The paper examines the claim that significance testing violates the Principle of Total Evidence. I argue that p-values violate PTE for two-sided tests but satisfy PTE for one-sided tests invoking a sufficient test statistic independent of the preferred theory of evidence. While the focus of the paper is to evaluate a particular claim about the relationship of significance testing and PTE, I clarify the reading of this methodological principle along the way.

We review the definition of the Full Bayesian Significance Test (FBST), and summarize its main statistical and epistemological characteristics. We review also the Abstract Belief Calculus (ABC) of Darwiche and Ginsberg, and use it to analyze the FBST’s value of evidence. This analysis helps us understand the FBST properties and interpretation. The definition of value of evidence against a sharp hypothesis, in the FBST setup, was motivated by applications of Bayesian statistical reasoning to legal matters where the sharp (...) hypotheses were defendants statements, to be judged according to the Onus Probandi juridical principle. (shrink)

Chow sets his version of statistical significance testing in an impoverished context of “theory corroboration” that explicitly excludes well-posed theories admitting of strong support by precise empirical evidence. He demonstrates no scientific usefulness for the problematic procedure he recommends instead. The important role played by significance testing in today's behavioral and brain sciences is wholly inconsistent with the rhetoric he would enforce.

The origins of testing scientific models with statistical techniques go back to 18th century mathematics. However, the modern theory of statistical testing was primarily developed through the work of Sir R.A. Fisher, Jerzy Neyman, and Egon Pearson in the inter-war period. Some of Fisher's papers on testing were published in economics journals (Fisher, 1923, 1935) and exerted a notable influence on the discipline. The development of econometrics and the rise of quantitative economic models in the mid-20th century made statistical (...) class='Hi'>significance testing a commonplace, albeit controversial tool within economics. -/- In the debate about significance testing, methodological controversies intertwine with epistemological issues and sociological developments. Our aim in this chapter is to expound these connections and to show how the use of, and the debate about, significance testing in economics differs from other social sciences, such as psychology. (shrink)

Frequentism and Bayesianism represent very different approaches to hypothesis testing, and this presents a skeptical challenge for Bayesians. Given that most empirical research uses frequentist methods, why (if at all) should we rely on it? While it is well known that there are conditions under which Bayesian and frequentist methods agree, without some reason to think these conditions are typically met, the Bayesian hasn’t shown why we are usually safe in relying on results reported by significance testers. In this (...) article, I provide arguments that such conditions will usually be met; the Bayesian can maintain her theoretical disagreement with the frequentist while holding that her error is mostly harmless in practice. (shrink)

Chow's (1996) Statistical significance is a defence of null-hypothesis significance testing (NHSTP). The most common and straightforward use of significance testing is for the statistical corroboration of general hypotheses. In this case, criticisms of NHSTP, at least those mentioned in the book, are unfounded or misdirected. This point is driven home by the author a bit too forcefully and meticulously. The awkward and cumbersome organisation and argumentation of the book makes it even harder to read.

A pure significance test would check the agreement of a statistical model with the observed data even when no alternative model was available. The paper proposes the use of a modified p -value to make such a test. The model will be rejected if something surprising is observed. It is shown that the relation between this measure of surprise and the surprise indices of Weaver and Good is similar to the relationship between a p -value, a corresponding (...) odds-ratio, and a logit or log-odds statistic. The s -value is always larger than the corresponding p -value, and is not uniformly distributed. Difficulties with the whole approach are discussed. (shrink)

Chow' efforts toward a methodology of theory-corroboration and the plea for significance testing are welcome, but there are many risky claims. A major omission is a discussion of significance testing in the Bayesian framework. We sketch here the Bayesian reinterpretation of the significance level for assessing direction of effects.

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. (shrink)

Chow's one-tailed null-hypothesis significance-test procedure, with its rationale based on the elimination of chance influences, is not appropriate for theory-corroboration experiments. Estimated effect sizes and their associated standard errors or confidence limits will always suffice.

