D. G. Mayo (Virginia Tech) "Error Statistical Control: Forfeit at your Peril" presented May 23 at the session on "The Philosophy of Statistics: Bayesianism, Frequentism and the Nature of Inference," 2015 APS Annual Convention in NYC.
"The Statistical Replication Crisis: Paradoxes and Scapegoats”jemille6
D. G. Mayo LSE Popper talk, May 10, 2016.
Abstract: Mounting failures of replication in the social and biological sciences give a practical spin to statistical foundations in the form of the question: How can we attain reliability when Big Data methods make illicit cherry-picking and significance seeking so easy? Researchers, professional societies, and journals are increasingly getting serious about methodological reforms to restore scientific integrity – some are quite welcome (e.g., preregistration), while others are quite radical. Recently, the American Statistical Association convened members from differing tribes of frequentists, Bayesians, and likelihoodists to codify misuses of P-values. Largely overlooked are the philosophical presuppositions of both criticisms and proposed reforms. Paradoxically, alternative replacement methods may enable rather than reveal illicit inferences due to cherry-picking, multiple testing, and other biasing selection effects. Popular appeals to “diagnostic testing” that aim to improve replication rates may (unintentionally) permit the howlers and cookbook statistics we are at pains to root out. Without a better understanding of the philosophical issues, we can expect the latest reforms to fail.
Stephen Senn slides:"‘Repligate’: reproducibility in statistical studies. What does it mean and in what sense does it matter?" presented May 23 at the session on "The Philosophy of Statistics: Bayesianism, Frequentism and the Nature of Inference"," at the 2015 APS Annual Convention in NYC
Deborah G. Mayo: Is the Philosophy of Probabilism an Obstacle to Statistical Fraud Busting?
Presentation slides for: Revisiting the Foundations of Statistics in the Era of Big Data: Scaling Up to Meet the Challenge[*] at the Boston Colloquium for Philosophy of Science (Feb 21, 2014).
D. Mayo: Replication Research Under an Error Statistical Philosophy jemille6
D. Mayo (Virginia Tech) slides from her talk June 3 at the "Preconference Workshop on Replication in the Sciences" at the 2015 Society for Philosophy and Psychology meeting.
Severe Testing: The Key to Error Correctionjemille6
D. G. Mayo's slides for her presentation given March 17, 2017 at Boston Colloquium for Philosophy of Science, Alfred I.Taub forum: "Understanding Reproducibility & Error Correction in Science"
Probing with Severity: Beyond Bayesian Probabilism and Frequentist Performancejemille6
Slides from Rutgers Seminar talk by Deborah G Mayo
December 3, 2014
Rutgers, Department of Statistics and Biostatistics
Abstract: Getting beyond today’s most pressing controversies revolving around statistical methods, I argue, requires scrutinizing their underlying statistical philosophies.Two main philosophies about the roles of probability in statistical inference are probabilism and performance (in the long-run). The first assumes that we need a method of assigning probabilities to hypotheses; the second assumes that the main function of statistical method is to control long-run performance. I offer a third goal: controlling and evaluating the probativeness of methods. An inductive inference, in this conception, takes the form of inferring hypotheses to the extent that they have been well or severely tested. A report of poorly tested claims must also be part of an adequate inference. I develop a statistical philosophy in which error probabilities of methods may be used to evaluate and control the stringency or severity of tests. I then show how the “severe testing” philosophy clarifies and avoids familiar criticisms and abuses of significance tests and cognate methods (e.g., confidence intervals). Severity may be threatened in three main ways: fallacies of statistical tests, unwarranted links between statistical and substantive claims, and violations of model assumptions.
A. Gelman "50 shades of gray: A research story," presented May 23 at the session on "The Philosophy of Statistics: Bayesianism, Frequentism and the Nature of Inference," 2015 APS Annual Convention in NYC.
Abstract: Mounting failures of replication in the social and biological sciences give a practical spin to statistical foundations in the form of the question: How can we attain reliability when methods make illicit cherry-picking and significance seeking so easy? Researchers, professional societies, and journals are increasingly getting serious about methodological reforms to restore scientific integrity – some are quite welcome (e.g., pre-registration), while others are quite radical. The American Statistical Association convened members from differing tribes of frequentists, Bayesians, and likelihoodists to codify misuses of P-values. Largely overlooked are the philosophical presuppositions of both criticisms and proposed reforms. Paradoxically, alternative replacement methods may enable rather than reveal illicit inferences due to cherry-picking, multiple testing, and other biasing selection effects. Crowd-sourced reproducibility research in psychology is helping to change the reward structure but has its own shortcomings. Focusing on purely statistical considerations, it tends to overlook problems with artificial experiments. Without a better understanding of the philosophical issues, we can expect the latest reforms to fail.
"The Statistical Replication Crisis: Paradoxes and Scapegoats”jemille6
D. G. Mayo LSE Popper talk, May 10, 2016.
Abstract: Mounting failures of replication in the social and biological sciences give a practical spin to statistical foundations in the form of the question: How can we attain reliability when Big Data methods make illicit cherry-picking and significance seeking so easy? Researchers, professional societies, and journals are increasingly getting serious about methodological reforms to restore scientific integrity – some are quite welcome (e.g., preregistration), while others are quite radical. Recently, the American Statistical Association convened members from differing tribes of frequentists, Bayesians, and likelihoodists to codify misuses of P-values. Largely overlooked are the philosophical presuppositions of both criticisms and proposed reforms. Paradoxically, alternative replacement methods may enable rather than reveal illicit inferences due to cherry-picking, multiple testing, and other biasing selection effects. Popular appeals to “diagnostic testing” that aim to improve replication rates may (unintentionally) permit the howlers and cookbook statistics we are at pains to root out. Without a better understanding of the philosophical issues, we can expect the latest reforms to fail.
Stephen Senn slides:"‘Repligate’: reproducibility in statistical studies. What does it mean and in what sense does it matter?" presented May 23 at the session on "The Philosophy of Statistics: Bayesianism, Frequentism and the Nature of Inference"," at the 2015 APS Annual Convention in NYC
Deborah G. Mayo: Is the Philosophy of Probabilism an Obstacle to Statistical Fraud Busting?
Presentation slides for: Revisiting the Foundations of Statistics in the Era of Big Data: Scaling Up to Meet the Challenge[*] at the Boston Colloquium for Philosophy of Science (Feb 21, 2014).
D. Mayo: Replication Research Under an Error Statistical Philosophy jemille6
D. Mayo (Virginia Tech) slides from her talk June 3 at the "Preconference Workshop on Replication in the Sciences" at the 2015 Society for Philosophy and Psychology meeting.
Severe Testing: The Key to Error Correctionjemille6
D. G. Mayo's slides for her presentation given March 17, 2017 at Boston Colloquium for Philosophy of Science, Alfred I.Taub forum: "Understanding Reproducibility & Error Correction in Science"
Probing with Severity: Beyond Bayesian Probabilism and Frequentist Performancejemille6
Slides from Rutgers Seminar talk by Deborah G Mayo
December 3, 2014
Rutgers, Department of Statistics and Biostatistics
Abstract: Getting beyond today’s most pressing controversies revolving around statistical methods, I argue, requires scrutinizing their underlying statistical philosophies.Two main philosophies about the roles of probability in statistical inference are probabilism and performance (in the long-run). The first assumes that we need a method of assigning probabilities to hypotheses; the second assumes that the main function of statistical method is to control long-run performance. I offer a third goal: controlling and evaluating the probativeness of methods. An inductive inference, in this conception, takes the form of inferring hypotheses to the extent that they have been well or severely tested. A report of poorly tested claims must also be part of an adequate inference. I develop a statistical philosophy in which error probabilities of methods may be used to evaluate and control the stringency or severity of tests. I then show how the “severe testing” philosophy clarifies and avoids familiar criticisms and abuses of significance tests and cognate methods (e.g., confidence intervals). Severity may be threatened in three main ways: fallacies of statistical tests, unwarranted links between statistical and substantive claims, and violations of model assumptions.
A. Gelman "50 shades of gray: A research story," presented May 23 at the session on "The Philosophy of Statistics: Bayesianism, Frequentism and the Nature of Inference," 2015 APS Annual Convention in NYC.
Abstract: Mounting failures of replication in the social and biological sciences give a practical spin to statistical foundations in the form of the question: How can we attain reliability when methods make illicit cherry-picking and significance seeking so easy? Researchers, professional societies, and journals are increasingly getting serious about methodological reforms to restore scientific integrity – some are quite welcome (e.g., pre-registration), while others are quite radical. The American Statistical Association convened members from differing tribes of frequentists, Bayesians, and likelihoodists to codify misuses of P-values. Largely overlooked are the philosophical presuppositions of both criticisms and proposed reforms. Paradoxically, alternative replacement methods may enable rather than reveal illicit inferences due to cherry-picking, multiple testing, and other biasing selection effects. Crowd-sourced reproducibility research in psychology is helping to change the reward structure but has its own shortcomings. Focusing on purely statistical considerations, it tends to overlook problems with artificial experiments. Without a better understanding of the philosophical issues, we can expect the latest reforms to fail.
