Classic analysis of the subject and the development of personal probability; one of the greatest controversies in modern statistcal thought.

ABSTRACTIn this article, we discuss the benefits of Bayesian statistics and how to utilize them in studies of moral education. To demonstrate concrete examples of the applications of Bayesian statistics to studies of moral education, we reanalyzed two data sets previously collected: one small data set collected from a moral educational intervention experiment, and one big data set from a large-scale Defining Issues Test-2 survey. The results suggest that Bayesian analysis of data sets collected from moral educational studies (...) can provide additional useful statistical information, particularly that associated with the strength of evidence supporting alternative hypotheses, which has not been provided by the classical frequentist approach focusing on P-values. Finally, we introduce several practical guidelines pertaining to how to utilize Bayesian statistics, including the utilization of newly developed free statistical software, Jeffrey’s Amazing Statistics Program, and thresholding based on Bayes Factors, to scholars in the field of moral education. (shrink)

This important collection of essays is a synthesis of foundational studies in Bayesian decision theory and statistics. An overarching topic of the collection is understanding how the norms for Bayesian decision making should apply in settings with more than one rational decision maker and then tracing out some of the consequences of this turn for Bayesian statistics. There are four principal themes to the collection: cooperative, non-sequential decisions; the representation and measurement of 'partially ordered' preferences; non-cooperative, sequential decisions; (...) and pooling rules and Bayesian dynamics for sets of probabilities. The volume will be particularly valuable to philosophers concerned with decision theory, probability, and statistics, statisticians, mathematicians, and economists. (shrink)

The explanatory filter is a proposed method to detect design in nature with the aim of refuting Darwinian evolution. The explanatory filter borrows its logical structure from the theory of statistical hypothesis testing but we argue that, when viewed within this context, the filter runs into serious trouble in any interesting biological application. Although the explanatory filter has been extensively criticized from many angles, we present the first rigorous criticism based on the theory of mathematical statistics.

CPT invariance and the spin-statistics connection are typically taken to be essential properties in relativistic quantum field theories (RQFTs), insofar as the CPT and Spin-Statistics theorems entail that any state of a physical system characterized by an RQFT must possess these properties. Moreover, in the physics literature, they are typically taken to be properties of particles. But there is a Received View among philosophers that RQFTs cannot fundamentally be about particles. This essay considers what proofs of the CPT (...) and Spin-Statistics theorems suggest about the ontology of RQFTs, and the extent to which this is compatible with the Received View. I will argue that such proofs suggest the Received View’s approach to ontology is flawed. (shrink)

After sketching the conflict between objectivists and subjectivists on the foundations of statistics, this paper discusses an issue facing statisticians of both schools, namely, model validation. Statistical models originate in the study of games of chance, and have been successfully applied in the physical and life sciences. However, there are basic problems in applying the models to social phenomena; some of the difficulties will be pointed out. Hooke's law will be contrasted with regression models for salary discrimination, the latter (...) being a fairly typical application in the social sciences. (shrink)

The social and cognitive science replication crisis is partly due to the limitations of commonly used statistical tools. Inferential statistics require that unsystematic measurement variation is independent of system history, and weak relative to systematic or causal sources of variation. However, contemporary systems research underscores the dynamic, adaptive nature of social, cognitive, and behavioral systems. Variation in human activity includes the influences of intrinsic dynamics intertwined with changing contextual circumstances. Conventional inferential techniques presume milder forms of variability, such as (...) unsystematic measurement error, as in a Gaussian distribution. Inferential statistics indicate an elementary Newtonian cause-effect metaphor for change that is inconsistent with known principles of change in complex systems. Pattern formation in self-organizing systems and quantum probability are used to illustrate theoretical metaphors that instantiate alternative notions of change in complex systems. Inferential statistics and related techniques are crucial scientific resources. However, in the social and behavioral sciences, they must be practiced in conjunction with an appropriate general systems framework that accommodates intrinsic fluctuations and contextual adaptation. (shrink)

There have been attempts to derive anti-haeccetistic conclusions from the fact that quantum mechanics (QM) appeals to non-standard statistics. Since in fact QM acknowledges two kinds of such statistics, Bose-Einstein and Fermi-Dirac, I argue that we could in the same vein derive the sharper anti-haeccetistic conclusion that bosons are bundles of tropes and fermions are bundles of universals. Moreover, since standard statistics is still appropriate at the macrolevel, we could also venture to say that no anti-haecceitistic conclusion (...) is warranted for ordinary objects, which could then tentatively be identified with substrates. In contrast to this, however, there has been so far no acknowledgement of the possibility of inclusivism, according to which ontological accounts of particulars as widely different as those can possibly coexist in one world picture. The success of the different statistics in physics at least calls for a revision in this respect. (shrink)