Chow's endorsement of a limited role for null hypothesis significance testing is a needed corrective of research malpractice, but his decision to place this procedure in a hypothetico-deductive framework of Popperian cast is unwise. Various failures of this version of the hypothetico-deductive method have negative implications for Chow's treatment of significance testing, meta-analysis, and theory evaluation.

Most psychometricians believe that the significance test is counterproductive. I have read Chow's book to see whether it addresses or rebuts any of the key facts brought out by the psychometricians. The book is empty on this score; it is entirely irrelevant to the current debate. It presents nothing new and is riddled with errors.

The Full Bayesian Significance Test, FBST, is extensively reviewed. Its test statistic, a genuine Bayesian measure of evidence, is discussed in detail. Its behavior in some problems of statistical inference like testing for independence in contingency tables is discussed.

Abstract: The Pull Bayesian Significance Test (FBST) for precise hy- potheses is applied to a Multivariate Normal Structure (MNS) model. In the FBST we compute the evidence against the precise hypothesis. This evi- dence is the probability of the Highest Relative Surprise Set (HRSS) tangent to the sub-manifold (of the parameter space) that defines the null hypothesis. The MNS model we present appears when testing equivalence conditions for genetic expression measurements, using micro-array technology.

Chow (1996) offers a reconceptualization of statistical significance that is reasoned and comprehensive. Despite a somewhat rough presentation, his arguments are compelling and deserve to be taken seriously by the scientific community. It is argued that his characterization of literal replication, types of research, effect size, and experimental control are in need of revision.

Much forensic inference based upon DNA evidence is made assuming Hardy-Weinberg Equilibrium (HWE) for the genetic loci being used. Several statistical tests to detect and measure deviation from HWE have been devised, and their limitations become more obvious when testing for deviation within multiallelic DNA loci. The most popular methods-Chi-square and Likelihood-ratio tests-are based on asymptotic results and cannot guarantee a good performance in the presence of low frequency genotypes. Since the parameter space dimension increases at a quadratic rate on (...) the number of alleles, some authors suggest applying sequential methods, where the multiallelic case is reformulated as a sequence of “biallelic” tests. However, in this approach it is not obvious how to assess the general evidence of the original hypothesis; nor is it clear how to establish the significance level for its acceptance/rejection. In this work, we introduce a straightforward method for the multiallelic HWE test, which overcomes the aforementioned issues of sequential methods. The core theory for the proposed method is given by the Full Bayesian Significance Test (FBST), an intuitive Bayesian approach which does not assign positive probabilities to zero measure sets when testing sharp hypotheses. We compare FBST performance to Chi-square, Likelihood-ratio and Markov chain tests, in three numerical experiments. The results suggest that FBST is a robust and high performance method for the HWE test, even in the presence of several alleles and small sample sizes. (shrink)

The pre-designationist, anti-inductivist and operationalist tenor of Neyman-Pearson theory give that theory an obvious affinity to several currently influential philosophies of science, most particularly, the Popperian. In fact, one might fairly regard Neyman-Pearson theory as the statistical embodiment of Popperian methodology. The difficulties raised in this paper have, then, wider purport, and should serve as something of a touchstone for those who would construct a theory of evidence adequate to statistics without recourse to the notion of inductive probability.

Gene clustering is a useful exploratory technique to group together genes with similar expression levels under distinct cell cycle phases or distinct conditions. It helps the biologist to identify potentially meaningful relationships between genes. In this study, we propose a clustering method based on multivariate normal mixture models, where the number of clusters is predicted via sequential hypothesis tests: at each step, the method considers a mixture model of m components (m = 2 in the first step) and tests if (...) in fact it should be m - 1. If the hypothesis is rejected, m is increased and a new test is carried out. The method continues (increasing m) until the hypothesis is accepted. The theoretical core of the method is the full Bayesian significance test, an intuitive Bayesian approach, which needs no model complexity penalization nor positive probabilities for sharp hypotheses. Numerical experiments were based on a cDNA microarray dataset consisting of expression levels of 205 genes belonging to four functional categories, for 10 distinct strains of Saccharomyces cerevisiae. To analyze the method’s sensitivity to data dimension, we performed principal components analysis on the original dataset and predicted the number of classes using 2 to 10 principal components. Compared to Mclust (model-based clustering), our method shows more consistent results. (shrink)