Replication Crises and the Statistics Wars: Hidden Controversiesjemille6
D. Mayo presentation at the X-Phil conference on "Reproducibility and Replicabililty in Psychology and Experimental Philosophy", University College London (June 14, 2018)
Statistical skepticism: How to use significance tests effectively jemille6
Prof. D. Mayo, presentation Oct. 12, 2017 at the ASA Symposium on Statistical Inference : “A World Beyond p < .05” in the session: “What are the best uses for P-values?“
Surrogate Science: How Fisher, Neyman-Pearson, and Bayes Were Transformed int...jemille6
Gerd Gigerenzer (Director of Max Planck Institute for Human Development, Berlin, Germany) in the PSA 2016 Symposium:Philosophy of Statistics in the Age of Big Data and Replication Crises
D. Mayo: The Science Wars and the Statistics Wars: scientism, popular statist...jemille6
I will explore the extent to which concerns about ‘scientism’– an unwarranted obeisance to scientific over other methods of inquiry – are intertwined with issues in the foundations of the statistical data analyses on which (social, behavioral, medical and physical) science increasingly depends. The rise of big data, machine learning, and high-powered computer programs have extended statistical methods and modeling across the landscape of science, law and evidence-based policy, but this has been accompanied by enormous hand wringing as to the reliability, replicability, and valid use of statistics. Legitimate criticisms of scientism often stem from insufficiently self-critical uses of statistical methodology, broadly construed — i.e., from what might be called “statisticism”-- particularly when those methods are applied to matters of controversy.
D. G. Mayo: Your data-driven claims must still be probed severelyjemille6
In the session "Philosophy of Science and the New Paradigm of Data-Driven Science at the American Statistical Association Conference on Statistical Learning and Data Science/Nonparametric Statistics
Controversy Over the Significance Test Controversyjemille6
Deborah Mayo (Professor of Philosophy, Virginia Tech, Blacksburg, Virginia) in PSA 2016 Symposium: Philosophy of Statistics in the Age of Big Data and Replication Crises
Exploratory Research is More Reliable Than Confirmatory Researchjemille6
PSA 2016 Symposium:
Philosophy of Statistics in the Age of Big Data and Replication Crises
Presenter: Clark Glymour (Alumni University Professor in Philosophy, Carnegie Mellon University, Pittsburgh, Pennsylvania)
ABSTRACT: Ioannidis (2005) argued that most published research is false, and that “exploratory” research in which many hypotheses are assessed automatically is especially likely to produce false positive relations. Colquhoun (2014) with simulations estimates that 30 to 40% of positive results using the conventional .05 cutoff for rejection of a null hypothesis is false. Their explanation is that true relationships in a domain are rare and the selection of hypotheses to test is roughly independent of their truth, so most relationships tested will in fact be false. Conventional use of hypothesis tests, in other words, suffers from a base rate fallacy. I will show that the reverse is true for modern search methods for causal relations because: a. each hypothesis is tested or assessed multiple times; b. the methods are biased against positive results; c. systems in which true relationships are rare are an advantage for these methods. I will substantiate the claim with both empirical data and with simulations of data from systems with a thousand to a million variables that result in fewer than 5% false positive relationships and in which 90% or more of the true relationships are recovered.
Mayo: Evidence as Passing a Severe Test (How it Gets You Beyond the Statistic...jemille6
D. G. Mayo April 28, 2021 presentation to the CUNY Graduate Center Philosophy Colloquium "Evidence as Passing a Severe Test (How it Gets You Beyond the Statistics Wars)"
D. G. Mayo: The Replication Crises and its Constructive Role in the Philosoph...jemille6
Constructive role of replication crises teaches a lot about 1.) Non-fallacious uses of statistical tests, 2.) Rationale for the role of probability in tests, 3.) How to reformulate tests.
Byrd statistical considerations of the histomorphometric test protocol (1)jemille6
"Statistical considerations of the histomorphometric test protocol"
John E. Byrd, Ph.D. D-ABFA
Maria-Teresa Tersigni-Tarrant, Ph.D.
Central Identification Laboratory
JPAC
D. Mayo: Philosophy of Statistics & the Replication Crisis in Sciencejemille6
D. Mayo discusses various disputes-notably the replication crisis in science-in the context of her just released book: Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars.
D. Mayo: Philosophical Interventions in the Statistics Warsjemille6
ABSTRACT: While statistics has a long history of passionate philosophical controversy, the last decade especially cries out for philosophical illumination. Misuses of statistics, Big Data dredging, and P-hacking make it easy to find statistically significant, but spurious, effects. This obstructs a test's ability to control the probability of erroneously inferring effects–i.e., to control error probabilities. Disagreements about statistical reforms reflect philosophical disagreements about the nature of statistical inference–including whether error probability control even matters! I describe my interventions in statistics in relation to three events. (1) In 2016 the American Statistical Association (ASA) met to craft principles for avoiding misinterpreting P-values. (2) In 2017, a "megateam" (including philosophers of science) proposed "redefining statistical significance," replacing the common threshold of P ≤ .05 with P ≤ .005. (3) In 2019, an editorial in the main ASA journal called for abandoning all P-value thresholds, and even the words "significant/significance".
A word on each. (1) Invited to be a "philosophical observer" at their meeting, I found the major issues were conceptual. P-values measure how incompatible data are from what is expected under a hypothesis that there is no genuine effect: the smaller the P-value, the more indication of incompatibility. The ASA list of familiar misinterpretations–P-values are not posterior probabilities, statistical significance is not substantive importance, no evidence against a hypothesis need not be evidence for it–I argue, should not be the basis for replacing tests with methods less able to assess and control erroneous interpretations of data. (Mayo 2016, 2019). (2) The "redefine statistical significance" movement appraises P-values from the perspective of a very different quantity: a comparative Bayes Factor. Failing to recognize how contrasting approaches measure different things, disputants often talk past each other (Mayo 2018). (3) To ban P-value thresholds, even to distinguish terrible from warranted evidence, I say, is a mistake (2019). It will not eradicate P-hacking, but it will make it harder to hold P-hackers accountable. A 2020 ASA Task Force on significance testing has just been announced. (I would like to think my blog errorstatistics.com helped.)
To enter the fray between rival statistical approaches, it helps to have a principle applicable to all accounts. There's poor evidence for a claim if little if anything has been done to find it flawed even if it is. This forms a basic requirement for evidence I call the severity requirement. A claim passes with severity only if it is subjected to and passes a test that probably would have found it flawed, if it were. It stems from Popper, though he never adequately cashed it out. A variant is the frequentist principle of evidence developed with Sir David Cox (Mayo and Cox 20
Fusion Confusion? Comments on Nancy Reid: "BFF Four-Are we Converging?"jemille6
D. Mayo's comments on Nancy Reid's "BFF Four-Are we Converging?" given May 2, 2017 at The Fourth Bayesian, Fiducial and Frequentists Workshop held at Harvard University.
Today we’ll try to cover a number of things:
1. Learning philosophy/philosophy of statistics
2. Situating the broad issues within philosophy of science
3. Little bit of logic
4. Probability and random variables
Statistical Inference as Severe Testing: Beyond Performance and Probabilismjemille6
A talk given by Deborah G Mayo
(Dept of Philosophy, Virginia Tech) to the Seminar in Advanced Research Methods at the Dept of Psychology, Princeton University on
November 14, 2023
TITLE: Statistical Inference as Severe Testing: Beyond Probabilism and Performance
ABSTRACT: I develop a statistical philosophy in which error probabilities of methods may be used to evaluate and control the stringency or severity of tests. A claim is severely tested to the extent it has been subjected to and passes a test that probably would have found flaws, were they present. The severe-testing requirement leads to reformulating statistical significance tests to avoid familiar criticisms and abuses. While high-profile failures of replication in the social and biological sciences stem from biasing selection effects—data dredging, multiple testing, optional stopping—some reforms and proposed alternatives to statistical significance tests conflict with the error control that is required to satisfy severity. I discuss recent arguments to redefine, abandon, or replace statistical significance.
Replication Crises and the Statistics Wars: Hidden Controversiesjemille6
D. Mayo presentation at the X-Phil conference on "Reproducibility and Replicabililty in Psychology and Experimental Philosophy", University College London (June 14, 2018)
Statistical skepticism: How to use significance tests effectively jemille6
Prof. D. Mayo, presentation Oct. 12, 2017 at the ASA Symposium on Statistical Inference : “A World Beyond p < .05” in the session: “What are the best uses for P-values?“
Surrogate Science: How Fisher, Neyman-Pearson, and Bayes Were Transformed int...jemille6
Gerd Gigerenzer (Director of Max Planck Institute for Human Development, Berlin, Germany) in the PSA 2016 Symposium:Philosophy of Statistics in the Age of Big Data and Replication Crises
D. Mayo: The Science Wars and the Statistics Wars: scientism, popular statist...jemille6
I will explore the extent to which concerns about ‘scientism’– an unwarranted obeisance to scientific over other methods of inquiry – are intertwined with issues in the foundations of the statistical data analyses on which (social, behavioral, medical and physical) science increasingly depends. The rise of big data, machine learning, and high-powered computer programs have extended statistical methods and modeling across the landscape of science, law and evidence-based policy, but this has been accompanied by enormous hand wringing as to the reliability, replicability, and valid use of statistics. Legitimate criticisms of scientism often stem from insufficiently self-critical uses of statistical methodology, broadly construed — i.e., from what might be called “statisticism”-- particularly when those methods are applied to matters of controversy.
