This article investigates relationships between countries' legal traditions and their quality of life as measured by a number of widely reported social indicators; in so doing it also offers a critique of a highly influential body of work which is widely cited in the literatures of corporate governance, economics and finance. That body of work has shown, inter alia, statistically significant relationships between legal traditions and various proxies for investor protection. We show statistically significant relationships between legal traditions and various (...) proxies for societal health. Our comparative evidence suggests that the interests of investors are not congruent with the interests of wider society, and that the criteria for judging the effectiveness of approaches to corporate governance should be broadened. (shrink)

Achieving a good clinical trial design increases the likelihood that a trial will take place as planned, including that data will be obtained from a sufficient number of participants, and the total number of participants will be the minimal required to gain the knowledge sought. A good trial design also increases the likelihood that the knowledge sought by the experiment will be forthcoming. Achieving such a design is more than good sense—it is ethically required in experiments when participants are at (...) risk of harm. This paper argues that doing a power analysis effectively contributes to ensuring that a trial design is good. The ethical importance of good trial design has long been recognized for trials in which there is risk of serious harm to participants. However, whether the quality of a trial design, when the risk to participants is only minimal, is an ethical issue is rarely discussed. This paper argues that even in cases when the risk is minimal, the quality of the trial design is an ethical issue, and that this is reflected in the emphasis the Belmont Report places on the importance of the benefit of knowledge gained by society. The paper also argues that good trial design is required for true informed consent. (shrink)

It has been claimed that if statistical power and p-values are both used to measure the strength of our evidence for the null-hypothesis when the results of our tests are not significant, then they can also be used to derive inconsistent epistemic judgements as we compare two different experiments. Those problematic derivations are known as power approach paradoxes. The consensus is that we can avoid them if we abandon the idea that statistical power can measure (...) the strength of our evidence. In this paper however, I put forward a different solution. I argue that every power approach paradox rests on an equivocation on "strong evidence". The main idea is that we need to make a careful distinction between the evidence provided by the quality of the test and the evidence provided by the outcome of the test. Both provide different types of evidence and their respective strength are to be evaluated differently. (shrink)

Chow attacks statistical power analysis on theoretical grounds. I argue that if significance testing is defensible, so is power analysis. A number of Chow's criticisms seem to suggest that power analysts are confused about certain fundamental issues. I claim that few power analysts make the mistakes Chow describes. Finally, I address Chow's claim that power analysis is irrelevant to NHSTP because it deals with a different issue.

Responsible research and good science are concepts with various meanings depending on one’s perspective and assumptions. Fellow researchers, research participants, policy makers and the general public also have differing expectations of the benefits of research ranging from accurate and reliable data that extend the body of knowledge, to solutions to societal concerns. Unless these differing constituencies articulate their differing views they may fail to communicate and undermine the value of research to society.

“Responsible research” and “good science” are concepts with various meanings depending on one’s perspective and assumptions. Fellow researchers, research participants, policy makers and the general public also have differing expectations of the benefits of research ranging from accurate and reliable data that extend the body of knowledge, to solutions to societal concerns. Unless these differing constituencies articulate their differing views they may fail to communicate and undermine the value of research to society.

English speakers use vertical language to talk about power, such as when speaking of people being “at the bottom of the social hierarchy” or “rising to the top.” Experimental research has shown tha...

In discussions of the power of causal explanations, one often finds a commitment to two premises. The first is that, all else being equal, a causal explanation is powerful to the extent that it cites the full causal history of why the effect occurred. The second is that, all else being equal, causal explanations are powerful to the extent that the occurrence of a cause allows us to predict the occurrence of its effect. This article proves a representation theorem (...) showing that there is a unique family of functions measuring a causal explanation’s power that satisfies these two premises. (shrink)

