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)

Statistics and probability enabled students to better understand, process, and evaluate massive amounts of quantitative data that existed and had a probabilistic sense in uncertain situations. The research article aimed to elucidate the performance and self-efficacy as predictors of students' achievement in the statistics and probability courses. The study utilized a descriptive-predictive research method and was conducted at Sto. Tomas National High School, involving a sample of 263 grade 11 senior high school students. The gathered data were analyzed (...) using descriptive measures and multiple regression analysis. The study's results revealed that the performance in General Mathematics was very satisfactory, while self-efficacy was high. Moreover, the level of achievement in Statistics and Probability was very satisfactory. It was also revealed that both General Mathematics performance and self-efficacy had a positive and significant relationship with Statistics and Probability achievement. Through regression analysis, it was discovered that General Mathematics performance was the strongest predictor that influenced achievement in Statistics and Probability. The study identified a significant predictive model for Statistics and Probability achievement. These findings could provide valuable guidance to teachers in enhancing the achievement of senior high school students in Statistics and Probability. (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)

Otsuka (2023) argues for a correspondence between data science and traditional epistemology: Bayesian statistics is internalist; classical (frequentist) statistics is externalist, owing to its reliabilist nature; model selection is pragmatist; and machine learning is a version of virtue epistemology. Where he sees diversity, I see an opportunity for unity. In this article, I argue that classical statistics, model selection, and machine learning share a foundation that is reliabilist in an unconventional sense that aligns with internalism. Hence a (...) unification under internalist reliabilism. (shrink)

This article explores the intersection of philosophy and statistics by examining the philosophical assumptions underlying modern mathematical statistics from ontological and epistemological perspectives. Statistics holds interest for philosophers engaged with the problem of induction, as its mathematical apparatus serves as models for philosophical ideas. For instance, the much-discussed concepts of the uniformity of nature and natural kinds correspond to probability models and statistical models, which are fundamental to various statistical methods. Similarly, Dennett’s concept of a real pattern (...) echoes the spirit of various information criteria (such as AIC) used to determine the optimal level of complexity for maximizing a model’s predictive ability. Furthermore, the recent developments in machine learning models, such as deep learning, imply that these machines possess their own 'ontology,' which is potentially more complex and efficient at understanding the world than ours. This leads to a Quinean problem of radical translation between human and machine ontologies. We suggest that this issue is key to the successful application of AI technologies in our society. The other focus of this article is epistemology, where Bayesian and classical statistics are compared to internalist and externalist epistemologies, respectively. This comparison elucidates how and in what sense the statistical methods adopted in each camp are considered to justify scientific hypotheses and also sheds light on their epistemic problems. We conclude with a plea for more research and interdisciplinary dialogues between statistics and the philosophy of various traditions. (shrink)

Classic analysis of the subject and the development of personal probability; one of the greatest controversies in modern statistcal thought. New preface and new footnotes to 1954 edition, with a supplementary 180-item annotated bibliography by author. Calculus, probability, statistics, and Boolean algebra are recommended.

This paper argues that unusual coincidences, particularly those involving historical events, can be viewed as design patterns, suggesting an intelligent influence over the course of events. A compelling case examined in detail using probability theory concerns the presidencies of Abraham Lincoln (1809–1865) and John F. Kennedy (1917–1963). This and other coincidences involving historical figures disfavor the materialistic perspective and point to the presence of an intelligent agent acting on a global scale, beyond the arrow of time, influencing human lives and (...) the course of history. (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)

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)

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)

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)

Much of the science and religion debate has focussed on statistics. The chapters in this section go beyond bare statistics by examining more nuanced studies of science, religion and education with the aim of developing a deeper understanding of the issues at play when attempting to deal with the issues of science and religion in the classroom.