D. G. Mayo: Your data-driven claims must still be probed severelyjemille6
In the session "Philosophy of Science and the New Paradigm of Data-Driven Science at the American Statistical Association Conference on Statistical Learning and Data Science/Nonparametric Statistics
Controversy Over the Significance Test Controversyjemille6
Deborah Mayo (Professor of Philosophy, Virginia Tech, Blacksburg, Virginia) in PSA 2016 Symposium: Philosophy of Statistics in the Age of Big Data and Replication Crises
Exploratory Research is More Reliable Than Confirmatory Researchjemille6
PSA 2016 Symposium:
Philosophy of Statistics in the Age of Big Data and Replication Crises
Presenter: Clark Glymour (Alumni University Professor in Philosophy, Carnegie Mellon University, Pittsburgh, Pennsylvania)
ABSTRACT: Ioannidis (2005) argued that most published research is false, and that “exploratory” research in which many hypotheses are assessed automatically is especially likely to produce false positive relations. Colquhoun (2014) with simulations estimates that 30 to 40% of positive results using the conventional .05 cutoff for rejection of a null hypothesis is false. Their explanation is that true relationships in a domain are rare and the selection of hypotheses to test is roughly independent of their truth, so most relationships tested will in fact be false. Conventional use of hypothesis tests, in other words, suffers from a base rate fallacy. I will show that the reverse is true for modern search methods for causal relations because: a. each hypothesis is tested or assessed multiple times; b. the methods are biased against positive results; c. systems in which true relationships are rare are an advantage for these methods. I will substantiate the claim with both empirical data and with simulations of data from systems with a thousand to a million variables that result in fewer than 5% false positive relationships and in which 90% or more of the true relationships are recovered.
Mayo: Evidence as Passing a Severe Test (How it Gets You Beyond the Statistic...jemille6
D. G. Mayo April 28, 2021 presentation to the CUNY Graduate Center Philosophy Colloquium "Evidence as Passing a Severe Test (How it Gets You Beyond the Statistics Wars)"
D. G. Mayo: The Replication Crises and its Constructive Role in the Philosoph...jemille6
Constructive role of replication crises teaches a lot about 1.) Non-fallacious uses of statistical tests, 2.) Rationale for the role of probability in tests, 3.) How to reformulate tests.
Byrd statistical considerations of the histomorphometric test protocol (1)jemille6
"Statistical considerations of the histomorphometric test protocol"
John E. Byrd, Ph.D. D-ABFA
Maria-Teresa Tersigni-Tarrant, Ph.D.
Central Identification Laboratory
JPAC
D. Mayo: Philosophy of Statistics & the Replication Crisis in Sciencejemille6
D. Mayo discusses various disputes-notably the replication crisis in science-in the context of her just released book: Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars.
D. Mayo: Philosophical Interventions in the Statistics Warsjemille6
ABSTRACT: While statistics has a long history of passionate philosophical controversy, the last decade especially cries out for philosophical illumination. Misuses of statistics, Big Data dredging, and P-hacking make it easy to find statistically significant, but spurious, effects. This obstructs a test's ability to control the probability of erroneously inferring effects–i.e., to control error probabilities. Disagreements about statistical reforms reflect philosophical disagreements about the nature of statistical inference–including whether error probability control even matters! I describe my interventions in statistics in relation to three events. (1) In 2016 the American Statistical Association (ASA) met to craft principles for avoiding misinterpreting P-values. (2) In 2017, a "megateam" (including philosophers of science) proposed "redefining statistical significance," replacing the common threshold of P ≤ .05 with P ≤ .005. (3) In 2019, an editorial in the main ASA journal called for abandoning all P-value thresholds, and even the words "significant/significance".
A word on each. (1) Invited to be a "philosophical observer" at their meeting, I found the major issues were conceptual. P-values measure how incompatible data are from what is expected under a hypothesis that there is no genuine effect: the smaller the P-value, the more indication of incompatibility. The ASA list of familiar misinterpretations–P-values are not posterior probabilities, statistical significance is not substantive importance, no evidence against a hypothesis need not be evidence for it–I argue, should not be the basis for replacing tests with methods less able to assess and control erroneous interpretations of data. (Mayo 2016, 2019). (2) The "redefine statistical significance" movement appraises P-values from the perspective of a very different quantity: a comparative Bayes Factor. Failing to recognize how contrasting approaches measure different things, disputants often talk past each other (Mayo 2018). (3) To ban P-value thresholds, even to distinguish terrible from warranted evidence, I say, is a mistake (2019). It will not eradicate P-hacking, but it will make it harder to hold P-hackers accountable. A 2020 ASA Task Force on significance testing has just been announced. (I would like to think my blog errorstatistics.com helped.)
To enter the fray between rival statistical approaches, it helps to have a principle applicable to all accounts. There's poor evidence for a claim if little if anything has been done to find it flawed even if it is. This forms a basic requirement for evidence I call the severity requirement. A claim passes with severity only if it is subjected to and passes a test that probably would have found it flawed, if it were. It stems from Popper, though he never adequately cashed it out. A variant is the frequentist principle of evidence developed with Sir David Cox (Mayo and Cox 20
Fusion Confusion? Comments on Nancy Reid: "BFF Four-Are we Converging?"jemille6
D. Mayo's comments on Nancy Reid's "BFF Four-Are we Converging?" given May 2, 2017 at The Fourth Bayesian, Fiducial and Frequentists Workshop held at Harvard University.
Today we’ll try to cover a number of things:
1. Learning philosophy/philosophy of statistics
2. Situating the broad issues within philosophy of science
3. Little bit of logic
4. Probability and random variables
Statistical Inference as Severe Testing: Beyond Performance and Probabilismjemille6
A talk given by Deborah G Mayo
(Dept of Philosophy, Virginia Tech) to the Seminar in Advanced Research Methods at the Dept of Psychology, Princeton University on
November 14, 2023
TITLE: Statistical Inference as Severe Testing: Beyond Probabilism and Performance
ABSTRACT: I develop a statistical philosophy in which error probabilities of methods may be used to evaluate and control the stringency or severity of tests. A claim is severely tested to the extent it has been subjected to and passes a test that probably would have found flaws, were they present. The severe-testing requirement leads to reformulating statistical significance tests to avoid familiar criticisms and abuses. While high-profile failures of replication in the social and biological sciences stem from biasing selection effects—data dredging, multiple testing, optional stopping—some reforms and proposed alternatives to statistical significance tests conflict with the error control that is required to satisfy severity. I discuss recent arguments to redefine, abandon, or replace statistical significance.
The Statistics Wars: Errors and Casualtiesjemille6
ABSTRACT: Mounting failures of replication in the social and biological sciences give a new urgency to critically appraising proposed statistical reforms. While many reforms are welcome (preregistration of experiments, replication, discouraging cookbook uses of statistics), there have been casualties. The philosophical presuppositions behind the meta-research battles remain largely hidden. Too often the statistics wars have become proxy wars between competing tribe leaders, each keen to advance one or another tool or school, rather than build on efforts to do better science. Efforts of replication researchers and open science advocates are diminished when so much attention is centered on repeating hackneyed howlers of statistical significance tests (statistical significance isn’t substantive significance, no evidence against isn’t evidence for), when erroneous understanding of basic statistical terms goes uncorrected, and when bandwagon effects lead to popular reforms that downplay the importance of error probability control. These casualties threaten our ability to hold accountable the “experts,” the agencies, and all the data handlers increasingly exerting power over our lives.
The role of background assumptions in severity appraisal (jemille6
In the past decade discussions around the reproducibility of scientific findings have led to a re-appreciation of the importance of guaranteeing claims are severely tested. The inflation of Type 1 error rates due to flexibility in the data analysis is widely considered
one of the underlying causes of low replicability rates. Solutions, such as study preregistration, are becoming increasingly popular to combat this problem. Preregistration only allows researchers to evaluate the severity of a test, but not all
preregistered studies provide a severe test of a claim. The appraisal of the severity of a
test depends on background information, such as assumptions about the data generating process, and auxiliary hypotheses that influence the final choice for the
design of the test. In this article, I will discuss the difference between subjective and
inter-subjectively testable assumptions underlying scientific claims, and the importance
of separating the two. I will stress the role of justifications in statistical inferences, the
conditional nature of scientific conclusions following these justifications, and highlight
how severe tests could lead to inter-subjective agreement, based on a philosophical approach grounded in methodological falsificationism. Appreciating the role of background assumptions in the appraisal of severity should shed light on current discussions about the role of preregistration, interpreting the results of replication studies, and proposals to reform statistical inferences.
“The importance of philosophy of science for statistical science and vice versa”jemille6
My paper “The importance of philosophy of science for statistical science and vice
versa” presented (zoom) at the conference: IS PHILOSOPHY USEFUL FOR SCIENCE, AND/OR VICE VERSA? January 30 - February 2, 2024 at Chapman University, Schmid College of Science and Technology.