We start with the ambition -- dating back to the early days of the semantic web -- of assembling a significant portion human knowledge into a contradiction-free form using semantic web technology. We argue that this would not be desirable, because there are concepts, known as essentially contested concepts, whose definitions are contentious due to deep-seated ethical disagreements. Further, we argue that the ninetenth century hermeneutical tradition has a great deal to say, both about the ambition, and about why it (...) fails. We conclude with some remarks about statistics. (shrink)

In this essay David Labaree explores the historical and sociological elements that have made educational researchers dependent on statistics. He shows that educational research as a domain, with its focus on a radically soft and thoroughly applied form of knowledge and with its low academic standing, fits the pattern in which weak professions have been most likely to adopt quantification. One problem with educational researchers' seduction by the quantitative turn is that it deflects attention away from many of the (...) most important issues in the field, which are not easily reduced to standardized quanta. Another is that by adopting this rationalized, quantified, abstracted, statist, and reductionist vision of education, educational policymakers risk imposing reforms that will destroy the local practical knowledge that makes the ecology of the classroom function effectively. Quantification, Labaree suggests, may be useful for the professional interests of educational researchers, but it can be devastating for school and society. (shrink)

Jun Otsuka’s excellent book, Thinking about Statistics - the Philosophical Foundations (Otsuka 2023) is mostly organized around the idea that different statistical approaches can be illuminated by linking them to different ideas in general epistemology. Otsuka connects Bayesianism to internalism and foundationalism, frequentism to reliabilism, and the Akaike Information Criterion in model selection theory to instrumentalism. This useful mapping doesn’t cover all the interesting ideas he presents. His discussions of causal inference and machine learning are philosophically insightful, as is (...) his idea that statisticians embrace an assumption that is similar to Hume’s Principle of the Uniformity of Nature. I discuss these topics in what follows, sometimes disagreeing with details while at other times adding ideas that complement those presented in the book. (shrink)

ABSTRACT. Probability and statistics play an important role in contemporary -philosophy of causality. They are viewed as glasses through which we can see or detect causal relations. However, they may sometimes act as blinding glasses, as I will argue in this paper. In the 19th century, Francis Galton tried to statistically analyze hereditary phenomena. Although he was a far better statistician than Gregor Mendel, his biological theory turned out to be less fruitful. This was no sheer accident. His knowledge (...) of statistics generated two explananda (unknown to Mendel) which in turn generated constraints for any theory of heredity. These constraints misguided Galtons search for the causal mechanism of inheritance. This is not just. an interesting case for philosophers and historians of ·science. Notwithstanding the progress made by statitics, Galtons problem is still relevant today. In the final section, I briefly explore the implications for statistical techniques such as structural equation modelling. (shrink)

This article analyzes the role of entropy in Bayesian statistics, focusing on its use as a tool for detection, recognition and validation of eigen-solutions. “Objects as eigen-solutions” is a key metaphor of the cognitive constructivism epistemological framework developed by the philosopher Heinz von Foerster. Special attention is given to some objections to the concepts of probability, statistics and randomization posed by George Spencer-Brown, a figure of great influence in the field of radical constructivism.

Quantification has been constitutive of psychology since its inception and is core to its scientific status. The adoption of qualitative methods eschewing inferential statistics is therefore unlikely to obtain. Rather than discarding useful tools because of improper use, we recommend highlighting how inferential statistics can be more thoughtfully applied.

We contrast two theoretical positions on the relation between phenomenal and access consciousness. First, we discuss previous data supporting a mild Overflow position, according to which transient visual awareness can overflow report. These data are open to two interpretations: (i) observers transiently experience specific visual elements outside attentional focus without encoding them into working memory; (ii) no specific visual elements but only statistical summaries are experienced in such conditions. We present new data showing that under data-limited conditions observers cannot discriminate (...) a simple relation (same versus different) without discriminating the elements themselves and, based on additional computational considerations, we argue that this supports the first interpretation: summary statistics (same/different) are grounded on the transient experience of elements. Second, we examine recent data from a variant of ‘inattention blindness’ and argue that contrary to widespread assumptions, it provides further support for Overflow by highlighting another factor, ‘task relevance’, which affects the ability to conceptualize and report (but not experience) visual element. (shrink)

This article provides a concise summary of Thinking About Statistics: The Philosophical Foundations (Routledge, 2023), with a focus on the book’s exploration of ontological and epistemological topics.