Explanation is a central concept in human psychology. Drawing upon philosophical theories of explanation, psychologists have recently begun to examine the relationship between explanation, probability and causality. Our study advances this growing literature in the intersection of psychology and philosophy of science by systematically investigating how judgments of explanatory power are affected by the prior credibility of a potential explanation, the causal framing used to describe the explanation, the generalizability of the explanation, and its statistical relevance for the (...) evidence. Collectively, the results of our five experiments support the hypothesis that the prior credibility of a causal explanation plays a central role in explanatory reasoning: first, because of the presence of strong main effects on judgments of explanatory power, and second, because of the gate-keeping role it has for other factors. Highly credible explanations were not susceptible to causal framing effects. Instead, highly credible hypotheses were sensitive to the effects of factors which are usually considered relevant from a normative point of view: the generalizability of an explanation, and its statistical relevance for the evidence. These results advance current literature in the philosophy and psychology of explanation in three ways. First, they yield a more nuanced understanding of the determinants of judgments of explanatory power, and the interaction between these factors. Second, they illuminate the close relationship between prior beliefs and explanatory power. Third, they clarify the relationship between abductive and probabilistic reasoning. (shrink)

Ethical conduct is an essential component in research, especially in medical research. Statistical methods for design and analysis are powerful research tools if used properly. Abuse of these principles and methods are just as unethical as other laboratory or clinical misconduct. Inadequate research design can produce worthless results and thus wastes effort and valuable resources. For clinical research, patient resources are wasted. Inappropriate analysis of data can also produce misleading results and conclusions. For clinical research, inferior therapy might be (...) given to patients as a consequence. These ethical concerns can have implications for and affect the individuals responsible for the statistical design and analysis. Examples are provided which illustrate some possible abuses and inappropriate pressures. (shrink)

Many philosophers have pointed out that statistical evidence, or at least some forms of it, lack desirable epistemic or non-epistemic properties, and that this should make us wary of litigations in which the case against the defendant rests in whole or in part on statistical evidence. Others have responded that such broad reservations about statistical evidence are overly restrictive since appellate courts have expressed nuanced views about statistical evidence. In an effort to clarify and reconcile, I (...) put forward an interpretive analysis of why statistical evidence should raise concerns in some cases but not others. I argue that when there is a mismatch between the specificity of the evidence and the expected specificity of the accusation, statistical evidence—as any other kind of evidence—should be considered insufficient to sustain a conviction. I rely on different stylized court cases to illustrate the explanatory power of this analysis. (shrink)

Statistical distributions have great applicability for modeling data in almost every applied sector. Among the available classical distributions, the inverse Weibull distribution has received considerable attention. In the practice of distribution theory, numerous methods have been studied and suggested/introduced to increase the flexibility level of the traditional probability distributions. In this paper, we implement different distribution methods to obtain five new different versions of the inverse Weibull model. The new modifications of the inverse Weibull model are called the logarithm (...) transformed-inverse Weibull, a flexible reduced logarithmic-inverse Weibull, the weighted TX-inverse Weibull, a new generalized-inverse Weibull, and the alpha power transformed extended-inverse Weibull distributions. To illustrate the flexibility and applicability of the new modifications of the inverse Weibull model, a biomedical data set is analyzed. The data set consists of 108 observations and represents the mortality rate of the COVID-19-infected patients. The practical application shows that the new generalized-inverse Weibull is the best modification of the inverse Weibull distribution. (shrink)

In this paper I will argue that the two main approaches to statistical mechanics, that of Boltzmann and Gibbs, constitute two substantially different theoretical apparatuses. Particularly, I defend that this theoretical split must be philosophically understood as a separation of epistemic functions within this physical domain: while Boltzmannians are able to generate powerful explanations of thermal phenomena from molecular dynamics, Gibbsians can statistically predict observable values in a highly effective way. Therefore, statistical mechanics is a counterexample to Hempel's (...) (1958) symmetry thesis, where the predictive capacity of a theory is directly correlated with its explanatory potential and vice versa. (shrink)

