes for Fisherian contributions as well. Unlike museums, we won’ t remain static. The lesson from Tour I of this Excursion is that Fisherian and Neyman– Pearsonian tests may be seen as offering clusters of methods appropriate for different contexts within the large taxonomy of statistical inquiries. There is an overarching pattern: Continue reading

Categories: Error Statistics, Statistical Inference as Severe Testing | 4 Comments

Memento & Quiz (on SEV): Excursion 3, Tour I

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As you enjoy the weekend discussion & concert in the Captain’s Central Limit Library & Lounge, your Tour Guide has prepared a brief overview of Excursion 3 Tour I, and a short (semi-severe) quiz on severity, based on exhibit (i).*

 

We move from Popper through a gallery on “Data Analysis in the 1919 Eclipse tests of the General Theory of Relativity (GTR)” (3.1) which leads to the main gallery on the origin of statistical tests (3.2) by way of a look at where the main members of our statistical cast are in 1919: Fisher, Neyman and Pearson. From the GTR episode, we identify the key elements of a statistical test–the steps in E.S. Pearson’s opening description of tests in 3.2. The classical testing notions–type I and II errors, power, consistent tests–are shown to grow out of requiring probative tests. The typical (behavioristic) formulation of N-P tests came later. The severe tester breaks out of the behavioristic prison. A first look at the severity construal of N-P tests is in Exhibit (i). Viewing statistical inference as severe testing shows how to do all N-P tests do (and more) while a member of the Fisherian Tribe (3.3). We consider the frequentist principle of evidence FEV and the divergent interpretations that are called for by Cox’s taxonomy of null hypotheses. The last member of the taxonomy–substantively based null hypotheses–returns us to the opening episode of GTR. Continue reading

Categories: Severity, Statistical Inference as Severe Testing | 16 Comments

First Look at N-P Methods as Severe Tests: Water plant accident [Exhibit (i) from Excursion 3]

Excursion 3 Exhibit (i)

Exhibit (i) N-P Methods as Severe Tests: First Look (Water Plant Accident)

There’s been an accident at a water plant where our ship is docked, and the cooling system had to be repaired.  It is meant to ensure that the mean temperature of discharged water stays below the temperature that threatens the ecosystem, perhaps not much beyond 150 degrees Fahrenheit. There were 100 water measurements taken at randomly selected times and the sample mean x computed, each with a known standard deviation σ = 10.  When the cooling system is effective, each measurement is like observing X ~ N(150, 102). Because of this variability, we expect different 100-fold water samples to lead to different values of X, but we can deduce its distribution. If each X ~N(μ = 150, 102) then X is also Normal with μ = 150, but the standard deviation of X is only σ/√n = 10/√100 = 1. So X ~ N(μ = 150, 1). Continue reading

Categories: Error Statistics, Severity, Statistical Inference as Severe Testing | 44 Comments

Stephen Senn: Rothamsted Statistics meets Lord’s Paradox (Guest Post)

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Stephen Senn
Consultant Statistician
Edinburgh

The Rothamsted School

I never worked at Rothamsted but during the eight years I was at University College London (1995-2003) I frequently shared a train journey to London from Harpenden (the village in which Rothamsted is situated) with John Nelder, as a result of which we became friends and I acquired an interest in the software package Genstat®.

That in turn got me interested in John Nelder’s approach to analysis of variance, which is a powerful formalisation of ideas present in the work of others associated with Rothamsted. Nelder’s important predecessors in this respect include, at least, RA Fisher (of course) and Frank Yates and others such as David Finney and Frank Anscombe. John died in 2010 and I regard Rosemary Bailey, who has done deep and powerful work on randomisation and the representation of experiments through Hasse diagrams, as being the greatest living proponent of the Rothamsted School. Another key figure is Roger Payne who turned many of John’s ideas into code in Genstat®. Continue reading

Categories: Error Statistics | 11 Comments

The Replication Crises and its Constructive Role in the Philosophy of Statistics-PSA2018

Below are my slides from a session on replication at the recent Philosophy of Science Association meetings in Seattle.

 

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Tour Guide Mementos (Excursion 1, Tour I of How to Get Beyond the Statistics Wars)

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Tour guides in your travels jot down Mementos and Keepsakes from each Tour[i] of my new book: Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (CUP 2018). Their scribblings, which may at times include details, at other times just a word or two, may be modified through the Tour, and in response to questions from travelers (so please check back). Since these are just mementos, they should not be seen as replacements for the more careful notions given in the journey (i.e., book) itself. Still, you’re apt to flesh out your notes in greater detail, so please share yours (along with errors you’re bound to spot), and we’ll create Meta-Mementos. Continue reading

Categories: Error Statistics, Statistical Inference as Severe Testing | 8 Comments

Philosophy of Statistics & the Replication Crisis in Science: A philosophical intro to my book (slides)

a road through the jungle

In my talk yesterday at the Philosophy Department at Virginia Tech, I introduced my new book: Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (Cambridge 2018). I began with my preface (explaining the meaning of my title), and turned to the Statistics Wars, largely from Excursion 1 of the book. After the sum-up at the end, I snuck in an example from the replication crisis in psychology. Here are the slides.

 

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RSS 2018 – Significance Tests: Rethinking the Controversy

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Day 2, Wednesday 05/09/2018

11:20 – 13:20

Keynote 4 – Significance Tests: Rethinking the Controversy Assembly Room

Speakers:
Sir David Cox, Nuffield College, Oxford
Deborah Mayo, Virginia Tech
Richard Morey, Cardiff University
Aris Spanos, Virginia Tech

Intermingled in today’s statistical controversies are some long-standing, but unresolved, disagreements on the nature and principles of statistical methods and the roles for probability in statistical inference and modelling. In reaction to the so-called “replication crisis” in the sciences, some reformers suggest significance tests as a major culprit. To understand the ramifications of the proposed reforms, there is a pressing need for a deeper understanding of the source of the problems in the sciences and a balanced critique of the alternative methods being proposed to supplant significance tests. In this session speakers offer perspectives on significance tests from statistical science, econometrics, experimental psychology and philosophy of science. There will be also be panel discussion.