What justifies the use of Bayesian statistics in science? The traditional answer is that Bayesian statistics is simply an instance of orthodox expected utility theory. Thus, Bayesian statistical methods, like principles of utility theory, are justified by norms of individual rationality. In particular, most Bayesians argue that a scientist's credences must satisfy the probability axioms if she adheres to norms of practical and epistemic rationality. We argue that, to justify Bayesian statistics as a tool for science, it (...) is necessary that a scientist's public credences obey the probability axioms. We claim that norms of collective science help justify this restricted view, termed public probabilism. (shrink)

The efficient coding hypothesis posits that sensory systems are tuned to the regularities of their natural input. The statistics of natural image databases have been the topic of many studies, which have revealed biases in the distribution of orientations that are related to neural representations as well as behavior in psychophysical tasks. However, commonly used natural image databases contain images taken with a camera with a planar image sensor and limited field of view. Thus, these images do not incorporate (...) the physical properties of the visual system and its active use reflecting body and eye movements. Here, we investigate quantitatively, whether the active use of the visual system influences image statistics across the visual field by simulating visual behaviors in an avatar in a naturalistic virtual environment. Images with a field of view of 120° were generated during exploration of a virtual forest environment both for a human and cat avatar. The physical properties of the visual system were taken into account by projecting the images onto idealized retinas according to models of the eyes' geometrical optics. Crucially, different active gaze behaviors were simulated to obtain image ensembles that allow investigating the consequences of active visual behaviors on the statistics of the input to the visual system. In the central visual field, the statistics of the virtual images matched photographic images regarding their power spectra and a bias in edge orientations toward cardinal directions. At larger eccentricities, the cardinal bias was superimposed with a gradually increasing radial bias. The strength of this effect depends on the active visual behavior and the physical properties of the eye. There were also significant differences between the upper and lower visual field, which became stronger depending on how the environment was actively sampled. Taken together, the results show that quantitatively relating natural image statistics to neural representations and psychophysical behavior requires not only to take the structure of the environment into account, but also the physical properties of the visual system, and its active use in behavior. (shrink)

Increasingly, clinical research is evaluated on the quality of its statistical analysis. Traditionally, statistical analyses in clinical research have been carried out from a ‘frequentist’ perspective. The presence of an alternative paradigm – the Bayesian paradigm – has been relatively unknown in clinical research until recently. There is currently a growing interest in the use of Bayesian statistics in health care research. This is due both to a growing realization of the limitations of frequentist methods and to the ability (...) of Bayesian methods explicitly to incorporate prior expert knowledge and belief into the analyses. This is in contrast to frequentist methods, where prior experience and beliefs tend to be incorporated into the analyses in an ad hoc fashion. This paper outlines the frequentist and Bayesian paradigms. Acute myocardial infarction mortality data are then analysed from both a Bayesian and a frequentist perspective. In some analyses, the two methods are seen to produce comparable results; in others, they produce different results. It is noted that in this example, there are clinically relevant questions that are more easily addressed from a Bayesian perspective. Finally, areas in clinical research where Bayesian ideas are increasingly common are highlighted. (shrink)

We introduce for the first time the appurtenance equation and inclusion equation, which help in understanding the operations with neutrosophic numbers within the frame of neutrosophic statistics. The way of solving them resembles the equations whose coefficients are sets (not single numbers).