The traditional standard theory of quantum mechanics is unable to solve the spin–statistics problem, i.e. to justify the utterly important “Pauli Exclusion Principle” but by the adoption of the complex standard relativistic quantum field theory. In a recent paper :858–873, 2015) we presented a proof of the spin–statistics problem in the nonrelativistic approximation on the basis of the “Conformal Quantum Geometrodynamics”. In the present paper, by the same theory the proof of the spin–statistics theorem is extended to (...) the relativistic domain in the general scenario of curved spacetime. The relativistic approach allows to formulate a manifestly step-by-step Weyl gauge invariant theory and to emphasize some fundamental aspects of group theory in the demonstration. No relativistic quantum field operators are used and the particle exchange properties are drawn from the conservation of the intrinsic helicity of elementary particles. It is therefore this property, not considered in the standard quantum mechanics, which determines the correct spin–statistics connection observed in Nature :858–873, 2015). The present proof of the spin–statistics theorem is simpler than the one presented in Santamato and De Martini :858–873, 2015), because it is based on symmetry group considerations only, without having recourse to frames attached to the particles. Second quantization and anticommuting operators are not necessary. (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.

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)

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)

Education in statistics, the application of statistics in scientific research, and statistics itself as a scientific discipline are in crisis. Within science, the main cause of the crisis is the insufficiently clarified concept of probability. This article aims to separate the concept of probability which is scientifically based from other concepts that do not have this characteristic. The scientifically based concept of probability is Kolmogorov’s concept of probability models together with the conditions of their applicability. Bayesian (...) class='Hi'>statistics is based on the subjective concept of probability, and as such can only have a heuristic value in searching for the truth, but it cannot and must not replace the truth. The way out of the crisis should take Kolmogorov and Bayesian analysis as elements, each of which has a well-defined and limited use. Only together with qualitative analysis and other types of quantitative analysis, and combined with experiments, they can contribute to reaching correct conclusions. (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.

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)

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)

In European countries (excluding the UK and Ireland), official statistics do not use racial or ethnic categories, but instead rely on proxies to collect data about discrimination. In the German microcensus, the proxy category adopted is ‘migration background’ (Migrationshintergrund): an individual has a ‘migration background’ when one or more of their parents does not have German citizenship by birth. We apply a coupled ethical-epistemic analysis to the ‘migration background’ category to illuminate how the epistemic issues contribute to ethical ones. (...) Our central claim is that these ethical-epistemic issues with the ‘migration background’ category are best analysed in terms of Charles Mills's ‘white ignorance’. Appealing to Annette Martín's structural account of white ignorance, we highlight the cyclical reinforcement of ignorance and racial injustice in the use of the ‘migration background’ variable. Colourblind eliminativism about race perpetuates the use of ‘migration background’, which sustains and intensifies racial injustices. (shrink)

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)

In this article I investigate the extent to which perspectival realism (PR) agrees with frequentist statistical methodology and philosophy, with an emphasis on J. Neyman’s frequentist statistical methods and philosophy. PR is clarified in the context of frequentist statistics. Based on the example of the stopping rule problem, PR is shown to be able to naturally be associated with frequentist statistics in general. I show that there are explicit and implicit aspects of Neyman’s methods and philosophy that are (...) incompatible and both partially agree and disagree with PR. Additionally, I provide clarifications and interpretations to make Neyman’s methods and philosophy more coherent with the realist aspect of PR. Furthermore, I deliver an argument that, based on Neyman’s methods and philosophy, one is dealing with genuine and non-trivial perspectives. I argue that, despite Neyman being a normative anti-pluralist, there are some elements of perspectival pluralism present in his methods and philosophy. In conclusion, firstly, due to their ambivalence, Neyman’s conceptions align more closely with PR than with alternative, less moderate stances. Secondly, from the perspective of the statistical approach analysed, PR should be treated as a descriptive rather than a normative position, and as case (or aspect)-dependent, rather than a universal, absolute, or binding stance. (shrink)

This article examines the impact of the reporting practice andpaper technologieslike forms on reports that were later used for national morbidity statistics by studying the Swiss reporting system for infectious diseases between 1886 and 1921. Analysing the production processes of notifications shows the difficulties and solutions in the implementation of the statutory reporting process. Two disease outbreaks—a smallpox outbreak in Schaffhausen and a typhoid outbreak in the canton of Lucerne—serve as case studies. It is shown that reports are not (...) only objective representations of diseases, but also symbolize the medico-social interactions that produce them, timed by administrative tools like reporting forms and the act of reporting. This destabilises historical statistics and illustrates the complexity of the historical source material, as these interactions and their impact on reporting must be considered. These findings are further supported by examining the Swiss reporting system during the Spanish flu of 1918 and its failure to record influenza cases. (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)

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)