In the article, the policies of local, provincial institutions of state power of the Russian Empire on the collection and analysis of statistical information on the Old Believers and sectarianism are studied on the example of the Kursk provincial statistical committee. The work reviewed the history of provincial statistical committees and the basic legal acts regulating their activities. The activity of the Kursk provincial statistical committee for collection and study of statistical data on the (...) Old Believers and sectarianism in the Kursk province is considered among with various statistical materials published by the local provincial authorities of Kursk, such as the commemorative book, the collections of official reference information about the province published annually by the Kursk provincial statistical committee, and the reviews of provinces that were an annex to the annual reports of governors. Statistical materials collected by the Committee allow one to determine the numerical and religious composition of the population of the Kursk province in second half of the 19th - early 20th centuries. On the basis of analysis of the given sources, the article presents extensive statistical information on the Old Believers and sectarianism in Kursk province by areas and settlements in different years. It also shows the change in the strength of the province population according to various sects and directions of the Old Believers in the second half of the 19th - early 20th centuries. (shrink)

The null-hypothesis significance-test procedure (NHSTP) is defended in the context of the theory-corroboration experiment, as well as the following contrasts: (a) substantive hypotheses versus statistical hypotheses, (b) theory corroboration versus statistical hypothesis testing, (c) theoretical inference versus statistical decision, (d) experiments versus nonexperimental studies, and (e) theory corroboration versus treatment assessment. The null hypothesis can be true because it is the hypothesis that errors are randomly distributed in data. Moreover, the null hypothesis is never used as a (...) categorical proposition. Statistical significance means only that chance influences can be excluded as an explanation of data; it does not identify the nonchance factor responsible. The experimental conclusion is drawn with the inductive principle underlying the experimental design. A chain of deductive arguments gives rise to the theoretical conclusion via the experimental conclusion. The anomalous relationship between statistical significance and the effect size often used to criticize NHSTP is more apparent than real. The absolute size of the effect is not an index of evidential support for the substantive hypothesis. Nor is the effect size, by itself, informative as to the practical importance of the research result. Being a conditional probability, statistical power cannot be the apriori probability of statistical significance. The validity of statistical power is debatable because statistical significance is determined with a single sampling distribution of the test statistic based on H0, whereas it takes two distributions to represent statistical power or effect size. Sample size should not be determined in the mechanical manner envisaged in power analysis. It is inappropriate to criticize NHSTP for nonstatistical reasons. At the same time, neither effect size, nor confidence interval estimate, nor posterior probability can be used to exclude chance as an explanation of data. Neither can any of them fulfill the nonstatistical functions expected of them by critics. (shrink)

The paper reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that the probability distribution of money is exponential for certain classes of models with interacting economic agents. Alternative scenarios are also reviewed. Data analysis of the empirical distributions of wealth and income reveals a two-class distribution. The majority of the population belongs to the lower class, characterized (...) by the exponential (“thermal”) distribution, whereas a small fraction of the population in the upper class is characterized by the power-law (“superthermal”) distribution. The lower part is very stable, stationary in time, whereas the upper part is highly dynamical and out of equilibrium. (shrink)

In some cases, there appears to be an asymmetry in the evidential value of statistical and more individualized evidence. For example, while I may accept that Alex is guilty based on eyewitness testimony that is 80% likely to be accurate, it does not seem permissible to do so based on the fact that 80% of a group that Alex is a member of are guilty. In this paper I suggest that rather than reflecting a deep defect in statistical (...) evidence, this asymmetry might arise from a general constraint on rational inquiry. Plausibly the degree of evidential support needed to justify taking a proposition to be true depends on the stakes of error. While relying on statistical evidence plausibly raises the stakes by introducing new kinds of risk to members of the reference class, paradigmatically `individualized' evidence---evidence tracing back to A's voluntary behavior---can lower the stakes. The net result explains the apparent evidential asymmetry without positing a deep difference in the brute justificatory power of different types of evidence. (shrink)

