A robust Spearman correlation coefficient permutation test.

In this work, we show that Spearman's correlation coefficient test about H0:ρs=0 found in most statistical software is theoretically incorrect and performs poorly when bivariate normality assumptions are not met or the sample size is small. There is common misconception that the tests about ρs=0 are robust to deviations from bivariate normality. However, we found under certain scenarios violation of the bivariate normality assumption has severe effects on type I error control for the common tests. To address this issue, we developed a robust permutation test for testing the hypothesis H0:ρs=0 based on an appropriately studentized statistic. We will show that the test is asymptotically valid in general settings. This was demonstrated by a comprehensive set of simulation studies, where the proposed test exhibits robust type I error control, even when the sample size is small. We also demonstrated the application of this test in two real world examples.

Definition of normal, neutral, deviant and aberrant coronal knee alignment for total knee arthroplasty.

PURPOSE: One of the most pertinent questions in total knee arthroplasty (TKA) is: what could be considered normal coronal alignment? This study aims to define normal, neutral, deviant and aberrant coronal alignment using large data from a computed tomography (CT)-scan database and previously published phenotypes. METHODS: Coronal alignment parameters from 11,191 knee osteoarthritis (OA) patients were measured based on three dimensional reconstructed CT data using a validated planning software. Based on these measurements, patients' coronal alignment was phenotyped according to the functional knee phenotype concept. These phenotypes represent an alignment variation of the overall hip knee ankle angle (HKA), femoral mechanical angle (FMA) and tibial mechanical angle (TMA). Each phenotype is defined by a specific mean and covers a range of ±1.5° from this mean. Coronal alignment is classified as normal, neutral, deviant and aberrant based on distribution frequency. Mean values and distribution among the phenotypes are presented and compared between two populations (OA patients in this study and non-OA patients from a previously published study). RESULTS: The arithmetic HKA (aHKA), combined normalised data of FMA and TMA, showed that 36.0% of knees were neutral within ±1 SD from the mean in both angles, 44.3% had either a TMA or a FMA within ±1-2 SD (normally aligned), 15.3% of the patients were deviant within ±2-3 SD and only 4.4% of them had an aberrant alignment (±3-4 SD in 3.4% and >4 SD in 1.0% of the patients respectively). However, combining the normalised data of HKA, FMA and TMA, 15.4% of patients were neutral in all three angles, 39.7% were at least normal, 27.7% had at least one deviant angle and 17.2% had at least one aberrant angle. For HKA, the males exhibited 1° varus and females were neutral. For FMA, the females exhibited 0.7° more valgus in mean than males and grew 1.8° per category (males grew 2.1° per category). For TMA, the males exhibited 1.3° more varus than females and both grew 2.3° and 2.4° (females) per category. Normal coronal alignment was 179.2° ± 2.8-5.6° (males) and 180.5 > ± 2.8-5.6° (females) for HKA, 93.1 > ± 2.1-4.2° (males) and 93.8 > ± 1.8-3.6° (females) for FMA and 86.7 > ± 2.3-4.6° (males) and 88 > ± 2.4-4.8° (females) for TMA. This means HKA 6.4 varus or 4.8° valgus (males) or 5.1° varus to 6.1° valgus was considered normal. For FMA HKA 1.1 varus or 7.3° valgus (males) or 0.2° valgus to 7.4° valgus was considered normal. For TMA HKA 7.9 varus or 1.3° valgus (males) or 6.8° varus to 2.8° valgus was considered normal. Aberrant coronal alignment started from 179.2° ± 8.4° (males) and 180.5 > ± 8.4° (females) for HKA, 93.1 > ± 6.3° (males) 93.8 > ± 5.4° (females) for FMA and 86.7 > ± 6.9° (males) and 88 > ± 7.2° (females) for TMA. This means HKA > 9.2° varus or 7.6° valgus (males) or 7.9° varus to 8.9° valgus was considered aberrant. CONCLUSION: Definitions of neutrality, normality, deviance as well as aberrance for coronal alignment in TKA were proposed in this study according to their distribution frequencies. This can be seen as an important first step towards a safe transition from the conventional one-size-fits-all to a more personalised coronal alignment target. There should be further definitions combining bony alignment, joint surfaces' morphology, soft tissue laxities and joint kinematics. LEVEL OF EVIDENCE: III.