D. Mayo (Dept of Philosophy, VT)
Sir David Cox’s Statistical Philosophy and Its Relevance to Today’s Statistical Controversies
ABSTRACT: This talk will explain Sir David Cox's views of the nature and importance of statistical foundations and their relevance to today's controversies about statistical inference, particularly in using statistical significance testing and confidence intervals. Two key themes of Cox's statistical philosophy are: first, the importance of calibrating methods by considering their behavior in (actual or hypothetical) repeated sampling, and second, ensuring the calibration is relevant to the specific data and inquiry. A question that arises is: How can the frequentist calibration provide a genuinely epistemic assessment of what is learned from data? Building on our jointly written papers, Mayo and Cox (2006) and Cox and Mayo (2010), I will argue that relevant error probabilities may serve to assess how well-corroborated or severely tested statistical claims are.
Nancy Reid, Dept. of Statistics, University of Toronto. Inaugural receiptant of the "David R. Cox Foundations of Statistics Award".
Slides from Invited presentation at 2023 JSM: “The Importance of Foundations in Statistical Science“
Ronald Wasserstein, Chair (American Statistical Association)
ABSTRACT: David Cox wrote “A healthy interplay between theory and application is crucial for statistics… This is particularly the case when by theory we mean foundations of statistical analysis, rather than the theoretical analysis of specific statistical methods.” These foundations distinguish statistical science from the many fields of research in which statistical thinking is a key intellectual component. In this talk I will emphasize the ongoing importance and relevance of theoretical advances and theoretical thinking through some illustrative examples.
Errors of the Error Gatekeepers: The case of Statistical Significance 2016-2022jemille6
ABSTRACT: Statistical significance tests serve in gatekeeping against being fooled by randomness, but recent attempts to gatekeep these tools have themselves malfunctioned. Warranted gatekeepers formulate statistical tests so as to avoid fallacies and misuses of P-values. They highlight how multiplicity, optional stopping, and data-dredging can readily invalidate error probabilities. It is unwarranted, however, to argue that statistical significance and P-value thresholds be abandoned because they can be misused. Nor is it warranted to argue for abandoning statistical significance based on presuppositions about evidence and probability that are at odds with those underlying statistical significance tests. When statistical gatekeeping malfunctions, I argue, it undermines a central role to which scientists look to statistics. In order to combat the dangers of unthinking, bandwagon effects, statistical practitioners and consumers need to be in a position to critically evaluate the ramifications of proposed "reforms” (“stat activism”). I analyze what may be learned from three recent episodes of gatekeeping (and meta-gatekeeping) at the American Statistical Association (ASA).
Causal inference is not statistical inferencejemille6
Jon Williamson (University of Kent)
ABSTRACT: Many methods for testing causal claims are couched as statistical methods: e.g.,
randomised controlled trials, various kinds of observational study, meta-analysis, and
model-based approaches such as structural equation modelling and graphical causal
modelling. I argue that this is a mistake: causal inference is not a purely statistical
problem. When we look at causal inference from a general point of view, we see that
methods for causal inference fit into the framework of Evidential Pluralism: causal
inference is properly understood as requiring mechanistic inference in addition to
statistical inference.
Evidential Pluralism also offers a new perspective on the replication crisis. That
observed associations are not replicated by subsequent studies is a part of normal
science. A problem only arises when those associations are taken to establish causal
claims: a science whose established causal claims are constantly overturned is indeed
in crisis. However, if we understand causal inference as involving mechanistic inference
alongside statistical inference, as Evidential Pluralism suggests, we avoid fallacious
inferences from association to causation. Thus, Evidential Pluralism offers the means to
prevent the drama of science from turning into a crisis.
Stephan Guttinger (Lecturer in Philosophy of Data/Data Ethics, University of Exeter, UK)
ABSTRACT: The idea of “questionable research practices” (QRPs) is central to the narrative of a replication crisis in the experimental sciences. According to this narrative the low replicability of scientific findings is not simply due to fraud or incompetence, but in large part to the widespread use of QRPs, such as “p-hacking” or the lack of adequate experimental controls. The claim is that such flawed practices generate flawed output. The reduction – or even elimination – of QRPs is therefore one of the main strategies proposed by policymakers and scientists to tackle the replication crisis.
What counts as a QRP, however, is not clear. As I will discuss in the first part of this paper, there is no consensus on how to define the term, and ascriptions of the qualifier “questionable” often vary across disciplines, time, and even within single laboratories. This lack of clarity matters as it creates the risk of introducing methodological constraints that might create more harm than good. Practices labelled as ‘QRPs’ can be both beneficial and problematic for research practice and targeting them without a sound understanding of their dynamic and context-dependent nature risks creating unnecessary casualties in the fight for a more reliable scientific practice.
To start developing a more situated and dynamic picture of QRPs I will then turn my attention to a specific example of a dynamic QRP in the experimental life sciences, namely, the so-called “Far Western Blot” (FWB). The FWB is an experimental system that can be used to study protein-protein interactions but which for most of its existence has not seen a wide uptake in the community because it was seen as a QRP. This was mainly due to its (alleged) propensity to generate high levels of false positives and negatives. Interestingly, however, it seems that over the last few years the FWB slowly moved into the space of acceptable research practices. Analysing this shift and the reasons underlying it, I will argue a) that suppressing this practice deprived the research community of a powerful experimental tool and b) that the original judgment of the FWB was based on a simplistic and non-empirical assessment of its error-generating potential. Ultimately, it seems like the key QRP at work in the FWB case was the way in which the label “questionable” was assigned in the first place. I will argue that findings from this case can be extended to other QRPs in the experimental life sciences and that they point to a larger issue with how researchers judge the error-potential of new research practices.
David Hand (Professor Emeritus and Senior Research Investigator, Department of Mathematics,
Faculty of Natural Sciences, Imperial College London.)
ABSTRACT: Science progresses through an iterative process of formulating theories and comparing
them with empirical real-world data. Different camps of scientists will favour different
theories, until accumulating evidence renders one or more untenable. Not unnaturally,
people become attached to theories. Perhaps they invented a theory, and kudos arises
from being the originator of a generally accepted theory. A theory might represent a
life's work, so that being found wanting might be interpreted as failure. Perhaps
researchers were trained in a particular school, and acknowledging its shortcomings is
difficult. Because of this, tensions can arise between proponents of different theories.
The discipline of statistics is susceptible to precisely the same tensions. Here, however,
the tensions are not between different theories of "what is", but between different
strategies for shedding light on the real world from limited empirical data. This can be in
the form of how one measures discrepancy between the theory's predictions and
observations. It can be in the form of different ways of looking at empirical results. It can
be, at a higher level, because of differences between what is regarded as important in a
particular context. Or it can be for other reasons.
Perhaps the most familiar example of this tension within statistics is between different
approaches to inference. However, there are many other examples of such tensions.
This paper illustrates with several examples. We argue that the tension generally arises
as a consequence of inadequate care being taken in question formulation. That is,
insufficient thought is given to deciding exactly what one wants to know - to determining
"What is the question?".
The ideas and disagreements are illustrated with several examples.
The neglected importance of complexity in statistics and Metasciencejemille6
Daniele Fanelli
London School of Economics Fellow in Quantitative Methodology, Department of
Methodology, London School of Economics and Political Science.
ABSTRACT: Statistics is at war, and Metascience is ailing. This is partially due, the talk will argue, to
a paradigmatic blind-spot: the assumption that one can draw general conclusions about
empirical findings without considering the role played by context, conditions,
assumptions, and the complexity of methods and theories. Whilst ideally these
particularities should be unimportant in science, in practice they cannot be neglected in
most research fields, let alone in research-on-research.
This neglected importance of complexity is supported by theoretical arguments and
empirical findings (or the lack thereof) in the recent meta-analytical and metascientific
literature. The talk will overview this background and suggest how the complexity of
theories and methodologies may be explicitly factored into particular methodologies of
statistics and Metaresearch. The talk will then give examples of how this approach may
usefully complement existing paradigms, by translating results, methods and theories
into quantities of information that are evaluated using an information-compression logic.
Mathematically Elegant Answers to Research Questions No One is Asking (meta-a...jemille6
Uri Simonsohn (Professor, Department of Operations, Innovation and Data Sciences at Esade)
ABSTRACT: The statistical tools listed in the title share that a mathematically elegant solution has
become the consensus advice of statisticians, methodologists and some
mathematically sophisticated researchers writing tutorials and textbooks, and yet,
they lead research workers to meaningless answers, that are often also statistically
invalid. Part of the problem is that advice givers take the mathematical abstractions
of the tools they advocate for literally, instead of taking the actual behavior of
researchers seriously.
On Severity, the Weight of Evidence, and the Relationship Between the Twojemille6
Margherita Harris
Visiting fellow in the Department of Philosophy, Logic and Scientific Method at the London
School of Economics and Political Science.
ABSTRACT: According to the severe tester, one is justified in declaring to have evidence in support of a
hypothesis just in case the hypothesis in question has passed a severe test, one that it would be very
unlikely to pass so well if the hypothesis were false. Deborah Mayo (2018) calls this the strong
severity principle. The Bayesian, however, can declare to have evidence for a hypothesis despite not
having done anything to test it severely. The core reason for this has to do with the
(infamous) likelihood principle, whose violation is not an option for anyone who subscribes to the
Bayesian paradigm. Although the Bayesian is largely unmoved by the incompatibility between
the strong severity principle and the likelihood principle, I will argue that the Bayesian’s never-ending
quest to account for yet an other notion, one that is often attributed to Keynes (1921) and that is
usually referred to as the weight of evidence, betrays the Bayesian’s confidence in the likelihood
principle after all. Indeed, I will argue that the weight of evidence and severity may be thought of as
two (very different) sides of the same coin: they are two unrelated notions, but what brings them
together is the fact that they both make trouble for the likelihood principle, a principle at the core of
Bayesian inference. I will relate this conclusion to current debates on how to best conceptualise
uncertainty by the IPCC in particular. I will argue that failure to fully grasp the limitations of an
epistemology that envisions the role of probability to be that of quantifying the degree of belief to
assign to a hypothesis given the available evidence can be (and has been) detrimental to an
adequate communication of uncertainty.