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 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. The defensible hypothetico-deductive structure of the framework is used to make explicit the distinctions between substantive and statistical hypotheses, statistical alternative and conceptual alternative hypotheses, and making statistical decisions (...) and drawing theoretical conclusions. These distinctions make it easier to show that H0 can be true, the effect size is irrelevant to theory corroboration, and “strong” hypotheses make no difference to NHSTP. Reservations about statistical power, meta-analysis, and the Bayesian approach are still warranted. (shrink)

The unit root problem plays a central role in empirical applications in the time series econometric literature. However, significance tests developed under the frequentist tradition present various conceptual problems that jeopardize the power of these tests, especially for small samples. Bayesian alternatives, although having interesting interpretations and being precisely defined, experience problems due to the fact that that the hypothesis of interest in this case is sharp or precise. The Bayesian significance test used in this article, for (...) the unit root hypothesis, is based solely on the posterior density function, without the need of imposing positive probabilities to sets of zero Lebesgue measure. Furthermore, it is conducted under strict observance of the likelihood principle. It was designed mainly for testing sharp null hypotheses and it is called FBST for Full Bayesian Significance Test. (shrink)

To estimate causal relationships, time series econometricians must be aware of spurious correlation, a problem first mentioned by Yule (1926). To deal with this problem, one can work either with differenced series or multivariate models: VAR (VEC or VECM) models. These models usually include at least one cointegration relation. Although the Bayesian literature on VAR/VEC is quite advanced, Bauwens et al. (1999) highlighted that “the topic of selecting the cointegrating rank has not yet given very useful and convincing results”. The (...) present article applies the Full Bayesian Significance Test (FBST), especially designed to deal with sharp hypotheses, to cointegration rank selection tests in VECM time series models. It shows the FBST implementation using both simulated and available (in the literature) data sets. As illustration, standard non informative priors are used. (shrink)

The first of 3 objectives in this study was to address the major problem with Null Hypothesis Significance Testing (NHST) and 2 common misconceptions related to NHST that cause confusion for students and researchers. The misconcep- tions are (a) a smaller p indicates a stronger relationship and (b) statistical signifi- cance indicates practical importance. The second objective was to determine how this problem and the misconceptions were treated in 12 recent textbooks used in edu- cation research methods and statistics (...) classes. The third objective was to examine how the textbooks’ presentations relate to current best practices and how much help they provide for students. The results show that almost all of the textbooks fail to acknowledge that there is controversy surrounding NHST. Most of the textbooks dealt, at least minimally, with the alleged misconceptions of interest, but they pro- vided relatively little help for students. (shrink)

If the NHSTP procedure is essential for controlling for chance, why is there little, if any, discussion of the nature of chance by Chow and other advocates of the procedure. Also, many criticisms that Chow takes to be aimed against the NHSTP procedure are actually directed against the kind of theory that is tested by the procedure.

Statistical tests that detect and measure deviation from the Hardy-Weinberg equilibrium (HWE) have been devised but are limited when testing for deviation at multiallelic DNA loci is attempted. Here we present the full Bayesian significance test (FBST) for the HWE. This test depends neither on asymptotic results nor on the number of possible alleles for the particular locus being evaluated. The FBST is based on the computation of an evidence index in favor of the HWE hypothesis. A (...) great deal of forensic inference based on DNA evidence assumes that the HWE is valid for the genetic loci being used. We applied the FBST to genotypes obtained at several multiallelic short tandem repeat loci during routine parentage testing; the locus Penta E exemplifies those clearly in HWE while others such as D10S1214 and D19S253 do not appear to show this. (shrink)

Even in a theory corroboration context, attention to effect size is called for if significance testing is to be of any value. I sketch a Popperian construal of significance tests that better fits into scientific inference as a whole. Because of its many errors Chow's book cannot be recommended to the novice.