Groundwater quality assessment for drinking purpose using traditional and fuzzy-GIS-based water quality index in Gurugram District of Haryana, India.

Primarily groundwater is consumed for the drinking and irrigation purpose. However, due to increasing anthropogenic activities, its quality and quantity have substantially declined over time. The focus of this study is to evaluate the pre-monsoonal groundwater quality and its spatial variability for drinking purposes in the Gurugram, Haryana, India. Ground Water quality index (GWQI) developed on the basis of the Geographical Information System is effective in the assessment of groundwater quality and its spatial variability, but it is unable to account for uncertainties related to environmental problems. Thus, a Hybrid Fuzzy-GIS-based Water Quality Index (FGQI) has been proposed for the assessment of groundwater quality. The study conducted factor analysis to identify the prime factors responsible for groundwater contamination and collected pre-monsoonal groundwater samples through primary sampling. The groundwater quality was assessed based on eight hydro geochemical parameters (pH, TDS, Calcium, Chloride, Sulfate, Fluoride, Potassium, and Sodium). The spatial interpolation of each parameter was performed using appropriate techniques, selected based on a normality test. The guidelines of the World Health Organization and Bureau of Indian Standard were incorporated in the development of GWQI and FGQI, respectively. Correlation analysis was performed to determine the best fuzzy overlay technique for FGQI, and the Fuzzy GAMMA technique with gamma equal to 0.9 was selected. Finally, the GWQI and FGQI were classified into three classes: unsuitable, moderate suitable, and suitable using "natural break". A higher index indicates a higher water quality. The results show that the groundwater in the central part of Gurugram is suitable for drinking, while it is not suitable in the extreme north, south-east, and western regions. In conclusion, this study finds that FGQI effectively assesses the groundwater quality in the region better than GWQI.

Examining the normality assumption of a design-comparable effect size in single-case designs.

What Works Clearinghouse (WWC, 2022) recommends a design-comparable effect size (D-CES; i.e., gAB) to gauge an intervention in single-case experimental design (SCED) studies, or to synthesize findings in meta-analysis. So far, no research has examined gAB's performance under non-normal distributions. This study expanded Pustejovsky et al. (2014) to investigate the impact of data distributions, number of cases (m), number of measurements (N), within-case reliability or intra-class correlation (ρ), ratio of variance components (λ), and autocorrelation (ϕ) on gAB in multiple-baseline (MB) design. The performance of gAB was assessed by relative bias (RB), relative bias of variance (RBV), MSE, and coverage rate of 95% CIs (CR). Findings revealed that gAB was unbiased even under non-normal distributions. gAB's variance was generally overestimated, and its 95% CI was over-covered, especially when distributions were normal or nearly normal combined with small m and N. Large imprecision of gAB occurred when m was small and ρ was large. According to the ANOVA results, data distributions contributed to approximately 49% of variance in RB and 25% of variance in both RBV and CR. m and ρ each contributed to 34% of variance in MSE. We recommend gAB for MB studies and meta-analysis with N ≥ 16 and when either (1) data distributions are normal or nearly normal, m = 6, and ρ = 0.6 or 0.8, or (2) data distributions are mildly or moderately non-normal, m ≥ 4, and ρ = 0.2, 0.4, or 0.6. The paper concludes with a discussion of gAB's applicability and design-comparability, and sound reporting practices of ES indices.

Face Mask and Tear Film Stability: A Pilot Study of the Objective Measurement of Tear Break-Up Time.