Researchers rely on psychometric principles when trying to gain understanding of unobservable psychological phenomena disconfounded from the methods used. Psychometric models provide us with tools to support this endeavour, but they are agnostic to the meaning researchers intend to attribute to the data. We define method effects as resulting from actions which weaken the psychometric structure of measurement, and argue that solution to this confounding will ultimately rest on testing whether data collected fit a psychometric model based on a substantive (...) theory, rather than a search for a model that best fits the data. We highlight the importance of taking the notions of fundamental measurement seriously by reviewing distinctions between the Rasch measurement model and more generalised 2PL and 3PL IRT models. We then present two lines of research that highlight considerations of making method effects explicit in experimental designs. First, we contrast the use of experimental manipulations to study measurement reactivity during the assessment of metacognitive processes with factor-analytic research of the same. The former suggests differential performance-facilitating and -inhibiting reactivity as a function of other individual differences, whereas factor-analytic research suggests a ubiquitous monotonically predictive confidence factor. Second, we evaluate differential effects of context and source on within-individual variability indices of personality derived from multiple observations, highlighting again the importance of a structured and theoretically grounded observational framework. We conclude by arguing that substantive variables can act as method effects and should be considered at the time of design rather than after the fact, and without compromising measurement ideals. (shrink)

There are many philosophical questions surrounding the notion of lying. Is it ever morally acceptable to lie? Can we acquire knowledge from people who might be lying to us? More fundamental, however, is the question of what, exactly, constitutes the concept of lying. According to one traditional definition, lying requires intending to deceive (Augustine. (1952). Lying (M. Muldowney, Trans.). In R. Deferrari (Ed.), Treatises on various subjects (pp. 53?120). New York, NY: Catholic University of America). More recently, Thomas Carson (2006. (...) The definition of lying. Nous, 40, 284?306) has suggested that lying requires warranting the truth of what you do not believe. This paper examines these two prominent definitions and some cases that seem to pose problems for them. Importantly, theorists working on this topic fundamentally disagree about whether these problem cases are genuine instances of lying and, thus, serve as counterexamples to the definitions on offer. To settle these disputes, we elicited judgments about the proposed counterexamples from ordinary language users unfettered by theoretical bias. The data suggest that everyday speakers of English count bald-faced lies and proviso lies as lies. Thus, we claim that a new definition is needed to capture common usage. Finally, we offer some suggestions for further research on this topic and about the moral implications of our investigation into the concept of lying. (shrink)

The ArgumentMost lay users of statistics think in terms of means (averages), variances or the square of the standard deviation, and Gaussians or bell-shaped curves. Such conventions are entrenched by statistical practice, by deep mathematical theorems from probability, and by theorizing in the various natural and social sciences. I am not claiming that the particular conventions (here, the statistics) we adopt are arbitrary. Entrenchment can be rational without its being as well categorical (excluding all other alternatives), even if (...) that entrenchment claims also to provide for categoricity. 1 provide a detailed description of how a science is “normal” and conventionalized. A characteristic feature of this entrenchment of conventions by practice, theorems, and theorizing, is its highly technical form, the canonizing work enabled by apparently formal and esoteric mathematical means. (shrink)

The last two decades have seen a welcome proliferation of the collection and dissemination of data on social progress, as well as considered public debates rethinking existing standards of measuring the progress of societies. These efforts are to be welcomed. However, they are only a nascent step on a longer road to the improved measurement of social progress. In this paper, I focus on the central role that gender should take in future efforts to measure progress in securing human rights, (...) with a particular focus on anti-poverty rights. I proceed in four parts. First, I argue that measurement of human rights achievements and human rights deficits is entailed by the recognition of human rights, and that adequate measurement of human rights must be genuinely gender-sensitive. Second, I argue that existing systems of information collection currently fail rights holders, especially women, by failing to adequately gather information on the degree to which their rights are secure. If my first two claims are correct, this failure represents a serious injustice, and in particular an injustice for women. Third, I make recommendations regarding changes to existing information collection that would generate gender-sensitive measures of anti-poverty rights. Fourth, I conclude by responding to various objections that have been raised regarding the rise of indicators to track human rights. (shrink)

In this paper we show that Neutrosophic Statistics is an extension of Interval Statistics, since it deals with all kinds of indeterminacy (with respect to data, inferential procedures, probability distributions, graphical representations, etc.), allows for indeterminacy reduction, and uses neutrosophic probability which is more general than imprecise and classical probabilities, and has more detailed corresponding probability density functions. Whereas Interval Statistics only deals with indeterminacy that can be represented by intervals. And we respond to the arguments of (...) Woodall et al [1]. We show that not all indeterminacies (uncertainties) can be represented by intervals. Moreover, in some applications, we should use hesitant sets (which have less indeterminacy) instead of intervals. We redirect the authors to Plitogenic Probability and Plitogenic Statistics which are the most general forms of Multivariate Probability and Multivariate Statistics respectively (including, of course, Imprecise Probability and Interval Statistics as subclasses). (shrink)

