Deborah Mayo

Despite its widespread use in science, the Neyman-Pearson Theory of Statistics (NPT) has been rejected as inadequate by most philosophers of induction and statistics. They base their rejection largely upon what the author refers to as after-trial criticisms of NPT. Such criticisms attempt to show that NPT fails to provide an adequate analysis of specific inferences after the trial is made, and the data is known. In this paper, the key types of after-trial criticisms are considered and it is argued that each fails to demonstrate the inadequacy of NPT because each is based on judging NPT on the grounds of a criterion that is fundamentally alien to NPT. As such, each may be seen to either misconstrue the aims of NPT, or to beg the question against it.

Cartwright argues for being a realist about theoretical entities but non-realist about theoretical laws. Her reason is that while the former involves causal explanation, the latter involves theoretical explanation; and inferences to causes, unlike inferences to theories, can avoid the redundancy objection--that one cannot rule out alternatives that explain the phenomena equally well. I sketch Cartwright's argument for inferring the most probable cause, focusing on Perrin's inference to molecular collisions as the cause of Brownian motion. I argue that either the inference she describes fails to be a genuinely causal one, or else it too is open to the redundancy objection. However, I claim there is a way to sustain Cartwright's main insight: that it is possible to avoid the redundancy objection in certain cases of causal inference from experiments (e.g., Perrin). But, contrary to Cartwright, I argue that in those cases one is able to infer causes only by inferring some theoretical laws about how they produce experimental effects.

I argue that although the judgments required to reach statistical risk assessments may reflect policy values, it does not follow that the task of evaluating whether a given risk assessment is warranted by the evidence need also be imbued with policy values. What has led many to conclude otherwise, I claim, stems from misuses of the statistical testing methods involved. I set out rules for interpreting what specific test results do and do not say about the extent of a given risk. By providing a more objective understanding of the evidence, such rules help in adjudicating conflicting risk assessments. To illustrate, I consider the risk assessment conflict at the EPA concerning the carcinogenicity of formaldehyde.

An important theme to have emerged from the new experimentalist movement is that much of actual scientific practice deals not with appraising full-blown theories but with the manifold local tasks required to arrive at data, distinguish fact from artifact, and estimate backgrounds. Still, no program for working out a philosophy of experiment based on this recognition has been demarcated. I suggest why the new experimentalism has come up short, and propose a remedy appealing to the practice of standard error statistics. I illustrate a portion of my proposal using Galison's experimental narrative on neutral currents

The issues of double-counting, use-constructing, and selection effects have long been the subject of debate in the philosophical as well as statistical literature. I have argued that it is the severity, stringency, or probativeness of the test—or lack of it—that should determine if a double-use of data is admissible. Hitchcock and Sober ([2004]) question whether this ‘severity criterion' can perform its intended job. I argue that their criticisms stem from a flawed interpretation of the severity criterion. Taking their criticism as a springboard, I elucidate some of the central examples that have long been controversial, and clarify how the severity criterion is properly applied to them. Severity and Use-Constructing: Four Points (and Some Clarificatory Notes) 1.1 Point 1: Getting beyond ‘all or nothing’ standpoints 1.2 Point 2: The rationale for prohibiting double-counting is the requirement that tests be severe 1.3 Point 3: Evaluate severity of a test T by its associated construction rule R 1.4 Point 4: The ease of passing vs. ease of erroneous passing: Statistical vs. ‘Definitional’ probability The False Dilemma: Hitchcock and Sober 2.1 Marsha measures her desk reliably 2.2 A false dilemma Canonical Errors of Inference 3.1 How construction rules may alter the error-probing performance of tests 3.2 Rules for accounting for anomalies 3.3 Hunting for statistically significant differences Concluding Remarks

Theories of statistical testing may be seen as attempts to provide systematic means for evaluating scientific conjectures on the basis of incomplete or inaccurate observational data. The Neyman-Pearson Theory of Testing (NPT) has purported to provide an objective means for testing statistical hypotheses corresponding to scientific claims. Despite their widespread use in science, methods of NPT have themselves been accused of failing to be objective; and the purported objectivity of scientific claims based upon NPT has been called into question. The purpose of this paper is first to clarify this question by examining the conceptions of (I) the function served by NPT in science, and (II) the requirements of an objective theory of statistics upon which attacks on NPT's objectivity are based. Our grounds for rejecting these conceptions suggest altered conceptions of (I) and (II) that might avoid such attacks. Second, we propose a reformulation of NPT, denoted by NPT*, based on these altered conceptions, and argue that it provides an objective theory of statistics. The crux of our argument is that by being able to objectively control error frequencies NPT* is able to objectively evaluate what has or has not been learned from the result of a statistical test.