(1) Background: Mask-associated dry eye (MADE) has been associated with increased dry eye symptoms, apparently due to reduced tear break-up time (TBUT). This study aimed to determine the short-term impact of surgical face mask (FM) on tear film stability by measuring non-invasive tear break-up time (NIBUT). (2) Methods: Twenty-six healthy participants had NIBUT evaluated without FM, with surgical FM and with a surgical FM secured to the skin with adhesive tape (TFM). NIBUT-first was measured with Keratograph 5M (K5M, Oculus, Wetzlar, Germany). Each participant had NIBUT measured in four sessions on four consecutive days. Session 1: without FM vs. with FM. Session 2: with FM vs. without FM. Session 3: without FM vs. with TFM. Session 4: with TFM vs. without FM (3). The time between each measured setting was 2 min. Results: The mean ± SD NIBUT without FM was 8.9 ± 3.7, with FM 10.2 ± 4.1, and with TFM 8.4 ± 3.8 s. No significant differences were observed in NIBUT in any of the evaluated settings: without FM vs. with FM (p = 0.247), without FM vs. with TFM (p = 0.915), and with FM vs. with TFM (p = 0.11). (4) Conclusions: This study did not find a significant short-term effect of FM on NIBUT. Other variables or longer periods of exposure might trigger the symptoms and ocular surface alterations in MADE.

The Ubiquity of Psychopathology and the Quandaries this Imposes for Determining "Reality".

In this article, I argue that psychopathology ubiquitously pervades individual and social life. As Freud wrote, each of us finds some way of distorting reality, and as Laing contended, human beings have an almost unlimited capacity for self-deception. History is a chronicle of fantasies, mirages, distortions, and metaphysical consolations believed as apodictic reality, and the bizarre magico-salvific stratagems people adopted to ward off disease, catastrophe, and death. And yet many (even psychoanalysts) maintain the notion (or fantasy) that we perceive reality clearly and sanely. I contend, on the contrary, that we have no epistemologically foolproof way of discerning our own deceptions and defects, and that we find all manner of ingenious excuses not to see ourselves.

Barriers and Challenges for Visually Impaired Students in PE-An Interview Study with Students in Austria, Germany, and the USA.

Physical education (PE) is an important part of school education worldwide, and at the same time, almost the only subject that explicitly deals with body and movement. PE is therefore of elementary importance in the upbringing of young people. This also applies to children with visual impairments. However, existing findings on participation and belonging in PE as well as on physical and motor development reveal that this group of children and adolescents is noticeably disadvantaged in this respect. Against this background, this paper aims to explore fundamental barriers and challenges across different types of schools, types of schooling, and countries from the perspective of visually impaired children. The qualitative interview study with 22 children with visual impairments at different types of schools in three countries (Austria, Germany, USA) reveals that none of the respondents could escape the power of social distinctions and related problematic and existing hierarchies. Hence, ideas of normality and associated values remain the main challenge for all of them. However, the type-forming analysis provides important insight across settings on how visually impaired children differ on this, allowing for greater sensitivity to the concerns of children with visual impairments.

Toward quantitative super-resolution microscopy: molecular maps with statistical guarantees.

Quantifying the number of molecules from fluorescence microscopy measurements is an important topic in cell biology and medical research. In this work, we present a consecutive algorithm for super-resolution (stimulated emission depletion (STED)) scanning microscopy that provides molecule counts in automatically generated image segments and offers statistical guarantees in form of asymptotic confidence intervals. To this end, we first apply a multiscale scanning procedure on STED microscopy measurements of the sample to obtain a system of significant regions, each of which contains at least one molecule with prescribed uniform probability. This system of regions will typically be highly redundant and consists of rectangular building blocks. To choose an informative but non-redundant subset of more naturally shaped regions, we hybridize our system with the result of a generic segmentation algorithm. The diameter of the segments can be of the order of the resolution of the microscope. Using multiple photon coincidence measurements of the same sample in confocal mode, we are then able to estimate the brightness and number of molecules and give uniform confidence intervals on the molecule counts for each previously constructed segment. In other words, we establish a so-called molecular map with uniform error control. The performance of the algorithm is investigated on simulated and real data.