Modern microscopic theory is employed to construct a powerful analytical algorithm that permits a clear description of characteristic features of strongly correlated quantum fluids in thermodynamic equilibrium. Using recently developed formal results we uncover an intricate relationship between strongly correlated systems and free quantum gases of appropriately defined constituents. The latter entities are precisely defined renormalized bosons or fermions. They carry all the information contained in the statistical correlations of the strongly interacting many-particle system by virtue of their effective (...) masses. The mass of such a renormalized boson or fermion depends in a specific form on temperature, bulk particle number density of the many-body system, and eventually on momentum. Due to these properties the renormalized bosons and fermions determine in particular the location and nature of the transition to non-normal phases. (shrink)

Statistics in public life .................................................................................................... .....5 Things and numbers............................................................................................. ...................8 Representative samples............................................................................................. ..........8 Averages: meaning and relevance .....................................................................................9 Correlations........................................................................................ ................................10 Applied statistics .................................................................................................... ................13 Relative risks .................................................................................................... ..................14 Relative risk versus absolute risk.....................................................................................16 Problems of classification and confounding factors....................................................17 Epidemiological research............................................................................................ ..........19 Publication bias................................................................................................ ..................20 Statistical significance versus scientific relevance................................................................24 Relative risk again............................................................................................... ...............24 P-values............................................................................................ ...................................25 Confidence intervals .................................................................................................... .....26 Correlation is not causation .............................................................................................26 An infamous episode .................................................................................................... ....27 Terror, utopianism and power .............................................................................................29 Faith and science .................................................................................................... ...........29 Fear and power: the precautionary principle.................................................................30 Utopian salvation........................................................................................... ....................32....

The paper reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that the probability distribution of money is exponential for certain classes of models with interacting economic agents. Alternative scenarios are also reviewed. Data analysis of the empirical distributions of wealth and income reveals a two-class distribution. The majority of the population belongs to the lower class, characterized (...) by the exponential (“thermal”) distribution, whereas a small fraction of the population in the upper class is characterized by the power-law (“superthermal”) distribution. The lower part is very stable, stationary in time, whereas the upper part is highly dynamical and out of equilibrium. (shrink)

This paper discusses the outstanding problem of replicability of empirical data in the context of recent work on meta-analysis, especially within the field of evidence-based medicine. Specifically, it deals with the methodological issue of how to determine the degrees of heterogeneity between different collected studies. After critically reviewing the standard measures used to quantify meta-analytical heterogeneity, we argue that they should be revised in such a way to take into account the statistical power of the individual studies. We (...) thus propose some new measures of heterogeneity. Subsequently, we apply them to re-assess concrete case-studies from clinical research, thereby showing explicitly how the relevant values of heterogeneity diverge from those obtained with the original measures. (shrink)

The rapidly increasing role of automation throughout the economy, culture and our personal lives has generated a large literature on the risks of algorithmic decision-making, particularly in high-stakes legal settings. Algorithmic tools are charged with bias, shrouded in secrecy, and frequently difficult to interpret. However, these criticisms have tended to focus on particular implementations, specific predictive techniques, and the idiosyncrasies of the American legal-regulatory regime. They do not address the more fundamental unease about the prospect that we might one day (...) replace judges with algorithms, no matter how fair, transparent, and intelligible they become. The aim of this paper is to propose an account of the source of that unease, and to evaluate its plausibility. I trace foundational unease with algorithmic decision-making in the law to the powerful intuition that there is a basic moral and legal difference between showing that something is true of many people just like you and showing that it is true of you. Human judgment attends to the exception; automation insists on blindly applying the rule. I show how this intuitive thought is connected to both epistemological arguments about the value of statistical evidence, as well as to court-centered conceptions of the rule of law. Unease with algorithmic decision-making in the law thus draws on an intuitive principle that underpins a disparate range of views in legal philosophy. This suggests the principle is deeply ingrained. Nonetheless, I argue that the powerful intuition is not as decisive as it may seem, and indeed runs into significant epistemological and normative challenges. At an epistemological level, I show how concerns about statistical evidence's ability to track the truth can be resolved by adopting a probabilistic, rather than modal, conception of truth-tracking. At a normative level, commitment to highly individualized decision-making co-exists with equally ingrained and competing principles, such as consistent application of law. This suggests that the “rule of law” may not identify a discrete set of institutional arrangements, as proponents of a court-centric conception would have it, but rather a more loosely defined set of values that could potentially be operationalized in multiple ways, including through some level of algorithmic adjudication. Although the prospect of replacing judges with algorithms is indeed unsettling, it does not necessarily entail unreasonable verdicts or an attack on the rule of law. (shrink)