Revisiting the Two Cultures in Statistical Modeling and Inference as they rel...jemille6
Aris Spanos (Wilson Schmidt Professor of Economics, Virginia Tech)
ABSTRACT: The discussion places the two cultures, the model-driven statistical modeling and the
algorithm-driven modeling associated with Machine Learning (ML) and Statistical
Learning Theory (SLT) in a broader context of paradigm shifts in 20th-century statistics,
which includes Fisher’s model-based induction of the 1920s and variations/extensions
thereof, the Data Science (ML, STL, etc.) and the Graphical Causal modeling in the
1990s. The primary objective is to compare and contrast the effectiveness of different
approaches to statistics in learning from data about phenomena of interest and relate
that to the current discussions pertaining to the statistics wars and their potential
casualties.
Comparing Frequentists and Bayesian Control of Multiple Testingjemille6
James Berger
ABSTRACT: A problem that is common to many sciences is that of having to deal with a multiplicity of statistical inferences. For instance, in GWAS (Genome Wide Association Studies), an experiment might consider 20 diseases and 100,000 genes, and conduct statistical tests of the 20x100,000=2,000,000 null hypotheses that a specific disease is associated with a specific gene. The issue is that selective reporting of only the ‘highly significant’ results could lead to many claimed disease/gene associations that turn out to be false, simply because of statistical randomness. In 2007, the seriousness of this problem was recognized in GWAS and extremely stringent standards were employed to resolve it. Indeed, it was recommended that tests for association should be conducted at an error probability of 5 x 10—7. Particle physicists similarly learned that a discovery would be reliably replicated only if the p-value of the relevant test was less than 5.7 x 10—7. This was because they had to account for a huge number of multiplicities in their analyses. Other sciences have continuing issues with multiplicity. In the Social Sciences, p-hacking and data dredging are common, which involve multiple analyses of data. Stopping rules in social sciences are often ignored, even though it has been known since 1933 that, if one keeps collecting data and computing the p-value, one is guaranteed to obtain a p-value less than 0.05 (or, indeed, any specified value), even if the null hypothesis is true. In medical studies that occur with strong oversight (e.g., by the FDA), control for multiplicity is mandated. There is also typically a large amount of replication, resulting in meta-analysis. But there are many situations where multiplicity is not handled well, such as subgroup analysis: one first tests for an overall treatment effect in the population; failing to find that, one tests for an effect among men or among women; failing to find that, one tests for an effect among old men or young men, or among old women or young women; …. I will argue that there is a single method that can address any such problems of multiplicity: Bayesian analysis, with the multiplicity being addressed through choice of prior probabilities of hypotheses. ... There are, of course, also frequentist error approaches (such as Bonferroni and FDR) for handling multiplicity of statistical inferences; indeed, these are much more familiar than the Bayesian approach. These are, however, targeted solutions for specific classes of problems and are not easily generalizable to new problems.
Clark Glamour
ABSTRACT: "Data dredging"--searching non experimental data for causal and other relationships and taking that same data to be evidence for those relationships--was historically common in the natural sciences--the works of Kepler, Cannizzaro and Mendeleev are examples. Nowadays, "data dredging"--using data to bring hypotheses into consideration and regarding that same data as evidence bearing on their truth or falsity--is widely denounced by both philosophical and statistical methodologists. Notwithstanding, "data dredging" is routinely practiced in the human sciences using "traditional" methods--various forms of regression for example. The main thesis of my talk is that, in the spirit and letter of Mayo's and Spanos’ notion of severe testing, modern computational algorithms that search data for causal relations severely test their resulting models in the process of "constructing" them. My claim is that in many investigations, principled computerized search is invaluable for reliable, generalizable, informative, scientific inquiry. The possible failures of traditional search methods for causal relations, multiple regression for example, are easily demonstrated by simulation in cases where even the earliest consistent graphical model search algorithms succeed. ... These and other examples raise a number of issues about using multiple hypothesis tests in strategies for severe testing, notably, the interpretation of standard errors and confidence levels as error probabilities when the structures assumed in parameter estimation are uncertain. Commonly used regression methods, I will argue, are bad data dredging methods that do not severely, or appropriately, test their results. I argue that various traditional and proposed methodological norms, including pre-specification of experimental outcomes and error probabilities for regression estimates of causal effects, are unnecessary or illusory in application. Statistics wants a number, or at least an interval, to express a normative virtue, the value of data as evidence for a hypothesis, how well the data pushes us toward the true or away from the false. Good when you can get it, but there are many circumstances where you have evidence but there is no number or interval to express it other than phony numbers with no logical connection with truth guidance. Kepler, Darwin, Cannizarro, Mendeleev had no such numbers, but they severely tested their claims by combining data dredging with severe testing.
The Duality of Parameters and the Duality of Probabilityjemille6
Suzanne Thornton
ABSTRACT: Under any inferential paradigm, statistical inference is connected to the logic of probability. Well-known debates among these various paradigms emerge from conflicting views on the notion of probability. One dominant view understands the logic of probability as a representation of variability (frequentism), and another prominent view understands probability as a measurement of belief (Bayesianism). The first camp generally describes model parameters as fixed values, whereas the second camp views parameters as random. Just as calibration (Reid and Cox 2015, “On Some Principles of Statistical Inference,” International Statistical Review 83(2), 293-308)--the behavior of a procedure under hypothetical repetition--bypasses the need for different versions of probability, I propose that an inferential approach based on confidence distributions (CD), which I will explain, bypasses the analogous conflicting perspectives on parameters. Frequentist inference is connected to the logic of probability through the notion of empirical randomness. Sample estimates are useful only insofar as one has a sense of the extent to which the estimator may vary from one random sample to another. The bounds of a confidence interval are thus particular observations of a random variable, where the randomness is inherited by the random sampling of the data. For example, 95% confidence intervals for parameter θ can be calculated for any random sample from a Normal N(θ, 1) distribution. With repeated sampling, approximately 95% of these intervals are guaranteed to yield an interval covering the fixed value of θ. Bayesian inference produces a probability distribution for the different values of a particular parameter. However, the quality of this distribution is difficult to assess without invoking an appeal to the notion of repeated performance. ... In contrast to a posterior distribution, a CD is not a probabilistic statement about the parameter, rather it is a data-dependent estimate for a fixed parameter for which a particular behavioral property holds. The Normal distribution itself, centered around the observed average of the data (e.g. average recovery times), can be a CD for θ. It can give any level of confidence. Such estimators can be derived through Bayesian or frequentist inductive procedures, and any CD, regardless of how it is obtained, guarantees performance of the estimator under replication for a fixed target, while simultaneously producing a random estimate for the possible values of θ.
Paper given at PSA 22 Symposium: Multiplicity, Data-Dredging and Error Control
MAYO ABSTRACT: I put forward a general principle for evidence: an error-prone claim C is warranted to the extent it has been subjected to, and passes, an analysis that very probably would have found evidence of flaws in C just if they are present. This probability is the severity with which C has passed the test. When a test’s error probabilities quantify the capacity of tests to probe errors in C, I argue, they can be used to assess what has been learned from the data about C. A claim can be probable or even known to be true, yet poorly probed by the data and model at hand. The severe testing account leads to a reformulation of statistical significance tests: Moving away from a binary interpretation, we test several discrepancies from any reference hypothesis and report those well or poorly warranted. A probative test will generally involve combining several subsidiary tests, deliberately designed to unearth different flaws. The approach relates to confidence interval estimation, but, like confidence distributions (CD) (Thornton), a series of different confidence levels is considered. A 95% confidence interval method, say using the mean M of a random sample to estimate the population mean μ of a Normal distribution, will cover the true, but unknown, value of μ 95% of the time in a hypothetical series of applications. However, we cannot take .95 as the probability that a particular interval estimate (a ≤ μ ≤ b) is correct—at least not without a prior probability to μ. In the severity interpretation I propose, we can nevertheless give an inferential construal post-data, while still regarding μ as fixed. For example, there is good evidence μ ≥ a (the lower estimation limit) because if μ < a, then with high probability .95 (or .975 if viewed as one-sided) we would have observed a smaller value of M than we did. Likewise for inferring μ ≤ b. To understand a method’s capability to probe flaws in the case at hand, we cannot just consider the observed data, unlike in strict Bayesian accounts. We need to consider what the method would have inferred if other data had been observed. For each point μ’ in the interval, we assess how severely the claim μ > μ’ has been probed. I apply the severity account to the problems discussed by earlier speakers in our session. The problem with multiple testing (and selective reporting) when attempting to distinguish genuine effects from noise, is not merely that it would, if regularly applied, lead to inferences that were often wrong. Rather, it renders the method incapable, or practically so, of probing the relevant mistaken inference in the case at hand. In other cases, by contrast, (e.g., DNA matching) the searching can increase the test’s probative capacity. In this way the severe testing account can explain competing intuitions about multiplicity and data-dredging, while blocking inferences based on problematic data-dredging
The Statistics Wars and Their Causalities (refs)jemille6
High-profile failures of replication in the social and biological sciences underwrite a
minimal requirement of evidence: If little or nothing has been done to rule out flaws in inferring a claim, then it has not passed a severe test. A claim is severely tested to the extent it has been subjected to and passes a test that probably would have found flaws, were they present. This probability is the severity with which a claim has passed. The goal of highly well-tested claims differs from that of highly probable ones, explaining why experts so often disagree about statistical reforms. Even where today’s statistical test critics see themselves as merely objecting to misuses and misinterpretations, the reforms they recommend often grow out of presuppositions about the role of probability in inductive-statistical inference. Paradoxically, I will argue, some of the reforms intended to replace or improve on statistical significance tests enable rather than reveal illicit inferences due to cherry-picking, multiple testing, and data-dredging. Some preclude testing and falsifying claims altogether. These are the “casualties” on which I will focus. I will consider Fisherian vs Neyman-Pearson tests, Bayes factors, Bayesian posteriors, likelihoodist assessments, and the “screening model” of tests (a quasiBayesian-frequentist assessment). Whether one accepts this philosophy of evidence, I argue, that it provides a standpoint for avoiding both the fallacies of statistical testing and the casualties of today’s statistics wars.