Despite the widespread use of key concepts of the Neyman–Pearson (N–P) statistical paradigm—type I and II errors, significance levels, power, confidence levels—they have been the subject of philosophical controversy and debate for over 60 years. Both current and long-standing problems of N–P tests stem from unclarity and confusion, even among N–P adherents, as to how a test's (pre-data) error probabilities are to be used for (post-data) inductive inference as opposed to inductive behavior. We argue that the relevance of error probabilities is to ensure that only statistical hypotheses that have passed severe or probative tests are inferred from the data. The severity criterion supplies a meta-statistical principle for evaluating proposed statistical inferences, avoiding classic fallacies from tests that are overly sensitive, as well as those not sensitive enough to particular errors and discrepancies. Introduction and overview 1.1 Behavioristic and inferential rationales for Neyman–Pearson (N–P) tests 1.2 Severity rationale: induction as severe testing 1.3 Severity as a meta-statistical concept: three required restrictions on the N–P paradigm Error statistical tests from the severity perspective 2.1 N–P test T(): type I, II error probabilities and power 2.2 Specifying test T() using p-values Neyman's post-data use of power 3.1 Neyman: does failure to reject H warrant confirming H? Severe testing as a basic concept for an adequate post-data inference 4.1 The severity interpretation of acceptance (SIA) for test T() 4.2 The fallacy of acceptance (i.e., an insignificant difference): Ms Rosy 4.3 Severity and power Fallacy of rejection: statistical vs. substantive significance 5.1 Taking a rejection of H0 as evidence for a substantive claim or theory 5.2 A statistically significant difference from H0 may fail to indicate a substantively important magnitude 5.3 Principle for the severity interpretation of a rejection (SIR) 5.4 Comparing significant results with different sample sizes in T(): large n problem 5.5 General testing rules for T(), using the severe testing concept The severe testing concept and confidence intervals 6.1 Dualities between one and two-sided intervals and tests 6.2 Avoiding shortcomings of confidence intervals Beyond the N–P paradigm: pure significance, and misspecification tests Concluding comments: have we shown severity to be a basic concept in a N–P philosophy of induction?

I document some of the main evidence showing that E. S. Pearson rejected the key features of the behavioral-decision philosophy that became associated with the Neyman-Pearson Theory of statistics (NPT). I argue that NPT principles arose not out of behavioral aims, where the concern is solely with behaving correctly sufficiently often in some long run, but out of the epistemological aim of learning about causes of experimental results (e.g., distinguishing genuine from spurious effects). The view Pearson did hold gives a deeper understanding of NPT tests than their typical formulation as accept-reject routines, against which criticisms of NPT are really directed. The Pearsonian view that emerges suggests how NPT tests may avoid these criticisms while still retaining what is central to these methods: the control of error probabilities.

We argue that a responsible analysis of today's evidence-based risk assessments and risk debates in biology demands a critical or metascientific scrutiny of the uncertainties, assumptions, and threats of error along the manifold steps in risk analysis. Without an accompanying methodological critique, neither sensitivity to social and ethical values, nor conceptual clarification alone, suffices. In this view, restricting the invitation for philosophical involvement to those wearing a "bioethicist" label precludes the vitally important role philosophers of science may be able to play as bioevidentialists. The goal of this paper is to give a brief and partial sketch of how a metascientific scrutiny of risk evidence might work.

The key problem in the controversy over group selection is that of defining a criterion of group selection that identifies a distinct causal process that is irreducible to the causal process of individual selection. We aim to clarify this problem and to formulate an adequate model of irreducible group selection. We distinguish two types of group selection models, labeling them type I and type II models. Type I models are invoked to explain differences among groups in their respective rates of production of contained individuals. Type II models are invoked to explain differences among groups in their respective rates of production of distinct new groups. Taking Elliott Sober's model as an exemplar, we argue that although type I models have some biological importance--they force biologists to consider the role of group properties in influencing the fitness of organisms--they fail to identify a distinct group-level causal selection process. Type II models if properly framed, however, do identify a group-level causal selection process that is not reducible to individual selection. We propose such a type II model and apply it to some of the major candidates for group selection

While many philosophers of science have accorded special evidential significance to tests whose results are "novel facts", there continues to be disagreement over both the definition of novelty and why it should matter. The view of novelty favored by Giere, Lakatos, Worrall and many others is that of use-novelty: An accordance between evidence e and hypothesis h provides a genuine test of h only if e is not used in h's construction. I argue that what lies behind the intuition that novelty matters is the deeper intuition that severe tests matter. I set out a criterion of severity akin to the notion of a test's power in Neyman-Pearson statistics. I argue that tests which are use-novel may fail to be severe, and tests that are severe may fail to be use-novel. I discuss the 1919 eclipse data as a severe test of Einstein's law of gravity