Setting optimal significance levels that minimize Type I and Type II errors allows for more transparent and well‐considered statistical decision making compared to the traditional α = 0.05 significance level. We use the optimal α approach to re‐assess conclusions reached by three recently published tests of the pace‐of‐life syndrome hypothesis, which attempts to unify occurrences of different physiological, behavioral, and life history characteristics under one theory, over different scales of biological organization. While some of the conclusions reached using optimal (...) α were consistent to those previously reported using the traditional α = 0.05 threshold, opposing conclusions were also frequently reached. The optimal α approach reduced probabilities of Type I and Type II errors, and ensured statistical significance was associated with biological relevance. Biologists should seriously consider their choice of α when conducting null hypothesis significance tests, as there are serious disadvantages with consistent reliance on the traditional but arbitrary α = 0.05 significance level. (shrink)

Statistics are key elements of contemporary life. They figure prominently in the media, in political discourse, and in daily conversations. They also weigh heavily within the economic and political spheres of modern societies. Yet, the study of statistics in the public sphere has been neglected by social scientists in favor of a focus on their production and history. This article remedies this lacuna by focusing on the public life of statistics. Through a case study of a financial indicator—country risk—that exhibited (...) a rich public life in Argentina in 2001, it argues that statistics are not simply transparent fragments of information, but rich symbols and collective representations able to condense multiple meanings and generate deep emotional reactions. Using in-depth interviews, newspaper covers, headlines, and leads, cartoons and archival materials, this article shows that country risk became a powerful collective representation and introduces a new concept, the fact-totem, to make visible the cultural life of statistics. A fact-totem is a statistic with high media presence that captures the imagination of diverse publics and becomes articulated with basic identity narratives of a collectivity. This article begins to elaborate dramatic dimensions of statistics in public. (shrink)

Frequentist inference typically is described in terms of hypothetical repeated sampling but there are advantages to an interpretation that uses a single random sample. Contemporary examples are given that indicate probabilities for random phenomena are interpreted as classical probabilities, and this interpretation of equally likely chance outcomes is applied to statistical inference using urn models. These are used to address Bayesian criticisms of frequentist methods. Recent descriptions of p-values, confidence intervals, and power are viewed through the lens of (...) classical probability based on a single random sample from the population. (shrink)

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

ABSTRACT While Jeffrey Friedman’s Power Without Knowledge offers a welcome corrective to the technocratic statism that dominates modern politics, Wittgenstein’s view of language suggests that the problem of ideational heterogeneity is less worrisome than Friedman maintains. In addition, Friedman’s “exitocracy” is as epistemically demanding as ordinary technocracy and thus cannot provide an alternative to it. Anarchism, however, might provide a more consistent alternative to technocracy.

Evidence-based medicine frequently uses statistical hypothesis testing. In this paradigm, data can only disconfirm a research hypothesis’ competitors: One tests the negation of a statistical hypothesis that is supposed to correspond to the research hypothesis. In practice, these hypotheses are often misaligned. For instance, directional research hypotheses are often paired with non-directional statistical hypotheses. Prima facie, one cannot gain proper evidence for one’s research hypothesis employing a misaligned statistical hypothesis. This paper sheds lights on the nature (...) of and the reasons for such misalignments and it provides a thorough analysis of whether they pose a threat to evidence-based medicine. The upshots are that the misalignments are often hidden for clinicians and that although some cases of misalignments can be partially counterbalanced, the overall threat is non-negligible. The counterbalances either lead to methodological inadequacy, loss of statistical power, or involve a lack of information that could be crucial for decision making. This result casts doubt on various findings of medical studies in addition to issues associated with under-powered studies or the replication crisis. (shrink)

