Deborah Mayo

After some general remarks about the interrelation between philosophical and statistical thinking, the discussion centres largely on significance tests. These are defined as the calculation of p-values rather than as formal procedures for ‘acceptance‘ and ‘rejection‘. A number of types of null hypothesis are described and a principle for evidential interpretation set out governing the implications of p- values in the specific circumstances of each application, as contrasted with a long-run interpretation. A number of more complicated situ- ations are discussed in which modification of the simple p-value may be essential.

Philosophers of science have long been concerned with the question of what a given scientific theory tells us about the contents of the world, but relatively little attention has been paid to how we set out to build theories and to the relevance of pre-theoretical methodology on a theory’s interpretation. In the traditional view, the form and content of a mature theory can be separated from any tentative ontological assumptions that went into its development. For this reason, the target of interpretation is taken to be the mature theory and nothing more. On this view, positions on ontology emerge only once a theory is to hand, not as part of the process of theory building. Serious attention to theory creation suggests this is too simple. In particular, data collection and experimentation are influenced both by theory and by assumptions about the entities thought to be the target of study. Initial reasoning about possible ontologies has an influence on the choice of theoretical variables as well as on the judgments of the methodology appropriate to investigate them.

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

The field of quantified risk assessment is a new field, only about 20 years old, and already it is considered to be in a crisis. As Funtowicz and J.R. Ravetz (1985) put it:The concept of risk in terms of probability has proved to be so elusive, and statistical inference so problematic, that many experts in the field have recently either lost hope of finding a scientific solution or lost faith in Risk Analysis as a tool for decisionmaking. (p.219)Thus the ‘art’ of the assessment of risks… is at an impasse. The early hopes that it could be reduced to a science are frustrated. …[O]thers are tending to introduce the ‘human’ and ‘cultural’ factors. The question now becomes, to what extent should these predominate? Would it be to the reduction or exclusion of the ‘scientific’ aspects? For, …if the perceived phenomena of ‘risks’ are interpreted as lacking all objective content or being merely a small part of some total cultural configuration, then there is no basis for dialogue between opposed positions on such problems, (pp.220-221)

In How the Laws of Physics Lie (1983)2 Cartwright argues for being a realist about theoretical entities but non-realist about theoretical laws. Her reason for this distinction is that only the former involves causal explanation, and accepting causal explanations commits us to the existence of the causal entity invoked. “What is special about explanation by theoretical entity is that it is causal explanation, and existence is an internal characteristic of causal claims. There is nothing similar for theoretical laws.” (p. 93). For, according to Cartwright, the acceptability of a theoretical explanation is a matter of its ability to satisfy such criteria as prganizing and simplifying, and in her view, “success at organizing, predicting, and classifying is never an argument for truth.” (p. 91). In contrast, Cartwright claims, “When I infer from an effect to a cause, I am asking what made the effect occur, what brought it about.

While the common procedure of statistical significance testing and its accompanying concept of p-values have long been surrounded by controversy, renewed concern has been triggered by the replication crisis in science. Many blame statistical significance tests themselves, and some regard them as sufficiently damaging to scientific practice as to warrant being abandoned. We take a contrary position, arguing that the central criticisms arise from misunderstanding and misusing the statistical tools, and that in fact the purported remedies themselves risk damaging science. We argue that banning the use of p-value thresholds in interpreting data does not diminish but rather exacerbates data-dredging and biasing selection effects. If an account cannot specify outcomes that will not be allowed to count as evidence for a claim—if all thresholds are abandoned—then there is no test of that claim. The contributions of this paper are: To explain the rival statistical philosophies underlying the ongoing controversy; To elucidate and reinterpret statistical significance tests, and explain how this reinterpretation ameliorates common misuses and misinterpretations; To argue why recent recommendations to replace, abandon, or retire statistical significance undermine a central function of statistics in science: to test whether observed patterns in the data are genuine or due to background variability.

A common intuition about evidence is that if data x have been used to construct a hypothesis H, then x should not be used again in support of H. It is no surprise that x fits H, if H was deliberately constructed to accord with x. The question of when and why we should avoid such “double-counting” continues to be debated in philosophy and statistics. It arises as a prohibition against data mining, hunting for significance, tuning on the signal, and ad hoc hypotheses, and as a preference for predesignated hypotheses and “surprising” predictions. I have argued that it is the severity or probativeness of the test—or lack of it—that should determine whether a double-use of data is admissible. I examine a number of surprising ambiguities and unexpected facts that continue to bedevil this debate

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

The crisis of replication has led many to blame statistical significance tests for making it too easy to find impressive looking effects that do not replicate. However, the very fact it becomes difficult to replicate effects when features of the tests are tied down actually serves to vindicate statistical significance tests. While statistical significance tests, used correctly, serve to bound the probabilities of erroneous interpretations of data, this error control is nullified by data-dredging, multiple testing, and other biasing selection effects. Arguments claiming to vitiate statistical significance tests attack straw person variants of tests that commit well-known fallacies and misinterpretations. There is a tension between popular calls for preregistration – arguably, one of the most promising ways to boost replication – and accounts that downplay error probabilities: Bayes Factors, Bayesian posteriors, likelihood ratios. By underscoring the importance of error control for well testedness, the replication crisis points to reformulating tests so as to avoid fallacies and report the extent of discrepancies that are and are not indicated with severity.

The growing availability of computer power and statistical software has greatly increased the ease with which practitioners apply statistical methods, but this has not been accompanied by attention to checking the assumptions on which these methods are based. At the same time, disagreements about inferences based on statistical research frequently revolve around whether the assumptions are actually met in the studies available, e.g., in psychology, ecology, biology, risk assessment. Philosophical scrutiny can help disentangle 'practical' problems of model validation, and conversely, a methodology of statistical model validation can shed light on a number of issues of interest to philosophers of science

Discussions of science and values in risk management have largely focused on how values enter into arguments about risks, that is, issues of acceptable risk. Instead this volume concentrates on how values enter into collecting, interpreting, communicating, and evaluating the evidence of risks, that is, issues of the acceptability of evidence of risk. By focusing on acceptable evidence, this volume avoids two barriers to progress. One barrier assumes that evidence of risk is largely a matter of objective scientific data and therefore uncontroversial. The other assumes that evidence of risk, being "just" a matter of values, is not amenable to reasoned critique. Denying both extremes, this volume argues for a more constructive conclusion: understanding the interrelations of scientific and value issues enables a critical scrutiny of risk assessments and better public deliberation about social choices. The contributors, distinguished philosophers, policy analysts, and natural and social scientists, analyze environmental and medical controversies, and assumptions underlying views about risk assessment and the scientific and statistical models used in risk management.

The growing acceptance and success of experimental economics has increased the interest of researchers in tackling philosophical and methodological challenges to which their work increasingly gives rise. I sketch some general issues that call for the combined expertise of experimental economists and philosophers of science, of experiment, and of inductive‐statistical inference and modeling. †To contact the author, please write to: 235 Major Williams, Virginia Tech, Blacksburg, VA 24061‐0126; e‐mail: [email protected].

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.

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