Statistical significance is almost universally equated with the attribution to some population of nonchance influences as the source of structure in the data. But statistical significance can be divorced from both parameter estimation and probability as, instead, a statement about the atypicality or lack of exchangeability over some distinction of the data relative to some set. From this perspective, the criticisms of significance tests evaporate.

In this paper, the notion of degree of inconsistency is introduced as a tool to evaluate the sensitivity of the Full Bayesian Significance Test (FBST) value of evidence with respect to changes in the prior or reference density. For that, both the definition of the FBST, a possibilistic approach to hypothesis testing based on Bayesian probability procedures, and the use of bilattice structures, as introduced by Ginsberg and Fitting, in paraconsistent logics, are reviewed. The computational and theoretical advantages (...) of using the proposed degree of inconsistency based sensitivity evaluation as an alternative to traditional statistical power analysis is also discussed. (shrink)

Significance testing is the primary method for establishing causal relationships in psychology. Meehl [1978, 1990a, 1990b] and Faust [1984] argue that significance tests and their interpretation are subject to actuarial and psychological biases, making continued adherence to these practices irrational, and even partially responsible for the slow progress of the ‘soft’ areas of psychology. I contend that familiar standards of testing and literature review, along with recently developed meta-analytic techniques, are able to correct the proposed actuarial and psychological (...) biases. In particular, psychologists embrace a principle of robustness which states that real psychological effects are (1) reproducible by similar methods, (2) detectable by diverse means, and (3) able to survive theoretical integration. By contrast, spurious significant findings perish under the strain of persistent tests of their robustness. The resulting vindication of significance testing confers on the world a role in determining the rationality of a method, and also affords us an explanation for the fast progress of ‘hard’ areas of psychology. *I would like to thank Dick Boyd and Phil Gasper for helpful comments on the ideas presented here. (shrink)

This article gives a conceptual review of the e-value, ev(H|X) – the epistemic value of hypothesis H given observations X. This statistical significance measure was developed in order to allow logically coherent and consistent tests of hypotheses, including sharp or precise hypotheses, via the Full Bayesian Significance Test (FBST). Arguments of analysis allow a full characterization of this statistical test by its logical or compositional properties, showing a mutual complementarity between results of mathematical statistics and the (...) logical desiderata lying at the foundations of this theory. (shrink)

Conventional discussion of research methodology contrast two approaches, the quantitative and the qualitative, presented as collectively exhaustive. But if qualitative is taken as the understanding of lifeworlds, the two approaches between them cover only a tiny fraction of research methodologies; and the quantitative, taken as the routine application to controlled experiments of frequentist statistics by way of the Null Hypothesis Significance Testing Procedure, is seriously flawed. It is contrary to the advice both of Fisher and of Neyman and Pearson, (...) the two sources from which it is drawn. (shrink)

Conventional discussion of research methodology contrast two approaches, the quantitative and the qualitative, presented as collectively exhaustive. But if qualitative is taken as the understanding of lifeworlds, the two approaches between them cover only a tiny fraction of research methodologies; and the quantitative, taken as the routine application to controlled experiments of frequentist statistics by way of the Null Hypothesis Significance Testing Procedure, is seriously flawed. It is contrary to the advice both of Fisher and of Neyman and Pearson, (...) the two sources from which it is drawn. (shrink)