The Power of Critical Thinking: Effective Reasoning About Ordinary and Extraordinary Claims explores the essentials of critical reasoning, argumentation, logic, and argumentative essay writing while also incorporating important topics that most other texts leave out, such as "inference to the best explanation," scientific reasoning, evidence and authority, visual reasoning, and obstacles to critical thinking.The text integrates many pedagogical features, including hundreds of diverse exercises, examples, and illustrations; text boxes that apply critical thinking to student experience; step-by-step guidelines for evaluating (...) claims, arguments, and explanations; a glossary of important terms; and many reminders, summaries, and review notes. New to this editionNew sections on topics suggested by reviewers - The coverage now includes more discussion of legal reasoning, rhetorical ploys, informal fallacies, probability and statistics, and necessary and sufficient conditions.New Essays for Analysis - Nine essays, several of them by women authors, have been added to the collection of "Essays for Evaluation" in Appendix A, each article accompanied by writing prompts and linked to writing assignments in every chapter. Four pairs of essays are arranged in a pro/con format, each pair debating a single issue. New topics include homosexuality, feminists and pornography, adultery, airport security screenings, women in Afghanistan, Islamic extremists and free speech, and fear of vaccines.New text boxes on current topics. The division of labor for the text boxes is the same, but some of the content is new. The three types of boxes are "Newsmakers" ; "From the Web" ; and "Further Thought".The chapter objectives now correspond to the point-by-point summary at the end of each chapter.Important Clarifications - The following discussions are now even clearer: scientific conservatism in theory choice, the relationship between enumerative induction and statistical syllogisms, and informal fallacies.Some new discussions: the straw man fallacy, biased opinion polls, dishonest political discourse, and gut reactions and intuitions. (shrink)

The concept of constituent power plays a major part in modern political and legal theory- in how we think about the political. This book tackles the twofold issue of public authority and public autonomy in the modern conception of the political by analysing the notion of constituent power, its function in the modern political apparatus, and debates about its meaning and function in our own context. Focusing on contemporary debates on constitutionalism "beyond" the state, Geneviève Nootens assesses the (...) prospects for recasting the notion of constituent power in a polycentric setting that challenges state sovereignty as embodying the autonomy of the political. In doing so, she argues that constituent power belongs with the conceptual apparatus of a theory of government peculiar to a statist way of knowing, and being into, the world, and that it is too much dependent upon the statist framework for it to have critical purchase on new mappings of public authority. Nootens stresses the critical need to frame public authority appropriately if we are to conceptualize a conception of collective political agency that can sustain public autonomy in the current era. Constituent Power Beyond the State will be of interest to students and scholars of political theory, democratic theory, law, and constitutionalism. (shrink)

The main argument of this paper is that an evaluation of the overall explanatory power of a theory is less problematic and more relevant as an assessment of the state of knowledge than evaluation of statistical explanations of single occurrences in terms of likelihoods that are assigned to explananda.

As an intellectual, economic, political and legal project, neoliberalism is not directed towards the rolling back of the state as an aim in itself. While its deregulatory tendencies, its commodification of public services and the undermining of systems of social welfare superficially suggest a generalised reduction in state power, it has been clear from the early 1980s that one of neoliberalism’s primary concerns has been the authoritarian reshaping of state power to engineer particular social outcomes, whether in criminal (...) justice, the disciplining of organised labour, the militarisation of national territory and migration, or the extension and deepening of regimes of austerity. This article introduces the recent work of Maurizio Lazzarato, who has argued that the asymmetrical creditor-debtor relationship is now the archetype of contemporary, neoliberal social relations. Ultimately, Lazzarato’s perspective tends to exaggerate the totalising powers of finance capital and leads him to endorse a form of political voluntarism, which fails to address the role of the neoliberal state as a site for forms of authoritarianism which are not solely generated by the debt relation. As a response, it will be suggested that aspects of Nicos Poulantzas’s concept of ‘authoritarian statism’ can be used to both strengthen our understanding of the authoritarian characteristics of the neoliberal state, and to imagine possibilities for resisting its expressions of power. (shrink)

