Monthly Archives: May 2019

SIST: All Excerpts and Mementos: May 2018-May 2019

view from a hot-air balloon

Introduction & Overview

The Meaning of My Title: Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars* 05/19/18

Blurbs of 16 Tours: Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (SIST) 03/05/19

 

Excursion 1

EXCERPTS

Tour I

Excursion 1 Tour I: Beyond Probabilism and Performance: Severity Requirement (1.1) 09/08/18

Excursion 1 Tour I (2nd stop): Probabilism, Performance, and Probativeness (1.2) 09/11/18

Excursion 1 Tour I (3rd stop): The Current State of Play in Statistical Foundations: A View From a Hot-Air Balloon (1.3) 09/15/18

Tour II

Excursion 1 Tour II: Error Probing Tools versus Logics of Evidence-Excerpt 04/04/19

Souvenir C: A Severe Tester’s Translation Guide (Excursion 1 Tour II) 11/08/18

MEMENTOS

Tour Guide Mementos (Excursion 1 Tour II of How to Get Beyond the Statistics Wars) 10/29/18

 

Excursion 2

EXCERPTS

Tour I

Excursion 2: Taboos of Induction and Falsification: Tour I (first stop) 09/29/18

“It should never be true, though it is still often said, that the conclusions are no more accurate than the data on which they are based” (Keepsake by Fisher, 2.1) 10/05/18

Tour II

Excursion 2 Tour II (3rd stop): Falsification, Pseudoscience, Induction (2.3) 10/10/18

MEMENTOS

Tour Guide Mementos and Quiz 2.1 (Excursion 2 Tour I Induction and Confirmation) 11/14/18

Mementos for Excursion 2 Tour II Falsification, Pseudoscience, Induction 11/17/18

 

Excursion 3

EXCERPTS

Tour I

Where are Fisher, Neyman, Pearson in 1919? Opening of Excursion 3 11/30/18

Neyman-Pearson Tests: An Episode in Anglo-Polish Collaboration: Excerpt from Excursion 3 (3.2) 12/01/18

First Look at N-P Methods as Severe Tests: Water plant accident [Exhibit (i) from Excursion 3] 12/04/18

Tour II

It’s the Methods, Stupid: Excerpt from Excursion 3 Tour II (Mayo 2018, CUP) 12/11/18

60 Years of Cox’s (1958) Chestnut: Excerpt from Excursion 3 tour II. 12/29/18

Tour III

Capability and Severity: Deeper Concepts: Excerpts From Excursion 3 Tour III 12/20/18

MEMENTOS

Memento & Quiz (on SEV): Excursion 3, Tour I 12/08/18

Mementos for “It’s the Methods, Stupid!” Excursion 3 Tour II (3.4-3.6) 12/13/18

Tour Guide Mementos From Excursion 3 Tour III: Capability and Severity: Deeper Concepts 12/26/18

 

Excursion 4

EXCERPTS

Tour I

Excerpt from Excursion 4 Tour I: The Myth of “The Myth of Objectivity” (Mayo 2018, CUP) 12/26/18

Tour II

Excerpt from Excursion 4 Tour II: 4.4 “Do P-Values Exaggerate the Evidence?” 01/10/19

Tour IV

Excerpt from Excursion 4 Tour IV: More Auditing: Objectivity and Model Checking 01/27/19

MEMENTOS

Mementos from Excursion 4: Blurbs of Tours I-IV 01/13/19

 

Excursion 5

Tour I

(full) Excerpt: Excursion 5 Tour I — Power: Pre-data and Post-data (from “SIST: How to Get Beyond the Stat Wars”) 04/27/19

Tour III

Deconstructing the Fisher-Neyman conflict wearing Fiducial glasses + Excerpt 5.8 from SIST 02/23/19

 

Excursion 6

Tour II

Excerpts: Souvenir Z: Understanding Tribal Warfare +  6.7 Farewell Keepsake from SIST + List of Souvenirs 05/04/19

*Statistical Inference as Severe Testing: How to Get Beyond the Statistics Wars (Mayo, CUP 2018).

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Excerpts: Final Souvenir Z, Farewell Keepsake & List of Souvenirs

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We’ve reached our last Tour (of SIST)*: Pragmatic and Error Statistical Bayesians (Excursion 6), marking the end of our reading with Souvenir Z, the final Souvenir, as well as the Farewell Keepsake in 6.7. Our cruise ship Statinfasst, currently here at Thebes, will be back at dock for maintenance for our next launch at the Summer Seminar in Phil Stat (July 28-Aug 11). Although it’s not my preference that new readers being with the Farewell Keepsake (it contains a few spoilers), I’m excerpting it together with Souvenir Z (and a list of all souvenirs A – Z) here, and invite all interested readers to peer in. There’s a check list on p. 437: If you’re in the market for a new statistical account, you’ll want to test if it satisfies the items on the list. Have fun!

Souvenir Z: Understanding Tribal Warfare

We began this tour asking: Is there an overarching philosophy that “matches contemporary attitudes”? More important is changing attitudes. Not to encourage a switch of tribes, or even a tribal truce, but something more modest and actually achievable: to understand and get beyond the tribal warfare. To understand them, at minimum, requires grasping how the goals of probabilism differ from those of probativeness. This leads to a way of changing contemporary attitudes that is bolder and more challenging. Snapshots from the error statistical lens let you see how frequentist methods supply tools for controlling and assessing how well or poorly warranted claims are. All of the links, from data generation to modeling, to statistical inference and from there to substantive research claims, fall into place within this statistical philosophy. If this is close to being a useful way to interpret a cluster of methods, then the change in contemporary attitudes is radical: it has never been explicitly unveiled. Our journey was restricted to simple examples because those are the ones fought over in decades of statistical battles. Much more work is needed. Those grappling with applied problems are best suited to develop these ideas, and see where they may lead. I never promised,when you bought your ticket for this passage, to go beyond showing that viewing statistics as severe testing will let you get beyond the statistics wars.