In a recent note Roger Carlson presented a rather negative appraisal of my treatment of the logic of Fisherian significance testing in [10]. The main issue between us involves Carlson's thesis that, within the limits set by Fisher, standard significance tests are valuable tools of data analysis as they stand, i.e., without modification of the structure of the reasoning they employ. Call this the adequacy thesis. In my paper I argued that the pattern of reasoning employed by tests (...) of significance needs to be justified in spite of its unquestioned acceptance by most researchers, The best justification offered to date—by R. A. Fisher—is seriously defective. Therefore the adequacy thesis is not justified. I proposed some alterations of the pattern of reasoning employed by tests of significance and argued that they guarantee that tests are adequate epistemological tools. (shrink)

A Bayesian measure of evidence for precise hypotheses is presented. The intention is to give a Bayesian alternative to significance tests or, equivalently, to p-values. In fact, a set is defined in the parameter space and the posterior probability, its credibility, is evaluated. This set is the “Highest Posterior Density Region” that is “tangent” to the set that defines the null hypothesis. Our measure of evidence is the complement of the credibility of the “tangent” region.

Chow's defense of the null-hypothesis significance- test procedure is thoughtful and compelling in many respects. Nevertheless, techniques such as meta-analysis, power analysis, effect size estimation, and confidence intervals can be useful supplements to NHSTP in furthering the cumulative nature of behavioral research, as illustrated by the history of research on the spontaneous recovery of verbal learning.

(2011). Korn and Freidlin's Misunderstanding of the Null Hypothesis Significance Testing Procedure. The American Journal of Bioethics: Vol. 11, No. 3, pp. 15-16.

Chow's book should be read only by those who already have a firm enough grasp of the logic of significance testing to separate the few valid, insightful points from the many incorrect statements and misrepresentations.

Chow's book provides a thorough analysis of the confusing array of issues surrounding conventional tests of statistical significance. This book should be required reading for behavioral and social scientists. Chow concludes that the null-hypothesis significance-testing procedure (NHSTP) plays a limited, but necessary, role in the experimental sciences. Another possibility is that – owing in part to its metaphorical underpinnings and convoluted logic – the NHSTP is declining in importance in those few sciences in which it ever played a (...) role. (shrink)

Reexamining William Rozeboom’s recommendations for the future direction of disciplines such as psychology and philosophy is imminent due to the pressing issues in null hypothesis significance testing. An overreliance on NHST forms the basis of the replication crisis in psychology. Likewise, the discipline’s stringent guidelines on significance levels convey a pressure to publish, which is also significantly contributing to the replication crisis. As researchers’ careers are staked on the extent to which they publish, reassessing the fundamental issues with (...) NHST within the context of Rozeboom’s ideas is paramount. In this brief review, I focus specifically on Rozeboom’s critiques of NHST and on a proposed alternative for evaluating the depth of findings within the framework of theoretical psychology. Thereafter, I compare his foreboding concerns with modern issues facing the validity of psychology and posit Rozeboom prophesized the failings of the discipline years ahead of his time. Keywords: Theoretical Psychology; NHST; William Rozeboom; P-Hacking; Explanatory Induction. (shrink)

Why do classic biostatistical studies, alleged to provide causal explanations of effects, often fail? This article argues that in statistics-relevant areas of biology—such as epidemiology, population biology, toxicology, and vector ecology—scientists often misunderstand epistemic constraints on use of the statistical-significance rule (SSR). As a result, biologists often make faulty causal inferences. The paper (1) provides several examples of faulty causal inferences that rely on tests of statistical significance; (2) uncovers the flawed theoretical assumptions, especially those related to randomization, (...) that likely contribute to flawed biostatistics; (3) re-assesses the three classic (SSR-warrant, avoiding-selection-bias, and avoiding-confounders) arguments for using SSR only with randomization; and (4) offers five new reasons for biologists to use SSR only with randomized experiments. (shrink)

We argue that Chow's defense of hypothesis-testing procedures attempts to restore an aura of objectivity to the core procedures, allowing these to take on the role of judgment that should be reserved for the researcher. We provide a brief overview of what we call the historical case against hypothesis testing and argue that the latter has led to a constrained and simplified conception of what passes for theory in psychology.