Normality and mental health: The ethical dimension / Normalidad y salud mental: La dimensión ética

Abstract This article applies the concept of normality, in both its descriptive and normative connotations, to the field of mental health, emphasizing its ethical undertones in different cultural and situational contexts. Ethics is defined as the linguistic justification of morals, and bioethics is characterized by arguments based on dialogical, discursive, and deliberative processes. Bioethical decision-making influences human relationships and has implications for diagnosis, prognosis, interventions, and evaluation of therapeutic results and outcomes. Normality in mental health should be reformulated on bioethical principles to avoid being a source of stigma and discrimination, at a time when human diversity and cultural change impose a redefinition of conceptual boundaries and depathologization of different forms of behavior and experience.

Resumen Se aplica el concepto de normalidad en sus connotaciones descriptiva y normativa al campo de la salud mental, destacando su tonalidad ética en diferentes contextos culturales y situacionales. Se define la ética como la justificación lingüística de la moral y se caracteriza a la bioética como fuente de argumentos basados en procesos dialógicos, discursivos y deliberativos. La toma de decisiones en clave bioética influencia las relaciones humanas y posee implicaciones para el diagnóstico, el pronóstico, las intervenciones y la evaluación de resultados y consecuencias. La normalidad en salud mental debiera ser reformulada sobre la base de principios bioéticos a fin de impedir ser fuente de estigma y discriminación en una época en que la diversidad y el cambio cultural imponen una redefinición de límites conceptuales y la despatologización de diferentes formas de conducta y vivencia.

Purity or perversion? from taboo to fact: kindergarten teachers' reflections on age-normal sexuality.

Many educators and pedagogues around the world face challenging situations in their everyday work. Being caught off guard when children begin to explore their bodies and show curiosity about body parts and sexual issues is one of the most uncomfortable realities in the work of educating our children and can generate a series of worrying questions, such as, "Is this child* normal? Should I stop him/ her from masturbating? What should I tell him/her?. Although talking to children about body changes and sexual matters may seem strange or embarrassing, providing correct and age-appropriate information is one of the most important things kindergarten employees can do to ensure that children grow up protected, healthy and safe in their bodies. The current study is based on empirical evidence from focus group interviews with 18 kindergarten teachers from four different kindergartens. The aim is to provide a real overview regarding kindergarten employees' experiences when it comes to their work with sexual development in small children. The findings show that sexuality is still a taboo even in western societies, as it is usually linked to abuse or pathological behavior. Additionally, key information about lack of focus on these topics in pedagogical educational programs is provided. Furthermore, the informants highlight the importance of knowledge and resources for them to feel in control and in confidence to face these challenges. Future directions and tips are provided to improve the educational field and ensure a healthy and balanced development which is after all part of all children's rights.

Psychological Normality or Abnormality: A Case Study on Salafi-Jihadists in the Middle-East.

The present study investigated Salafi-Jihadists in terms of mental health. The participants included 12 Salafi-Jihadists living in border areas of Iran, Kurdistan, selected using a purposeful sampling method. This primarily phenomenological case study gathered data, using open-ended interviews, field observations and in-depth clinical interviews. Results indicated that the participants reported no long-standing or acute mental or personality disorder. While they demonstrated abnormalities in their thought process and cognition, they were not severe enough to constitute symptoms of a mental disorder. The results indicate that situational and group factors, in conjunction with identifiable cognitive distortions, may play a more decisive role in fundamentalist radicalization than personality characteristics and mental disorders. Due to discrimination, feelings of oppression, cognitive distortions, and wrong attitudes toward other religious schools, some Muslims have decided to join Salafi-Jihad groups in order to feel a sense of belonging and identity.

Tensile Strength Statistics of High-Performance Mono- and Multifilament Polymeric Materials: On the Validity of Normality.