In Philosophical Problems of Statistical Inference, Seidenfeld argues that the Neyman-Pearson (NP) theory of confidence intervals is inadequate for a theory of inductive inference because, for a given situation, the 'best' NP confidence interval, [CIλ], sometimes yields intervals which are trivial (i.e., tautologous). I argue that (1) Seidenfeld's criticism of trivial intervals is based upon illegitimately interpreting confidence levels as measures of final precision; (2) for the situation which Seidenfeld considers, the 'best' NP confidence interval is not [CIλ] as Seidenfeld suggests, but rather a one-sided interval [CI0]; and since [CI0] never yields trivial intervals, NP theory escapes Seidenfeld's criticism entirely; (3) Seidenfeld's criterion of non-triviality is inadequate, for it leads him to judge an alternative confidence interval, [CI alt. ], superior to [CIλ] although [CI alt. ] results in counterintuitive inferences. I conclude that Seidenfeld has not shown that the NP theory of confidence intervals is inadequate for a theory of inductive inference

In seeking general accounts of evidence, confirmation, or inference, philosophers have looked to logical relationships between evidence and hypotheses. Such logics of evidential relationship, whether hypothetico-deductive, Bayesian, or instantiationist fail to capture or be relevant to scientific practice. They require information that scientists do not generally have (e.g., an exhaustive set of hypotheses), while lacking slots within which to include considerations to which scientists regularly appeal (e.g., error probabilities). Building on my co-symposiasts contributions, I suggest some directions in which a new and more adequate philosophy of evidence can move

I argue that the Bayesian Way of reconstructing Duhem's problem fails to advance a solution to the problem of which of a group of hypotheses ought to be rejected or "blamed" when experiment disagrees with prediction. But scientists do regularly tackle and often enough solve Duhemian problems. When they do, they employ a logic and methodology which may be called error statistics. I discuss the key properties of this approach which enable it to split off the task of testing auxiliary hypotheses from that of appraising a primary hypothesis. By discriminating patterns of error, this approach can at least block, if not also severely test, attempted explanations of an anomaly. I illustrate how this approach directs progress with Duhemian problems and explains how scientists actually grapple with them

In a recent discussion note Sober (1985) elaborates on the argument given in Sober (1982) to show the inadequacy of Ronald Giere's (1979, 1980) causal model for cases of frequency-dependent causation, and denies that Giere's (1984) response avoids the problem he raises. I argue that frequency-dependent effects do not pose a problem for Giere's original causal model, and that all parties in this dispute have been guity of misinterpreting the counterfactual populations involved in applying Giere's model

While orthodox (Neyman-Pearson) statistical tests enjoy widespread use in science, the philosophical controversy over their appropriateness for obtaining scientific knowledge remains unresolved. I shall suggest an explanation and a resolution of this controversy. The source of the controversy, I argue, is that orthodox tests are typically interpreted as rules for making optimal decisions as to how to behave--where optimality is measured by the frequency of errors the test would commit in a long series of trials. Most philosophers of statistics, however, view the task of statistical methods as providing appropriate measures of the evidential-strength that data affords hypotheses. Since tests appropriate for the behavioral-decision task fail to provide measures of evidential-strength, philosophers of statistics claim the use of orthodox tests in science is misleading and unjustified. What critics of orthodox tests overlook, I argue, is that the primary function of statistical tests in science is neither to decide how to behave nor to assign measures of evidential strength to hypotheses. Rather, tests provide a tool for using incomplete data to learn about the process that generated it. This they do, I show, by providing a standard for distinguishing differences (between observed and hypothesized results) due to accidental or trivial errors from those due to systematic or substantively important discrepancies. I propose a reinterpretation of a commonly used orthodox test to make this learning model of tests explicit

Kuhn maintains that what marks the transition to a science is the ability to carry out ‘normal’ science—a practice he characterizes as abandoning the kind of testing that Popper lauds as the hallmark of science. Examining Kuhn's own contrast with Popper, I propose to recast Kuhnian normal science. Thus recast, it is seen to consist of severe and reliable tests of low-level experimental hypotheses (normal tests) and is, indeed, the place to look to demarcate science. While thereby vindicating Kuhn on demarcation, my recasting of normal science is seen to tell against Kuhn's view of revolutionary science.