Categories: Error Statistics | 2 Comments

Neyman vs the ‘Inferential’ Probabilists continued (a)

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Today is Jerzy Neyman’s Birthday (April 16, 1894 – August 5, 1981).  I am posting a brief excerpt and a link to a paper of his that I hadn’t posted before: Neyman, J. (1962), ‘Two Breakthroughs in the Theory of Statistical Decision Making‘ [i] It’s chock full of ideas and arguments, but the one that interests me at the moment is Neyman’s conception of “his breakthrough”, in relation to a certain concept of “inference”.  “In the present paper” he tells us, “the term ‘inferential theory’…will be used to describe the attempts to solve the Bayes’ problem with a reference to confidence, beliefs, etc., through some supplementation …either a substitute a priori distribution [exemplified by the so called principle of insufficient reason] or a new measure of uncertainty” such as Fisher’s fiducial probability. Now Neyman always distinguishes his error statistical performance conception from Bayesian and Fiducial probabilisms [ii]. The surprising twist here is semantical and the culprit is none other than…Allan Birnbaum. Yet Birnbaum gets short shrift, and no mention is made of our favorite “breakthrough” (or did I miss it?). [iii] I’ll explain in later stages of this post & in comments…(so please check back); I don’t want to miss the start of the birthday party in honor of Neyman, and it’s already 8:30 p.m in Berkeley!

Note: In this article,”attacks” on various statistical “fronts” refers to ways of attacking problems in one or another statistical research program. HAPPY BIRTHDAY NEYMAN! Continue reading

Categories: Bayesian/frequentist, Error Statistics, Neyman, Statistics | Leave a comment

S. Senn: Being a statistician means never having to say you are certain (Guest Post)

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

Being a statistician means never having to say you are certain

A recent discussion of randomised controlled trials[1] by Angus Deaton and Nancy Cartwright (D&C) contains much interesting analysis but also, in my opinion, does not escape rehashing some of the invalid criticisms of randomisation with which the literatures seems to be littered. The paper has two major sections. The latter, which deals with generalisation of results, or what is sometime called external validity, I like much more than the former which deals with internal validity. It is the former I propose to discuss.

Continue reading

Categories: Error Statistics, RCTs, Statistics | 26 Comments

How to avoid making mountains out of molehills (using power and severity)

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In preparation for a new post that takes up some of the recent battles on reforming or replacing p-values, I reblog an older post on power, one of the most misunderstood and abused notions in statistics. (I add a few “notes on howlers”.)  The power of a test T in relation to a discrepancy from a test hypothesis H0 is the probability T will lead to rejecting H0 when that discrepancy is present. Power is sometimes misappropriated to mean something only distantly related to the probability a test leads to rejection; but I’m getting ahead of myself. This post is on a classic fallacy of rejection. Continue reading

Categories: CIs and tests, Error Statistics, power | 9 Comments

Yoav Benjamini, “In the world beyond p < .05: When & How to use P < .0499…"

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These were Yoav Benjamini’s slides,”In the world beyond p<.05: When & How to use P<.0499…” from our session at the ASA 2017 Symposium on Statistical Inference (SSI): A World Beyond p < 0.05. (Mine are in an earlier post.) He begins by asking:

However, it’s mandatory to adjust for selection effects, and Benjamini is one of the leaders in developing ways to carry out the adjustments. Even calling out the avenues for cherry-picking and multiple testing, long known to invalidate p-values, would make replication research more effective (and less open to criticism). Continue reading

Categories: Error Statistics, P-values, replication research, selection effects | 22 Comments

Revisiting Popper’s Demarcation of Science 2017

28 July 1902- 17 Sept. 1994

Karl Popper died on September 17 1994. One thing that gets revived in my new book (Statistical Inference as Severe Testing, 2018, CUP) is a Popperian demarcation of science vs pseudoscience Here’s a snippet from what I call a “live exhibit” (where the reader experiments with a subject) toward the end of a chapter on Popper:

Live Exhibit. Revisiting Popper’s Demarcation of Science: Here’s an experiment: Try shifting what Popper says about theories to a related claim about inquiries to find something out. To see what I have in mind, join me in watching a skit over the lunch break:

Physicist: “If mere logical falsifiability suffices for a theory to be scientific, then, we can’t properly oust astrology from the scientific pantheon. Plenty of nutty theories have been falsified, so by definition they’re scientific. Moreover, scientists aren’t always looking to subject well corroborated theories to “grave risk” of falsification.”

Fellow traveler: “I’ve been thinking about this. On your first point, Popper confuses things by making it sound as if he’s asking: When is a theory unscientific? What he is actually asking or should be asking is: When is an inquiry into a theory, or an appraisal of claim H unscientific? We want to distinguish meritorious modes of inquiry from those that are BENT. If the test methods enable ad hoc maneuvering, sneaky face-saving devices, then the inquiry–the handling and use of data–is unscientific. Despite being logically falsifiable, theories can be rendered immune from falsification by means of cavalier methods for their testing. Adhering to a falsified theory no matter what is poor science. On the other hand, some areas have so much noise that you can’t pinpoint what’s to blame for failed predictions. This is another way that inquiries become bad science.”

She continues: Continue reading

Categories: Error Statistics, Popper, pseudoscience, science vs pseudoscience | Tags: | 10 Comments

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

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

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