The concept of classical indistinguishability is analyzed and defended against a number of well-known criticisms, with particular attention to the Gibbs’paradox. Granted that it is as much at home in classical as in quantum statistical mechanics, the question arises as to why indistinguishability, in quantum mechanics but not in classical mechanics, forces a change in statistics. The answer, illustrated with simple examples, is that the equilibrium measure on classical phase space is continuous, whilst on Hilbert space it is discrete. (...) The relevance of names, or equivalently, properties stable in time that can be used as names, is also discussed. (shrink)

While cultural sociology has recently made a comeback in research on social inequality both in the context of poverty studies and studies of immigrant integration, it has rarely investigated how particular constructions of the problem of socioeconomic mobility are themselves culturally situated. The article addresses this neglect by investigating the problematization of disadvantaged lives within the relational framework of Bourdieu’s cultural theory of the state. Here, the state exercises symbolic violence by transforming one arbitrary cultural standpoint in social space into (...) a universal standard, or a taken-for-granted “doxa,” against which other cultural positions can only come off as deficient. The article extends this perspective by addressing the role of official statistics in this process. Taking Germany’s official monitoring of the socioeconomic integration of immigrants as its case and drawing from document analysis, interviews, ethnographic observation, and data from the German General Social Survey, the article shows how such statistical instruments of the welfare state in fact tacitly universalize a model of the good life particular to civil servants, the very constructors of the monitors, as a benchmark for immigrant integration. (shrink)

In this third paper in a series on stochastic electrodynamics (SED), the nonrelativistic dipole approximation harmonic oscillator-zero-point field system is subjected to an arbitrary classical electromagnetic radiation field. The ensemble-averaged phase-space distribution and the two independent ensemble-averaged Liouville or Fokker-Planck equations that it satisfies are derived in closed form without furtner approximation. One of these Liouville equations is shown to be exactly equivalent to the usual Schrödinger equation supplemented by small radiative corrections and an explicit radiation reaction (RR) vector potential (...) that is similar to the Crisp-Jaynes semiclassical theory (SCT) RR potential. The wave function in this SED Schrödinger equation is shown to have thea priori significance of position probability amplitude. The other Liouville equation has no counterpart in ordinary quantum mechanics, and is shown to restrict initial conditions such that (i) The Wigner-type phase-space distribution is always positive, (ii) in the absence of an applied field, the only allowed solution of both equations is the quantum ground state, and (iii) if a previously applied field is suddenly turned off, then spontaneous transitions occur, with no need for a triggering perturbation as in SCT, until the system is in the ground state. It is also shown that the oscillator energy is a fluctuating quantity that must take on a continuum of values, with average value equal to the quantum ground-state energy plus a contribution due to the applied classical field. (shrink)

Alternative displays of effect size statistics can enhance the understandability and impact of validity evidence in a variety of applied settings. Arguably, the proliferation of alternative effect size statistics has been limited due to the lack of user-friendly tools to create them. Common statistical packages do not readily produce these alternative effect sizes and existing tools are outdated and inaccessible. In this paper, I introduce a free-to-use web-based calculator (https://dczhang.shinyapps.io/expectancyApp/) for generating alternative effect size displays from empirical data. (...) This calculator requires no mathematical or programming expertise, and therefore, is ideal for academics and practitioners. I also present results from an empirical study that demonstrates the benefits of alternative effect size displays for enhancing lay people’s perceived understandability of validity information and attitudes toward the use of standardized testing for college admissions. (shrink)

We investigate the hypothesis that within a combination of a ‘number concept’ plus a ‘substantive concept’, such as ‘eleven animals’, the identity and indistinguishability present on the level of the concepts, i.e., all eleven animals are identical and indistinguishable, gives rise to a statistical structure of the Bose–Einstein type similar to how Bose–Einstein statistics is present for identical and indistinguishable quantum particles. We proceed by identifying evidence for this hypothesis by extracting the statistical data from the World-Wide-Web utilizing the (...) Google Search tool. By using the Kullback–Leibler divergence method, we then compare the obtained distribution with the Maxwell–Boltzmann as well as with the Bose–Einstein distributions and show that the Bose–Einstein’s provides a better fit as compared to the Maxwell–Boltzmann’s. (shrink)

With special attention being paid to recent developments in Artificial Intelligence and the Law, specifically related to evidentiary reasoning, this book ...