This paper emphasizes that, contrary to the claims of ECT experts and the ECT industry, a majority, not "a small minority," of ECT recipients sustain permanent memory dysfunction each year as a result of ECT. The paper exposes the convulsion hypothesis, upon which ECT is allegedly based, as mythological. Finally, through hidden and comparative electrical parameters, it exposes the extreme destructive power of today's "new and improved" ECT devices.

The development of both the modern state and modern scientific discourses in the non-Western world are closely linked together, both being the outcome of the colonial encounter. Using a Foucauldian framework of power/knowledge and his notions of ‘episteme’ and ‘governmentality’, this article explores how colonial governmentality in India produced statistical knowledge of the country thus ushering in a new social scientific discourse of ‘progress’, ‘history’, ‘economy’ and ‘society’.

We summarize the essential ingredients, which enabled us to derive the path-integral for a system of harmonically interacting spin-polarized identical particles in a parabolic confining potential, including both the statistics (Bose–Einstein or Fermi–Dirac) and the harmonic interaction between the particles. This quadratic model, giving rise to repetitive Gaussian integrals, allows to derive an analytical expression for the generating function of the partition function. The calculation of this generating function circumvents the constraints on the summation over the cycles of the permutation (...) group. Moreover, it allows one to calculate the canonical partition function recursively for the system with harmonic two-body interactions. Also, static one-point and two-point correlation functions can be obtained using the same technique, which make the model a powerful trial system for further variational treatments of realistic interactions. (shrink)

To date researchers planning experiments have always lived by the mantra that 'using equal sample sizes gives the best results' and although unequal groups are also used in experimentation, it is not the preferred method of many and indeed actively discouraged in literature. However, during live study planning there are other considerations that we must take into account such as availability of study participants, statistical power and, indeed, the cost of the study. These can all make allocating equal (...) sample sizes difficult, and sometimes near impossible. This, some might say, means that the study would not adhere to rigorous statistical standard (Rosenbaum and Rubin, 1985). However, here we present evidence that, not only is this a false assumption, but that we may actually gain more power in the study by actually using unequal groups. Here, data from a Sepsis Biomarker study is used, in which the aim is to predict, by biomarker level and presence, whether the patient would go on to develop sepsis. It was found that larger control groups may give more power to studies looking for an effect in the mid range but not for large or small effects. This study shows merit in the hypothesis that more power can be achieved when a larger control group is used. Published by the Ministry of Defence at dstl - Reference DSTLTR92592 P2PP2R-2016-02-23T13:39:45. (shrink)

Error statistics is an important methodological view in philosophy of statistics and philosophy of science that can be applied to scientific experiments such as clinical trials. In this paper, I raise two potential issues for ES when it comes to guiding, and explaining early stopping of randomized controlled trials : ES provides limited guidance in cases of early unfavorable trends due to the possibility of trend reversal; ES is silent on how to prospectively control error rates in experiments requiring multiple (...) interim analyses. The method of conditional power, together with a rationing principle for RCTs, can assist ES in addressing such issues. (shrink)

In this talk I present the main results from Anta (2021), namely, that the theoretical division between Boltzmannian and Gibbsian statistical mechanics should be understood as a separation in the epistemic capabilities of this physical discipline. In particular, while from the Boltzmannian framework one can generate powerful explanations of thermal processes by appealing to their microdynamics, from the Gibbsian framework one can predict observable values in a computationally effective way. Finally, I argue that this statistical mechanical schism contradicts (...) the Hempelian (1958) thesis that the predictive power of a scientific theory is directly proportional to its explanatory potential, and vice versa. (shrink)