The Statistics Wars and Their Casualties (w/refs)jemille6
High-profile failures of replication in the social and biological sciences underwrite a minimal requirement of evidence: If little or nothing has been done to rule out flaws in inferring a claim, then it has not passed a severe test. A claim is severely tested to the extent it has been subjected to and passes a test that probably would have found flaws, were they present. This probability is the severity with which a claim has passed. The goal of highly well-tested claims differs from that of highly probable ones, explaining why experts so often disagree about statistical reforms. Even where today’s statistical test critics see themselves as merely objecting to misuses and misinterpretations, the reforms they recommend often grow out of presuppositions about the role of probability in inductive-statistical inference. Paradoxically, I will argue, some of the reforms intended to replace or improve on statistical significance tests enable rather than reveal illicit inferences due to cherry-picking, multiple testing, and data-dredging. Some preclude testing and falsifying claims altogether. These are the “casualties” on which I will focus. I will consider Fisherian vs Neyman-Pearson tests, Bayes factors, Bayesian posteriors, likelihoodist assessments, and the “screening model” of tests (a quasi-Bayesian-frequentist assessment). Whether one accepts this philosophy of evidence, I argue, that it provides a standpoint for avoiding both the fallacies of statistical testing and the casualties of today’s statistics wars.
On the interpretation of the mathematical characteristics of statistical test...jemille6
Statistical hypothesis tests are often misused and misinterpreted. Here I focus on one
source of such misinterpretation, namely an inappropriate notion regarding what the
mathematical theory of tests implies, and does not imply, when it comes to the
application of tests in practice. The view taken here is that it is helpful and instructive to be consciously aware of the essential difference between mathematical model and
reality, and to appreciate the mathematical model and its implications as a tool for
thinking rather than something that has a truth value regarding reality. Insights are presented regarding the role of model assumptions, unbiasedness and the alternative hypothesis, Neyman-Pearson optimality, multiple and data dependent testing.
The two statistical cornerstones of replicability: addressing selective infer...jemille6
Tukey’s last published work in 2020 was an obscure entry on multiple comparisons in the
Encyclopedia of Behavioral Sciences, addressing the two topics in the title. Replicability
was not mentioned at all, nor was any other connection made between the two topics. I shall demonstrate how these two topics critically affect replicability using recently completed studies. I shall review how these have been addressed in the past. I shall
review in more detail the available ways to address selective inference. My conclusion is that conducting many small replicability studies without strict standardization is the way to assure replicability of results in science, and we should introduce policies to make this happen.
The replication crisis: are P-values the problem and are Bayes factors the so...jemille6
Today’s posterior is tomorrow’s prior. Dennis Lindley
It has been claimed that science is undergoing a replication crisis and that when looking for culprits, the cult of significance is the chief suspect. It has also been claimed that Bayes factors might provide a solution.
In my opinion, these claims are misleading and part of the problem is our understanding
of the purpose and nature of replication, which has only recently been subject to formal
analysis.
What we are or should be interested in is truth. Replication is a coherence not a correspondence requirement and one that has a strong dependence on the size
of the replication study
.
Consideration of Bayes factors raises a puzzling question. Should the Bayes factor for a replication study be calculated as if it were the initial study? If the answer is yes, the approach is not fully Bayesian and furthermore the Bayes factors will be subject to
exactly the same replication ‘paradox’ as P-values. If the answer is no, then in what
sense can an initially found Bayes factor be replicated and what are the implications for how we should view replication of P-values?
A further issue is that little attention has been paid to false negatives and, by extension
to true negative values. Yet, as is well known from the theory of diagnostic tests, it is
meaningless to consider the performance of a test in terms of false positives alone.
I shall argue that we are in danger of confusing evidence with the conclusions we draw and that any reforms of scientific practice should concentrate on producing evidence
that is reliable as it can be qua evidence. There are many basic scientific practices in
need of reform. Pseudoreplication, for example, and the routine destruction of
information through dichotomisation are far more serious problems than many matters of inferential framing that seem to have excited statisticians.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Francesca Gottschalk - How can education support child empowerment.pptxEduSkills OECD
Francesca Gottschalk from the OECD’s Centre for Educational Research and Innovation presents at the Ask an Expert Webinar: How can education support child empowerment?
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
Advantages and Disadvantages of CMS from an SEO Perspective
Final mayo's aps_talk
1.
Final APS Mayo / 1
Error Statistical Control: Forfeit at your Peril
Deborah Mayo
• A central task of philosophers of science is to address
conceptual, logical, methodological discomforts of
scientific practices—still we’re rarely called in
• Psychology has always been more self-conscious than most
• To its credit, replication crises led to programs to restore
credibility: fraud busting, reproducibility studies.
• There are proposed methodological reforms––many
welcome, some of them quite radical
• Without a better understanding of the problems, many
reforms are likely to leave us worse off.
2.
Final APS Mayo / 2
1. A Paradox for Significance Test Critics
Critic1: It’s much too easy to get a small P-value.
Critic2: We find it very difficult to replicate the small P-values
others found.
Is it easy or is it hard?
R.A. Fisher: it’s easy to lie with statistics by selective reporting
(he called it the “political principle”)
Sufficient finagling—cherry-picking, P-hacking, significance
seeking—may practically guarantee a researcher’s preferred
hypothesis gets support, even if it’s unwarranted by evidence.
3.
Final APS Mayo / 3
2. Bad Statistics
Severity Requirement: If data x0 agree with a hypothesis
H, but the test procedure had little or no capability, i.e.,
little or no probability of finding flaws with H (even if H is
incorrect), then x0 provide poor evidence for H.
Such a test we would say fails a minimal requirement for a
stringent or severe test.
• This seems utterly uncontroversial.
4.
Final APS Mayo / 4
• Methods that scrutinize a test’s capabilities, according to
their severity, I call error statistical.
• Existing error probabilities (confidence levels, significance
levels) may but need not provide severity assessments.
• New name: frequentist, sampling theory, Fisherian,
Neyman-Pearsonian—are too associated with hard line
views.
5.
Final APS Mayo / 5
3. Two main views of the role of probability in inference
Probabilism. To provide an assignment of degree of
probability, confirmation, support or belief in a hypothesis,
absolute or comparative, given data x0. (e.g., Bayesian,
likelihoodist)—with due regard for inner coherency
Performance. To ensure long-run reliability of methods,
coverage probabilities, control the relative frequency of
erroneous inferences in a long-run series of trials (behavioristic
Neyman-Pearson)
What happened to using probability to assess the error probing
capacity by the severity criterion?
6.
Final APS Mayo / 6
• Neither “probabilism” nor “performance” directly captures
it.
• Good long-run performance is a necessary, not a sufficient,
condition for avoiding insevere tests.
• The problems with selective reporting, cherry picking,
stopping when the data look good, P-hacking, barn hunting,
are not problems about long-runs—
• It’s that we cannot say about the case at hand that it has
done a good job of avoiding the sources of misinterpreting
data.
7.
Final APS Mayo / 7
• Probabilism
says
H
is
not
warranted
unless
it’s
true
or
probable
(or
increases
probability,
makes
firmer–some
use
Bayes
rule,
but
its
use
doesn’t
make
you
Bayesian).
• Performance
says
H
is
not
warranted
unless
it
stems
from
a
method
with
low
long-‐run
error.
• Error
Statistics
(Probativism)
says
H
is
not
warranted
unless
something
(a
fair
amount)
has
been
done
to
probe
ways
we
can
be
wrong
about
H.
8.
Final APS Mayo / 8
• If
you
assume
probabilism
is
required
for
inference,
it
follows
error
probabilities
are
relevant
for
inference
only
by
misinterpretation.
False!
• Error
probabilities
have
a
crucial
role
in
appraising
well-‐
testedness,
which
is
very
different
from
appraising
believability,
plausibility,
confirmation.
• It’s
crucial
to
be
able
to
say,
H
is
highly
believable
or
plausible
but
poorly
tested.
