Online research in philosophy

Some accounts of evidence regard it as an objective relationship holding between data and hypotheses, perhaps mediated by a testing procedure. Mayo’s error-statistical theory of evidence is an example of such an approach. Such a view leaves open the question of when an epistemic agent is justified in drawing an inference from such data to a hypothesis. Using Mayo’s account as an illustration, I propose a framework for addressing the justification question via a relativized notion, which I designate security , meant to conceptualize practices aimed at the justification of inferences from evidence. I then show how the notion of security can be put to use by showing how two quite different theoretical approaches to model criticism in statistics can both be viewed as strategies for securing claims about statistical evidence.

: I propose an epistemological extension of the error-statistical (ES) account of inference advocated by Deborah Mayo. To supplement the unrelativized account of evidence provided by ES, I propose a relativized notion, which I designate security, meant to conceptualize practices aimed at the justification of inferences from evidence. I then show how the notion of security can be put to use by showing how two very different theoretical approaches to model criticism in statistics can both be viewed as strategies for securing (in my sense) claims about statistical evidence.

Inferential statistical tests-such as analysis of variance, t-tests, chi-square and Wilcoxin signed ranks-now constitute a principal class of methods for the testing of scientific hypotheses. In this paper I will consider the role of one statistical concept (statistical power) and two statistical principles or assumptions (homogeneity of variance and the independence of random error), in the reliable application of selected statistical methods. I defend a tacit but widely-deployed naturalistic principle of explanation (E): Philosophers should not treat as inexplicable or basic those correlational facts that scientists themselves do not treat as irreducible. In light of (E), I contend that the conformity of epistemically reliable statistical tests to these concepts and assumptions entails at least the following modest or austere realist commitment: (C) The populations under study have a stable theoretical or unobserved structure that metaphysically grounds the observed values; the objects therefore have a fixed value independent of our efforts to measure them. (C) provides the best explanation for the correlation between the joint use of statistical assumptions and statistical tests, on the one hand, and methodological success on the other.

This paper addresses the problem that Bayesian statistical inference cannot accommodate theory change, and proposes a framework for dealing with such changes. It first presents a scheme for generating predictions from observations by means of hypotheses. An example shows how the hypotheses represent the theoretical structure underlying the scheme. This is followed by an example of a change of hypotheses. The paper then presents a general framework for hypotheses change, and proposes the minimization of the distance between hypotheses as a rationality criterion. Finally the paper discusses the import of this for Bayesian statistical inference.

Behind this question are two fundamentally different approaches about how to reason with chance hypotheses. One approach, due to Ronald Fisher, rejects a chance hypothesis provided sample data appear in a prespecified rejection region. The other, due to Thomas Bayes, rejects a chance hypothesis provided an alternative hypothesis confers a bigger probability on the data in question than the original hypothesis. In the Fisherian approach, chance hypotheses are rejected in isolation for rendering data too improbable. In the Bayesian approach, chance hypotheses are eliminated provided some other hypotheses render the data more probable. Whereas in the Fisherian approach the emphasis is on elimination, in the Bayesian approach the emphasis is on comparison. These approaches are incompatible, and the statistical community itself is deeply riven over which of these approaches to adopt as the right canon for statistical rationality. The difference reflects a deep divergence in fundamental intuitions about the nature of statistical rationality and in particular about what counts as statistical evidence.

Entertaining diverse assumptions about empirical research, commentators give a wide range of verdicts on the NHSTP defence in Statistical significance. The null-hypothesis significance-test procedure (NHSTP) is defended in a framework in which deductive and inductive rules are deployed in theory corroboration in the spirit of Popper's Conjectures and refutations (1968b). The defensible hypothetico-deductive structure of the framework is used to make explicit the distinctions between (1) substantive and statistical hypotheses, (2) statistical alternative and conceptual alternative hypotheses, and (3) making statistical decisions and drawing theoretical conclusions. These distinctions make it easier to show that (1) H0 can be true, (2) the effect size is irrelevant to theory corroboration, and (3) “strong” hypotheses make no difference to NHSTP. Reservations about statistical power, meta-analysis, and the Bayesian approach are still warranted.

I contrast two modes of error-elimination relevant to evaluating evidence in accounts that emphasize frequentist reliability. The contrast corresponds to that between the use of of a reliable inference procedure and the critical scrutiny of a procedure with regard to its reliability, in light of what is and is not known about the setting in which the procedure is used. I propose a notion of security as a category of evidential assessment for the latter. In statistical settings, robustness theory and misspecification testing exemplify two distinct strategies for securing statistical inferences.

The error statistical account of testing uses statistical considerations, not to provide a measure of probability of hypotheses, but to model patterns of irregularity that are useful for controlling, distinguishing, and learning from errors. The aim of this paper is (1) to explain the main points of contrast between the error statistical and the subjective Bayesian approach and (2) to elucidate the key errors that underlie the central objection raised by Colin Howson at our PSA 96 Symposium.

From the perspective of Mayo’s error statistical theory of evidence, I explore problems and prospects for an account of the objectivity of scientific evidence. A recent proposal by Peter Achinstein provides the starting point. I consider a challenge to this proposal arising from the role of agents in carrying out the testing procedures that are central to the error statistical theory. Achinstein’s objective concept of unrelativized potential evidence initially resolves these difficulties, only to give way to a deeper incompatibility between Achinstein’s conception of objectivity of reasons to believe and the error statistical theory of evidence. I propose an alternative account of objectivity of reasons that is compatible with the error statistical theory.

The Falsification of Statistical Hypotheses. It is widely held that falsification of statistical hypotheses is impossible. This view is supported by an analysis of the most important theories of statistical testing: these theories are not compatible with falsificationism. On the other hand, falsificationism yields a basically viable solution to the problems of explanation, prediction and theory testing in a deterministic context. The present paper shows how to introduce the falsificationist solution into the realm of statistics. This is done mainly by applying the concept of empirical content to statistical hypotheses. It is shown that empirical content is a substitute for 'power' as defined by Neyman and Pearson. Since the empirical content of a hypothesis is independent of alternative hypotheses, the proposed theory of statistical testing allows for tests of isolated hypotheses.