Recently, the statistical distributions of the mechanical properties, including tensile strength (σ), of several high-strength high-modulus oriented polymeric materials have been analyzed by employing the Weibull's and Gaussian statistical models. However, a more detailed comprehensive analysis of the distributions of the mechanical properties of these materials aimed to estimate the validity of normality by employing some other statistical approaches, is needed. In the present work, the σ statistical distributions of the seven high-strength oriented polymeric materials based on the polymers with three different chain architectures and conformations, ultra-high-molecular-weight polyethylene (UHMWPE), polyamide 6 (PA 6), and polypropylene (PP), each in the form of both single and multifilament fibers, have been investigated using graphical methods, such as the normal probability and quantile-quantile plots, and six selected formal normality tests, such as the Kolmogorov-Smirnov, Shapiro-Wilk, Lilliefors, Anderson-Darling, D'Agostino-K squared, and Chen-Shapiro tests. It has been found that the conformity of the σ distribution curves to the normal distribution, including the linearity of the normal probability plots, for the materials with lower strengths (σ < 1 GPa, quasi-ductile PA 6- and PP-based materials) is more correct as compared to those for the materials with markedly higher strengths (σ > 4 GPa, quasi-brittle UHMWPE-based materials). The impact of the sample type (single or multifilament fibers) on this behavior turned out to be negligible.

Multivariate single index modeling of longitudinal data with multiple responses.

In medical studies, composite indices and/or scores are routinely used for predicting medical conditions of patients. These indices are usually developed from observed data of certain disease risk factors, and it has been demonstrated in the literature that single index models can provide a powerful tool for this purpose. In practice, the observed data of disease risk factors are often longitudinal in the sense that they are collected at multiple time points for individual patients, and there are often multiple aspects of a patient's medical condition that are of our concern. However, most existing single-index models are developed for cases with independent data and a single response variable, which are inappropriate for the problem just described in which within-subject observations are usually correlated and there are multiple mutually correlated response variables involved. This paper aims to fill this methodological gap by developing a single index model for analyzing longitudinal data with multiple responses. Both theoretical and numerical justifications show that the proposed new method provides an effective solution to the related research problem. It is also demonstrated using a dataset from the English Longitudinal Study of Aging.

Application of a Hermite-based measure of non-Gaussianity to normality tests and independent component analysis.

In the analysis of neural data, measures of non-Gaussianity are generally applied in two ways: as tests of normality for validating model assumptions and as Independent Component Analysis (ICA) contrast functions for separating non-Gaussian signals. Consequently, there is a wide range of methods for both applications, but they all have trade-offs. We propose a new strategy that, in contrast to previous methods, directly approximates the shape of a distribution via Hermite functions. Applicability as a normality test was evaluated via its sensitivity to non-Gaussianity for three families of distributions that deviate from a Gaussian distribution in different ways (modes, tails, and asymmetry). Applicability as an ICA contrast function was evaluated through its ability to extract non-Gaussian signals in simple multi-dimensional distributions, and to remove artifacts from simulated electroencephalographic datasets. The measure has advantages as a normality test and, for ICA, for heavy-tailed and asymmetric distributions with small sample sizes. For other distributions and large datasets, it performs comparably to existing methods. Compared to standard normality tests, the new method performs better for certain types of distributions. Compared to contrast functions of a standard ICA package, the new method has advantages but its utility for ICA is more limited. This highlights that even though both applications-normality tests and ICA-require a measure of deviation from normality, strategies that are advantageous in one application may not be advantageous in the other. Here, the new method has broad merits as a normality test but only limited advantages for ICA.

The causality-chance binomial: explanatory principle of scientific knowledge in medicine?

This essay questions mathematical truths as an explanatory principle of the medical scientific knowledge. It analyzes, in the first place, the current concept of normality based on a distribution of probabilistic values and its limitations and mistakes to capture the complexity of the human condition are highlighted. The closed systems (gambling) origin of the theory of probabilities and the binomial causality-chance are compared with open systems typical of the complexity of the vital process, and their extreme differences are argued. The nonsense of depositing in the causality-chance binomial the meaning of associations between events typical of the complexity of human life in health and disease is highlighted. The characteristics of mechanistic causality (punctual, homogeneous, linear, unidirectional and fixed), which equates the organism with a machine and is the only accepted scientific explanation of events of human life, are confronted with those of contextual causality (diffuse, heterogeneous, hierarchical, multidirectional and changing), which specifies various interacting causal orders that shape of human condition: the historical, the social, the political, the economical, the cultural or the biological that represents a scrutinizing and penetrating look at the complexity of human beings. It concludes the superiority of contextual causality over mechanistic causality that opens up explanatory possibilities of the vital events that are usually put away as "effects of chance". This integrative approach to the human complexity can enrich and strengthen the clinical method that is now degraded and at risk of extinction.