Vox pops, interviews with ordinary people on the street, are one of the most common ways to represent public opinion in television news. Research found that they influence audience judgments more than static base-rate information such as poll results. However, little research has compared vox pops with vivified base-rate information. Most research studying vox pops assumed they are included in the news because of their apparent attractiveness and trustworthiness to audiences. Using a television news experiment comparing statistical base-rate information (...) vivified by an expert with vox pop statements, this study shows that news items containing vox pop statements are perceived as being less attractive and trustworthy than items containing the expert statement. No difference is found between the two types of public opinion information in their influence on perceived public opinion, but vox pops do influence audiences’ personal opinion more strongly. (shrink)

Overreliance on statistics, and even faith in them—which Richard Smith in this essay calls a branch of “metricophilia”—is a common feature of research in education and in the social sciences more generally. Of course accurate statistics are important, but they often constitute essentially a powerful form of rhetoric. For purposes of analysis and understanding, they have their limitations. In particular they tend to tell us more about correlation than causality. The extended example Smith discusses here—The Spirit Level: Why More Equal (...) Societies Almost Always Do Better, by Richard Wilkinson and Kate Pickett—shows that while statistics can be valuable guides to where further investigation needs to take place, such investigation needs the tools of other disciplines, such as philosophy and anthropology, if it is to discover matters of fundamental importance. (shrink)

This paper introduces the new novel four-parameter Weibull distribution named as the Marshall–Olkin alpha power Weibull distribution. Some statistical properties of the distribution are examined. Based on Type-I censored and Type-II censored samples, maximum likelihood estimation, maximum product spacing, and Bayesian estimation for the MOAPW distribution parameters are discussed. Numerical analysis using real data sets and Monte Carlo simulation are accomplished to compare various estimation methods. This novel model’s supremacy upon some famous distributions is explained using two real (...) data sets and it is shown that the MOAPW model can achieve better fits than other competitive distributions. (shrink)

In Feminism and the Power of Law Carol Smart argued that feminists should use non-legal strategies rather than looking to law to bring about women’s liberation. This article seeks to demonstrate that, as far as marriage is concerned, she was right. Statistics and contemporary commentary show how marriage, once the ultimate and only acceptable status for women, has declined in social significance to such an extent that today it is a mere lifestyle choice. This is due to many factors, (...) including the ‘sexual revolution’ of the 1960s, improved education and job opportunities for women, and divorce law reform, but the catalyst for change was the feminist critique that called for the abandonment (rather than the reform) of the institution and made the unmarried state possible for women. I conclude that this loss of significance has been more beneficial to British women in terms of the possibility of ‘liberation’ than appeals for legal change and recognition, and that we should continue to be wary of looking to law to solve women’s problems. (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)

Small things loom large as a distinct category in social and cultural analysis. However, the social construction and effects of this idiom of scale commonly remain vague and underexplored. Bringing the literature on quantification in conversation with the literature on scale-making, this article offers a theoretically-informed analysis of how smallness consolidates as a publicly salient social attribute, and how it feeds collective narratives. The empirical focus is on American Jewry – an ethnoreligious minority group whose leaders and experts have invested (...) in its quantification, including its representation as a small population. Drawing on a variety of texts and images, as well as on interviews and fieldwork, I show that American Jewish research bodies and public figures engage in a myriad of comparative arithmetic exercises and spectacles of scale to assert the smallness of the population. Deploying smallness as a generative narrative tool allows them to engage with the ambivalences implicated in the American-Jewish post-Holocaust, minority, and diasporic experience. In particular, exercises around notions of numerical negligibility, disproportional success, and numerical inferiority elicit protean narratives around endangerment, power, and a questioned diasporic future. The broader theoretical intervention of this article is to offer scalemaking as a valuable prism for understanding the narrative potency and poignancy of arithmetically-based constructs such as smallness. Instead of emphasizing the assumed epistemological strengths of numbers, this article considers the narrative work that statistics do when they lend themselves to multimodal scaling. It argues that through scaling, statistics are infused with perspective, relevance and meaning, descriptively and prescriptively. (shrink)