6.7 Farewell Keepsake

Despite the eclecticism of statistical practice, conflicting views about the roles of probability and the nature of statistical inference – holdovers from long-standing frequentist–Bayesian battles – still simmer below the surface of today’s debates. Reluctance to reopen wounds from old battles has allowed them to fester. To assume all we need is an agreement on numbers – even if they’re measuring different things – leads to statistical schizophrenia. Rival conceptions of the nature of statistical inference show up unannounced in the problems of scientific integrity, irreproducibility, and questionable research practices, and in proposed methodological reforms. If you don’t understand the assumptions behind proposed reforms, their ramifications for statistical practice remain hidden from you.

Rival standards reflect a tension between using probability (a) to constrain the probability that a method avoids erroneously interpreting data in a series of applications (performance), and (b) to assign degrees of support, confirmation, or plausibility to hypotheses (probabilism). We set sail on our journey with an informal tool for telling what’s true about statistical inference: If little if anything has been done to rule out flaws in taking data as evidence for a claim, then that claim has not passed a severe test . From this minimal severe-testing requirement, we develop a statistical philosophy that goes beyond probabilism and performance. The goals of the severe tester (probativism) arise in contexts sufficiently different from those of probabilism that you are free to hold both, for distinct aims (Section 1.2). For statistical inference in science, it is severity we seek. A claim passes with severity only to the extent that it is subjected to, and passes, a test that it probably would have failed, if false. Viewing statistical inference as severe testing alters long-held conceptions of what’s required for an adequate account of statistical inference in science. In this view, a normative statistical epistemology –  an account of what’ s warranted to infer –  must be:

  directly altered by biasing selection effects
  able to falsify claims statistically
  able to test statistical model assumptions
  able to block inferences that violate minimal severity

These overlapping and interrelated requirements are disinterred over the course of our travels. This final keepsake collects a cluster of familiar criticisms of error statistical methods. They are not intended to replace the detailed arguments, pro and con, within; here we cut to the chase, generally keeping to the language of critics. Given our conception of evidence, we retain testing language even when the statistical inference is an estimation, prediction, or proposed answer to a question. The concept of severe testing is sufficiently general to apply to any of the methods now in use. It follows that a variety of statistical methods can serve to advance the severity goal, and that they can, in principle, find their foundations in an error statistical philosophy. However, each requires supplements and reformulations to be relevant to real-world learning. Good science does not turn on adopting any formal tool, and yet the statistics wars often focus on whether to use one type of test (or estimation, or model selection) or another. Meta-researchers charged with instigating reforms do not agree, but the foundational basis for the disagreement is left unattended. It is no wonder some see the statistics wars as proxy wars between competing tribe leaders, each keen to advance one or another tool, rather than about how to do better science. Leading minds are drawn into inconsequential battles, e.g., whether to use a prespecified cut-off  of 0.025 or 0.0025 –  when in fact good inference is not about cut-offs altogether but about a series of small-scale steps in collecting, modeling and analyzing data that work together to find things out. Still, we need to get beyond the statistics wars in their present form. By viewing a contentious battle in terms of a difference in goals –  finding highly probable versus highly well probed hypotheses – readers can see why leaders of rival tribes often talk past each other. To be clear, the standpoints underlying the following criticisms are open to debate; we’re far from claiming to do away with them. What should be done away with is rehearsing the same criticisms ad nauseum. Only then can we hear the voices of those calling for an honest standpoint about responsible science.

1. NHST Licenses Abuses. First, there’s the cluster of criticisms directed at an abusive NHST animal: NHSTs infer from a single P-value below an arbitrary cut-off to evidence for a research claim, and they encourage P-hacking, fishing, and other selection effects. The reply: this ignores crucial requirements set by Fisher and other founders: isolated significant results are poor evidence of a genuine effect and statistical significance doesn’t warrant substantive, (e.g., causal) inferences. Moreover, selective reporting invalidates error probabilities. Some argue significance tests are un-Popperian because the higher the sample size, the easier to infer one’s research hypothesis. It’s true that with a sufficiently high sample size any discrepancy from a null hypothesis has a high probability of being detected, but statistical significance does not license inferring a research claim H. Unless H’s errors have been well probed by merely finding a small P-value, H passes an extremely insevere test. No mountains out of molehills (Sections 4.3 and 5.1). Enlightened users of statistical tests have rejected the cookbook, dichotomous NHST, long lampooned: such criticisms are behind the times. When well-intentioned aims of replication research are linked to these retreads, it only hurts the cause. One doesn’t need a sharp dichotomy to identify rather lousy tests – a main goal for a severe tester. Granted, policy-making contexts may require cut-offs, as do behavioristic setups. But in those contexts, a test’s error probabilities measure overall error control, and are not generally used to assess well-testedness. Even there, users need not fall into the NHST traps (Section 2.5). While attention to banning terms is the least productive aspect of the statistics wars, since NHST is not used by Fisher or N-P, let’s give the caricature its due and drop the NHST acronym; “statistical tests” or “error statistical tests” will do. Simple significance tests are a small part of a conglomeration of error statistical methods.

To continue reading: Excerpt Souvenir Z, Farewell Keepsake & List of Souvenirs can be found here.

*We are reading Statistical Inference as Severe Testing: How to Get beyond the Statistics Wars (2018, CUP)

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Where YOU are in the journey.

 


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