Este ensayo cuestiona las verdades matemáticas como principio explicativo del conocimiento científico médico. Se analiza, en primer término, el concepto de normalidad actual basado en una distribución de valores probabilísticos, y se destacan sus limitaciones y equívocos para captar la complejidad de la condición humana. Los sistemas cerrados (juegos de azar), origen de la teoría de las probabilidades y del binomio causalidad-azar, se comparan con los sistemas abiertos propios del proceso vital y se argumentan sus diferencias extremas. Se destaca el despropósito de depositar en el binomio causalidad-azar el significado de asociaciones entre sucesos propios de la complejidad de la vida humana en salud y enfermedad. Se confrontan las características de la causalidad mecanicista (puntual, lineal, unidireccional, homogénea y fija), que equipara al organismo con una máquina y es la única explicación científica aceptada del acontecer de la vida humana, con las de la causalidad contextual (difusa, heterogénea, jerárquica, multidireccional y cambiante), que especifica diversos órdenes causales interactuantes que dan forma a la condición humana: el histórico, el social, el político, el económico, el cultural o el biológico, que representa una mirada escrutadora y penetrante de la complejidad de los seres humanos. Se concluye la superioridad de la causalidad contextual sobre la mecanicista, que abre posibilidades explicativas de sucesos vitales que suelen arrumbarse como «efectos del azar¼. Esta aproximación integradora a la complejidad humana puede enriquecer y fortalecer el método clínico, hoy degradado y en riesgo de extinción.

El binomio causalidad-azar: ¿principio explicativo del conocimiento científico en medicina? / The causality-chance binomial: explanatory principle of scientific knowledge in medicine?

Resumen Este ensayo cuestiona las verdades matemáticas como principio explicativo del conocimiento científico médico. Se analiza, en primer término, el concepto de normalidad actual basado en una distribución de valores probabilísticos, y se destacan sus limitaciones y equívocos para captar la complejidad de la condición humana. Los sistemas cerrados (juegos de azar), origen de la teoría de las probabilidades y del binomio causalidad-azar, se comparan con los sistemas abiertos propios del proceso vital y se argumentan sus diferencias extremas. Se destaca el despropósito de depositar en el binomio causalidad-azar el significado de asociaciones entre sucesos propios de la complejidad de la vida humana en salud y enfermedad. Se confrontan las características de la causalidad mecanicista (puntual, lineal, unidireccional, homogénea y fija), que equipara al organismo con una máquina y es la única explicación científica aceptada del acontecer de la vida humana, con las de la causalidad contextual (difusa, heterogénea, jerárquica, multidireccional y cambiante), que especifica diversos órdenes causales interactuantes que dan forma a la condición humana: el histórico, el social, el político, el económico, el cultural o el biológico, que representa una mirada escrutadora y penetrante de la complejidad de los seres humanos. Se concluye la superioridad de la causalidad contextual sobre la mecanicista, que abre posibilidades explicativas de sucesos vitales que suelen arrumbarse como «efectos del azar¼. Esta aproximación integradora a la complejidad humana puede enriquecer y fortalecer el método clínico, hoy degradado y en riesgo de extinción.

Abstract This essay questions mathematical truths as an explanatory principle of the medical scientific knowledge. It analyzes, in the first place, the current concept of normality based on a distribution of probabilistic values and its limitations and mistakes to capture the complexity of the human condition are highlighted. The closed systems (gambling) origin of the theory of probabilities and the binomial causality-chance are compared with open systems typical of the complexity of the vital process, and their extreme differences are argued. The nonsense of depositing in the causality-chance binomial the meaning of associations between events typical of the complexity of human life in health and disease is highlighted. The characteristics of mechanistic causality (punctual, homogeneous, linear, unidirectional and fixed), which equates the organism with a machine and is the only accepted scientific explanation of events of human life, are confronted with those of contextual causality (diffuse, heterogeneous, hierarchical, multidirectional and changing), which specifies various interacting causal orders that shape of human condition: the historical, the social, the political, the economical, the cultural or the biological that represents a scrutinizing and penetrating look at the complexity of human beings. It concludes the superiority of contextual causality over mechanistic causality that opens up explanatory possibilities of the vital events that are usually put away as "effects of chance". This integrative approach to the human complexity can enrich and strengthen the clinical method that is now degraded and at risk of extinction.