[Both
H
and
not-‐H
may
be
poorly
tested)
• Probabilists
can
allow
for
the
distinct
task
of
severe
testing
9.
Final APS Mayo / 9
• It’s not that I’m keen to defend many common uses of
significance tests; my
work
in
philosophy
of
statistics
has
been
to
provide
the
long
sought
“evidential
interpretation”
(Birnbaum)
of
frequentist
methods,
to
avoid
classic
fallacies.
• It’s just that the criticisms are based on serious
misunderstandings of the nature and role of these methods;
consequently so are many “reforms”.
• Note: The severity construal blends testing and subsumes
(improves) interval estimation, but I keep to testing talk to
underscore the probative demand.
10.
Final APS Mayo / 10
4.
Biasing
selection
effects:
One
function
of
severity
is
to
identify
which
selection
effects
are
problematic
(not
all
are)
Biasing
selection
effects:
when
data
or
hypotheses
are
selected
or
generated
(or
a
test
criterion
is
specified),
in
such
a
way
that
the
minimal
severity
requirement
is
violated,
seriously
altered
or
incapable
of
being
assessed.
Picking up on these alterations is precisely what enables error
statistics to be self-correcting—
Let me illustrate.
11.
Final APS Mayo / 11
Capitalizing
on
Chance
We
often
see
articles
on
fallacious
significance
levels:
When
the
hypotheses
are
tested
on
the
same
data
that
suggested
them
and
when
tests
of
significance
are
based
on
such
data,
then
a
spurious
impression
of
validity
may
result.
The
computed
level
of
significance
may
have
almost
no
relation
to
the
true
level…Suppose
that
twenty
sets
of
differences
have
been
examined,
that
one
difference
seems
large
enough
to
test
and
that
this
difference
turns
out
to
be
‘significant
at
the
5
percent
level.’
….The
actual
level
of
significance
is
not
5
percent,
but
64
percent!
(Selvin,
1970,
p.
104)
12.
Final APS Mayo / 12
• This
is
from
a
contributor
to
Morrison
and
Henkel’s
Significance
Test
Controversy
way
back
in
1970!
• They
were
clear
on
the
fallacy:
blurring
the
“computed”
or
“nominal”
significance
level,
and
the
“actual”
or
“warranted”
level.
• There
are
many
more
ways
you
can
be
wrong
with
hunting
(different
sample
space).
• Nowadays,
we’re
likely
to
see
the
tests
blamed
for
permitting
such
misuses
(instead
of
the
testers).
• Even
worse
are
those
statistical
accounts
where
the
abuse
vanishes!
13.
Final APS Mayo / 13
What
defies
scientific
sense?
On
some
views,
biasing
selection
effects
are
irrelevant….
Stephen
Goodman
(epidemiologist):
Two
problems
that
plague
frequentist
inference:
multiple
comparisons
and
multiple
looks,
or,
as
they
are
more
commonly
called,
data
dredging
and
peeking
at
the
data.
The
frequentist
solution
to
both
problems
involves
adjusting
the
P-‐value…But
adjusting
the
measure
of
evidence
because
of
considerations
that
have
nothing
to
do
with
the
data
defies
scientific
sense,
belies
the
claim
of
‘objectivity’
that
is
often
made
for
the
P-‐value.”
(1999,
p.
1010).
14.
Final APS Mayo / 14
5.
Likelihood
Principle
(LP)
The
vanishing
act
takes
us
to
the
pivot
point
around
which
much
debate
in
philosophy
of
statistics
revolves:
In probabilisms, the import of the data is via the ratios of
likelihoods of hypotheses
P(x0;H1)/P(x0;H0)
Different
forms:
posterior
probabilities,
positive
B-‐boost,
Bayes
factor
The
data
x0
is
fixed,
while
the
hypotheses
vary
15.
Final APS Mayo / 15
Savage on the LP:
“According to Bayes’s theorem, P(x|µ)...constitutes the entire
evidence of the experiment, that is, it tells all that the
experiment has to tell. More fully and more precisely, if y is
the datum of some other experiment, and if it happens that
P(x|µ) and P(y|µ) are proportional functions of µ (that is,
constant multiples of each other), then each of the two data x
and y have exactly the same thing to say about the values of
µ… (Savage 1962, p. 17).
16.
Final APS Mayo / 16
All
error
probabilities
violate
the
LP
(even
without
selection
effects):
“Sampling
distributions,
significance
levels,
power,
all
depend
on
something
more
[than
the
likelihood
function]–something
that
is
irrelevant
in
Bayesian
inference–namely
the
sample
space”.
(Lindley
1971,
p.
436)
That is why properties of the sampling distribution of test
statistic d(X) disappear for accounts that condition on the
particular data x0
17.
Final APS Mayo / 17
Paradox
of
Optional
Stopping:
Error
probing
capabilities
are
altered
not
just
by
cherry
picking
and
data
dredging,
but
also
via
data
dependent
stopping
rules:
We
have
a
random
sample
from
a
Normal
distribution
with
mean
µ
and
standard
deviation
σ, Xi
~
N(µ,σ2
),
2-‐sided
H0:
µ
=
0
vs.
H1:
µ
≠
0.
Instead
of
fixing
the
sample
size
n
in
advance,
in
some
tests,
n
is
determined
by
a
stopping
rule:
Keep
sampling
until
H0
is
rejected
at
the
.05
level
i.e.,
keep
sampling
until
| 𝑋|
≥
1.96
σ/ 𝑛.
18.
Final APS Mayo / 18
“Trying
and
trying
again”:
having
failed
to
rack
up
a
1.96
SD
difference
after,
say,
10
trials,
the
researcher
went
on
to
20,
30
and
so
on
until
finally
obtaining
a
1.96
SD
difference.
Nominal
vs.
Actual
significance
levels:
with
n
fixed
the
type
1
error
probability
is
.05.
With
this
stopping
rule
the
actual
significance
level
differs
from,
and
will
be
greater
than
.05.
19.
Final APS Mayo / 19
Jimmy
Savage
(1959
forum)
audaciously
declared:
“optional
stopping
is
no
sin”
so
the
problem
must
be
with
significance
levels
(because
they
pick
up
on
it).
On
the
other
side:
Peter
Armitage,
who
had
brought
up
the
problem,
also
uses
biblical
language
“thou
shalt
be
misled”
if
thou
dost
not
know
the
person
tried
and
tried
again.
(72)
20.
Final APS Mayo / 20
Where the Bayesians here claim:
“This irrelevance of stopping rules to statistical inference restores a
simplicity and freedom to experimental design that had been lost
by classical emphasis on significance levels” (in the sense of
Neyman and Pearson) (Edwards, Lindman, Savage 1963, p. 239).
The frequentists:
While it may restore "simplicity and freedom" it does so at the
cost of being unable to adequately control probabilities of
misleading interpretations of data) (Birnbaum).
21.
Final APS Mayo / 21
6. Current Reforms are Probabilist
Probabilist reforms to replace tests (and CIs) with likelihood
ratios, Bayes factors, HPD intervals, or just lower the P-value
(so that the maximal likely alternative gets .95 posterior)
while ignoring biasing selection effects, will fail
The same p-hacked hypothesis can occur in Bayes factors;
optional stopping can exclude true nulls from HPD intervals
With one big difference: Your direct basis for criticism and
possible adjustments has just vanished
To repeat: Properties of the sampling distribution d(x)
disappear for accounts that condition on the particular data.
22.
Final APS Mayo / 22
7. How might probabilists block intuitively unwarranted
inferences? (Consider first subjective)
When we hear there’s statistical evidence of some unbelievable
claim (distinguishing shades of grey and being politically
moderate, ovulation and voting preferences), some probabilists
claim—you see, if our beliefs were mixed into the
interpretation of the evidence, we wouldn’t be fooled.
We know these things are unbelievable, a subjective Bayesian
might say.
That could work in some cases (though it still wouldn’t show
what researchers had done wrong)—battle of beliefs.
23.
Final APS Mayo / 23
It wouldn’t help with our most important problem: (2 critics)
How to distinguish the warrant for a single hypothesis H with
different methods (e.g., one has biasing selection effects,
another, registered results and precautions)?
Besides, as committees investigating questionable practices
know, researchers really do sincerely believe their hypotheses.
So now you’ve got two sources of flexibility, priors and
biasing selection effects (which can no longer be criticized).
24.
Final APS Mayo / 24
8.
Conventional:
Bayesian-‐Frequentist
reconciliations?
The most popular probabilisms these days are non-subjective,
default, reference:
• because of the difficulty of eliciting subjective priors,
• the reluctance of scientists to allow subjective beliefs to
overshadow the information provided by data.
Default,
or
reference
priors
are
designed
to
prevent
prior
beliefs
from
influencing
the
posteriors.
• A
classic
conundrum:
no
general
non-‐informative
prior
exists,
so
most
are
conventional.
25.
Final APS Mayo / 25
“The
priors
are
not
to
be
considered
expressions
of
uncertainty,
ignorance,
or
degree
of
belief.
Conventional
priors
may
not
even
be
probabilities…”
(Cox
and
Mayo
2010,
p.
299)
• Prior probability: An undefined mathematical construct
for obtaining posteriors (giving highest weight to data,
or satisfying invariance, or matching frequentists,
or….).
