Error statistical methods, deemed indirect for probabilism, are direct for severe probing and falsification. Severe testers do not view scientists as seeking highly probable hypotheses, but learning which interpretations of data are well and poorly tested. Of course we want well-warranted claims, but arriving at them does not presuppose a single probability pie with its requirements of exhaustiveness: science must be open ended. We want methods that efficiently find falsity, not ones that are based on updating values for parameters in an existing model. We want to infer local variants of theories piecemeal, falsify others, and be free to launch a probe of any hypothesis which we can subject to severe testing. If other ways to falsify satisfy error statistical requirements, then they are happily in sync with us.
9. Severe Testing Is Not All You Do in Inquiry. Agreed. I have used a neutral word “ warranted” to mean justified, adding “ with severity” when appropriate. There’ s a distinctive twist that goes with severely warranting claims – some prefer to say ” beliefs,” and you could substitute throughout if you wish. It is this twist that makes it possible to have your probabilist cake, and probativism too – each for distinct contexts. The severe testing assessment is not measuring how strong your belief in H is but how well you can show why H ought to be believed. It is relevant when the aim is to know why claims pass (or fail) the tests they do. View the error statistical notions as a picturesque representation of the real life, flesh and blood, capability or incapability to put to rest reasonable skeptical challenges. It’ s in the spirit of Fisher’ s requiring you know how to bring about results that would rarely fail to corroborate H . It’ s not merely knowing, but showing you’ re prepared, or would be, to tackle skeptical challenges. I’ m using “ you” but it could be a group or a machine. It’ s just not all that you do in inquiry. I admitted at the outset that we do not always want to find things out. If your goal is belief probabilism, or you’ re in a context where the aim is to assign direct probabilities to events (a deductive task), then you are better off recognizing the differences than trying to unify or reconcile. Let me be clear, severe testing isn’ t reserved for cases of strong evidence; it is operative at every stage of inquiry, but even more so in early stages – where skepticism is greatest. The severity demand is what we naturally want as consumers of statistics, namely, grounds that reports would very probably have revealed flaws of relevance when they’ re present. To pass tests with severity gives strong evidence, yes, but most of the time it’ s to learn that much less than was thought or hoped has passed. Showing (with severity!) that a study was poorly run is important in its own right, even if done semi-formally. Better still is to pinpoint a flaw that’ s been overlooked.
Our journey has taken you far beyond the hackneyed statistical battles that make up much of today’ s statistics wars. I’ ve chosen to focus on some of them in your final “ keepsake” because, if you have to refight them, you can begin from the places we’ ve reached. These criticisms can no longer be blithely put forward as having weight without wrestling with the underlying presuppositions and challenges about evidence and inference. You might say that the criticisms have force against garden-variety treatments of error statistical methods, that I’ ve changed things by adding an explicit severe testing philosophy. I’ ll happily concede this, but that is the whole reason for taking this journey. You needn’ t accept this statistical philosophy to use it to peel back the layers of the statistics wars; you will then be beyond them. It’ s time.
Live (Final) Exhibit. What Does the Severe Tester Say About Positions 1– 9? What do you say?
1 We know performance is necessary but not sufficient for severity, nor for confidence distributions or fiducial inference, but here we imagine we have got the relevant error probability.
2 There’ s no need for the philosopher’ s appeal to things like closest possible worlds to use counter factuals either.
3 They allow the possibility that the knowledge that optional stopping will be used alters their prior for 0. I take it they recognize this is at odds with the presumption that “ optional stopping is no sin,” and they don’ t press it. See Section 1.5 where we first took this up.
4 In observing that “ informative stopping rules occur only rarely in practice” (p. 90), Berger and Wolpert make the insightful point that disagreement on this is “ due to the misconception that an informative stopping rule is one for which N carries information about θ .”
5 One explanation is in Bernardo’ s appeal to a decision theory that considers the sampling distribution in computing utilities.
6 The error statistical account would suggest first checking the likelihood portion of the model, after which they could turn to the prior.
7 Note, for example, that for a given parameter θ , one has presumably only selected a single θ , not the n samples of our usual M-S test. It’ s not clear why we should expect it to produce typical outcomes. I owe this point to Christian Hennig.
8 A co-developer of posterior predictive checks, Xiao-Li Meng, is a leader of the “ Bayes– Fiducial– Frequentist” movement.
9 We would need predesignation of hypotheses (and/or other restrictions) if there is to be error control.
10 I allude to a pin and tumbler lock.
11 Some will use a P -value as a degree of inconsistency with a null hypothesis.
Souvenirs
Souvenir A: Postcard to Send
Souvenir B: Likelihood versus Error Statistical
Souvenir C: A Severe Tester’ s Translation Guide
Souvenir D: Why We Are So New
Souvenir E: An Array of Questions, Problems, Models
Souvenir F: Getting Free of Popperian Constraints on Language
Souvenir G: The Current State of Play in Psychology
Souvenir H: Solving Induction Is Showing Methods with Error Control
Souvenir I: So What Is a Statistical Test, Really?
Souvenir J: UMP Tests
Souvenir K: Probativism
Souvenir L: Beyond Incompatibilist Tunnels
Souvenir M: Quicksand Takeaway
Souvenir N: Rule of Thumb for SEV
Souvenir O: Interpreting Probable Flukes
Souvenir P: Transparency and Informativeness
Souvenir Q: Have We Drifted From Testing Country? (Notes From an Intermission)
Souvenir R: The Severity Interpretation of Rejection (SIR)
Souvenir S: Preregistration and Error Probabilities
Souvenir T: Even Big Data Calls for Theory and Falsification
Souvenir U: Severity in Terms of Problem-Solving
Souvenir V: Two More Points on M-S Tests and an Overview of Excursion 4
Souvenir W: The Severity Interpretation of Negative Results (SIN) for Test T+
Souvenir X: Power and Severity Analysis
Souvenir Y: Axioms Are To Be Tested by You (Not Vice Versa)
Souvenir Z: Understanding Tribal Warfare
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