An Updated Guide to Robust Statistical Methods in Neuroscience.

There is a vast array of new and improved methods for comparing groups and studying associations that offer the potential for substantially increasing power, providing improved control over the probability of false positives, and yielding a deeper and more nuanced understanding of data. These new techniques effectively deal with four insights into when and why conventional methods can be unsatisfactory. But for the non-statistician, this vast array of techniques for comparing groups and studying associations can seem daunting. This article briefly reviews when and why conventional methods can have relatively low power and yield misleading results. The main goal is to suggest guidelines regarding the use of modern techniques that improve upon classic approaches such as Pearson's correlation, ordinary linear regression, ANOVA, and ANCOVA. This updated version includes recent advances dealing with effect sizes, including situations where there is a covariate. The R code, figures, and accompanying notebooks have been updated as well. © 2023 The Authors. Current Protocols published by Wiley Periodicals LLC.

Prediction-based uncertainty quantification for exchangeable sequences.

Prediction has a central role in the foundations of Bayesian statistics and is now the main focus in many areas of machine learning, in contrast to the more classical focus on inference. We discuss that, in the basic setting of random sampling-that is, in the Bayesian approach, exchangeability-uncertainty expressed by the posterior distribution and credible intervals can indeed be understood in terms of prediction. The posterior law on the unknown distribution is centred on the predictive distribution and we prove that it is marginally asymptotically Gaussian with variance depending on the predictive updates, i.e. on how the predictive rule incorporates information as new observations become available. This allows to obtain asymptotic credible intervals only based on the predictive rule (without having to specify the model and the prior law), sheds light on frequentist coverage as related to the predictive learning rule, and, we believe, opens a new perspective towards a notion of predictive efficiency that seems to call for further research. This article is part of the theme issue 'Bayesian inference: challenges, perspectives, and prospects'.

The normality assumption on between-study random effects was questionable in a considerable number of Cochrane meta-analyses.

BACKGROUND: Studies included in a meta-analysis are often heterogeneous. The traditional random-effects models assume their true effects to follow a normal distribution, while it is unclear if this critical assumption is practical. Violations of this between-study normality assumption could lead to problematic meta-analytical conclusions. We aimed to empirically examine if this assumption is valid in published meta-analyses. METHODS: In this cross-sectional study, we collected meta-analyses available in the Cochrane Library with at least 10 studies and with between-study variance estimates > 0. For each extracted meta-analysis, we performed the Shapiro-Wilk (SW) test to quantitatively assess the between-study normality assumption. For binary outcomes, we assessed between-study normality for odds ratios (ORs), relative risks (RRs), and risk differences (RDs). Subgroup analyses based on sample sizes and event rates were used to rule out the potential confounders. In addition, we obtained the quantile-quantile (Q-Q) plot of study-specific standardized residuals for visually assessing between-study normality. RESULTS: Based on 4234 eligible meta-analyses with binary outcomes and 3433 with non-binary outcomes, the proportion of meta-analyses that had statistically significant non-normality varied from 15.1 to 26.2%. RDs and non-binary outcomes led to more frequent non-normality issues than ORs and RRs. For binary outcomes, the between-study non-normality was more frequently found in meta-analyses with larger sample sizes and event rates away from 0 and 100%. The agreements of assessing the normality between two independent researchers based on Q-Q plots were fair or moderate. CONCLUSIONS: The between-study normality assumption is commonly violated in Cochrane meta-analyses. This assumption should be routinely assessed when performing a meta-analysis. When it may not hold, alternative meta-analysis methods that do not make this assumption should be considered.