Leading conventional Bayesians (J. Berger) still tout their
methods as free of concerns with selection effects, stopping
rules (stopping rule principle)
26.
Final APS Mayo / 26
There are some Bayesians who don’t see themselves as fitting
under either the subjective or conventional heading, and may
even reject probabilism…..
27.
Final APS Mayo / 27
Before concluding…I don’t ignore fallacies of current methods
9. How
the
severity
analysis
avoids
classic
fallacies
Fallacies
of
Rejection:
Statistical
vs.
Substantive
Significance
i. Take
statistical
significance
as
evidence
of
substantive
theory
H*
that
explains
the
effect.
ii. Infer
a
discrepancy
from
the
null
beyond
what
the
test
warrants.
(i) Handled
with
severity:
flaws
in
the
substantive
alternative
H*
have
not
been
probed
by
the
test,
the
inference
from
a
statistically
significant
result
to
H*
fails
to
pass
with
severity.
28.
Final APS Mayo / 28
Merely refuting the null hypothesis is too weak to corroborate
substantive H*, “we have to have ‘Popperian risk’, ‘severe test’
[as in Mayo], or what philosopher Wesley Salmon called ‘a
highly improbable coincidence’” (Meehl and Waller 2002,184).
• NHSTs
(supposedly)
allow
moving
from
statistical
to
substantive;
if
so,
they
exist
only
as
abuses
of
tests:
they
are
not
licensed
by
any
legitimate
test.
• Severity
applies
informally:
Much
more
attention
to
these
quasi-‐formal
statistical
substantive
links:
Do
those
proxy
variables
capture
the
intended
treatments?
Do
the
measurements
reflect
the
theoretical
phenomenon?
29.
Final APS Mayo / 29
Fallacies
of
Rejection:
(ii)
Infer
a
discrepancy
beyond
what’s
warranted:
Severity
sets
up
a
discrepancy
parameter
γ (never
just
report
P-‐value)
A
statistically
significant
effect
may
not
warrant
a
meaningful
effect
—
especially
with n sufficiently large:
large
n
problem.
• Severity
tells
us:
an
α-‐significant
difference
is
indicative
of
less
of
a
discrepancy
from
the
null
if
it
results
from
larger
(n1)
rather
than
a
smaller
(n2)
sample
size
(n1
>
n2
)
What’s
more
indicative
of
a
large
effect
(fire),
a
fire
alarm
that
goes
off
with
burnt
toast
or
one
so
insensitive
that
it
doesn’t
go
off
unless
the
house
is
fully
ablaze?
The
larger
sample
size
is
like
the
one
that
goes
off
with
burnt
toast.)
30.
Final APS Mayo / 30
Fallacy
of
Non-‐Significant
results:
Insensitive
tests
• Negative
results
do
not
warrant
0
discrepancy
from
the
null,
but
we
can
use
severity
to
rule
out
discrepancies
that,
with
high
probability,
would
have
resulted
in
a
larger
difference
than
observed
• akin
to
power
analysis
(Cohen)
but
sensitive
to
x0
• We
hear
sometimes
negative
results
are
uninformative:
not
so.
No
point
in
running
replication
research
if
your
account
views
negative
results
as
uninformative
31.
Final APS Mayo / 31
Confidence
Intervals
also
require
supplementing
There’s
a
duality
between
tests
and
intervals:
values
within
the
(1
-‐
α)
CI
are
non-‐rejectable
at
the
α
level
(but
that
doesn’t
make
them
well-‐warranted)
• Still
too
dichotomous:
in
/out,
plausible/not
plausible
(Permit
fallacies
of
rejection/non-‐rejection)
• Justified
in
terms
of
long-‐run
coverage
• All
members
of
the
CI
treated
on
par
• Fixed
confidence
levels
(SEV
need
several
benchmarks)
• Estimation
is
important
but
we
need
tests
for
distinguishing
real
and
spurious
effects,
and
checking
assumptions
of
statistical
models
32.
Final APS Mayo / 32
10.
Error
Statistical
Control:
Forfeit
at
your
Peril
• The
role
of
error
probabilities
in
inference,
is
not
long-‐
run
error
control,
but
to
severely
probe
flaws
in
your
inference
today.
• It’s
not
a
high
posterior
probability
in
H
that’s
wanted
(however
construed)
but
a
high
probability
our
procedure
would
have
unearthed
flaws
in
H.
• Many
reforms
are
based
on
assuming
a
philosophy
of
probabilism
• The
danger
is
that
some
reforms
may
enable
rather
than
directly
reveal
illicit
inferences
due
to
biasing
selection
effects.
33.
Final APS Mayo / 33
Mayo
and
Cox
(2010):
Frequentist
Principle
of
Evidence
(FEV);
SEV:
Mayo
and
Spanos
(2006)
• FEV/SEV:
insignificant
result:
A
moderate
P-‐value
is
evidence
of
the
absence
of
a
discrepancy
δ
from
H0,
only
if
there
is
a
high
probability
the
test
would
have
given
a
worse
fit
with
H0
(i.e.,
d(X) > d(x0)
)
were
a
discrepancy
δ
to
exist.
• FEV/SEV
significant
result
d(X) > d(x0)
is
evidence
of
discrepancy
δ
from
H0,
if
and
only
if,
there
is
a
high
probability
the
test
would
have
d(X) <
d(x0)
were
a
discrepancy
as
large
as
δ
absent.
34.
Final APS Mayo / 34
Test
T+:
Normal
testing:
H0:
µ
<
µ0
vs.
H1:
µ
>
µ0
σ
known
(FEV/SEV):
If
d(x)
is
not
statistically
significant,
then
µ
<
M0
+
kεσ/√𝑛 passes
the
test
T+
with
severity
(1
–
ε).
(FEV/SEV):
If
d(x)
is
statistically
significant,
then
µ
>
M0
+
kεσ/√𝑛 passes
the
test
T+
with
severity
(1
–
ε).
where
P(d(X)
>
kε)
=
ε.
35.
Final APS Mayo / 35
REFERENCES:
Armitage, P. 1962. “Contribution to Discussion.” In The Foundations of Statistical Inference:
A Discussion, edited by L. J. Savage. London: Methuen.
Barnard, G. A. 1972. “The Logic of Statistical Inference (review of ‘The Logic of Statistical
Inference’ by Ian Hacking).” British Journal for the Philosophy of Science 23 (2) (May
1): 123–132.
Berger, J. O. 2006. “The Case for Objective Bayesian Analysis.” Bayesian Analysis 1 (3): 385–
402.
Birnbaum, A. 1970. “Statistical Methods in Scientific Inference (letter to the Editor).” Nature
225 (5237) (March 14): 1033.
Cox, D. R., and Deborah G. Mayo. 2010. “Objectivity and Conditionality in Frequentist
Inference.” In Error and Inference: Recent Exchanges on Experimental Reasoning,
Reliability, and the Objectivity and Rationality of Science, edited by Deborah G. Mayo
and Aris Spanos, 276–304. Cambridge: Cambridge University Press.
Edwards, W., H. Lindman, and L. J. Savage. 1963. “Bayesian Statistical Inference for
Psychological Research.” Psychological Review 70 (3): 193–242.
Fisher, R. A. 1955. “Statistical Methods and Scientific Induction.” Journal of the Royal
Statistical Society, Series B (Methodological) 17 (1) (January 1): 69–78.
Goodman SN. Toward evidence-based medical statistics. 2: The Bayes factor. Annals of
Internal Medicine 1999; 130:1005 –1013.
36.
Final APS Mayo / 36
Lindley, D. V. 1971. “The Estimation of Many Parameters.” In Foundations of Statistical
Inference, edited by V. P. Godambe and D. A. Sprott, 435–455. Toronto: Holt, Rinehart
and Winston.
Mayo, D. G. 1996. Error and the Growth of Experimental Knowledge. Science and Its
Conceptual Foundation. Chicago: University of Chicago Press.
Mayo, D. G., and A. Spanos. 2006. “Severe Testing as a Basic Concept in a Neyman–Pearson
Philosophy of Induction.” British Journal for the Philosophy of Science 57 (2) (June 1):
323–357.
Mayo, D. G., and A. Spanos. 2011. “Error Statistics.” In Philosophy of Statistics, edited by
Prasanta S. Bandyopadhyay and Malcom R. Forster, 7:152–198. Handbook of the
Philosophy of Science. The Netherlands: Elsevier.
Meehl, Paul E., and Niels G. Waller. 2002. “The Path Analysis Controversy: A New Statistical
Approach to Strong Appraisal of Verisimilitude.” Psychological Methods 7 (3): 283–300.
Morrison, Denton E., and Ramon E. Henkel, ed. 1970. The Significance Test Controversy: A
Reader. Chicago: Aldine De Gruyter.
Pearson, E.S. & Neyman, J. (1930). On the problem of two samples. Joint Statistical Papers by
J. Neyman & E.S. Pearson, 99-115 (Berkeley: U. of Calif. Press). First published in Bul.
Acad. Pol.Sci. 73-96.
Savage, L. J. 1962. The Foundations of Statistical Inference: A Discussion. London: Methuen.
Selvin, H. 1970. “A critique of tests of significance in survey research. In The significance test
controversy, edited by D. Morrison and R. Henkel, 94-106. Chicago: Aldine De Gruyter.