Constructing the exact significance level for a person fit statistic

This paper uses an extension of the network algorithm originally introduced by Mehta and Patel to construct exact tail probabilities for testing the general hypothesis that item responses are distributed according to the Rasch model. By assuming that item difficulties are known, the algorithm is applicable to the statistical tests either given the maximum likelihood ability estimate or conditioned on the total score. A simulation study indicates that the network algorithm is an efficient tool for computing the significance level of a person fit statistic based on test lengths of 30 items or less.     

Combinatorial data analysis: Association and partial association

A combinatorial data analysis strategy is reviewed that is designed to compare two arbitrary measures of proximity defined between the objects from some set. Based on a particular cross-product definition of correspondence between these two numerically specified notions of proximity (typically represented in the form of matrices), extensions are then pursued to indices of partial association that relate the observed pattern of correspondence between the first two proximity measures to a third. The attendant issues of index normalization and significance testing are discussed; the latter is approached through a simple randomization model implemented either through a Monte Carlo procedure or distributional approximations based on the first three moments. Applications of the original comparison strategy and its extensions to partial association may be developed for a variety of methodological and substantive tasks. Besides rank correlation, we emphasize the topics of spatial autocorrelation for one variable and spatial association between two and mention the connection to the usual randomization approach for one-way analysis-of-variance.     

Extending exploratory diagnostic classification models: Inferring the effect of covariates

Diagnostic models provide a statistical framework for designing formative assessments by classifying student knowledge profiles according to a collection of fine-grained attributes. The context and ecosystem in which students learn may play an important role in skill mastery, and it is therefore important to develop methods for incorporating student covariates into diagnostic models. Including covariates may provide researchers and practitioners with the ability to evaluate novel interventions or understand the role of background knowledge in attribute mastery. Existing research is designed to include covariates in confirmatory diagnostic models, which are also known as restricted latent class models. We propose new methods for including covariates in exploratory RLCMs that jointly infer the latent structure and evaluate the role of covariates on performance and skill mastery. We present a novel Bayesian formulation and report a Markov chain Monte Carlo algorithm using a Metropolis-within-Gibbs algorithm for approximating the model parameter posterior distribution. We report Monte Carlo simulation evidence regarding the accuracy of our new methods and present results from an application that examines the role of student background knowledge on the mastery of a probability data set.     

Time-series analysis in operant research

A time-series method is presented, nontechnically, for analysis of data generated in individual-subject operant studies, and is recommended as a supplement to visual analysis of behavior change in reversal or multiple-baseline experiments. The method can be used to identify three kinds of statistically significant behavior change: (a) changes in score levels from one experimental phase to another, (b) reliable upward or downward trends in scores, and (c) changes in trends between phases. The detection of, and reliance on, serial dependency (autocorrelation among temporally adjacent scores) in individual-subject behavioral scores is emphasized. Examples of published data from the operant literature are used to illustrate the time-series method.     

Considerations in the choice of interobserver reliability estimates

Two types of interobserver reliability values may be needed in treatment studies in which observers constitute the primary data-acquisition system: trial reliability and the reliability of the composite unit or score which is subsequently analyzed, e.g., daily or weekly session totals. Two approaches to determining interobserver reliability are described: percentage agreement and "correlational" measures of reliability. The interpretation of these estimates, factors affecting their magnitude, and the advantages and limitations of each approach are presented.     

贝叶斯统计方法的应用与现状

贝叶斯统计方法是心理学数据分析的热门方法。研究全面论述贝叶斯方法在心理学领域的应用与方向。现阶段贝叶斯方法以模拟研究为主,应用方向为心理学研究常用的项目反应理论、认知诊断、计算机自适应、结构方程模型。同时,评述发现贝叶斯方法正逐步被国内心理学研究者所接受。最后,文章讨论了当下贝叶斯统计在心理学研究中应用的局限性及可能的原因,建议统计学者开发界面友好的贝叶斯软件,并在心理学课程中加入贝叶斯知识。     

Too bored for sports? Adaptive and less-adaptive latent personality profiles for exercise behavior

Physical exercise is an effective tool for improving public health, but the general population exercises too little. Drawing on recent theorizing on the combined role of boredom and self-control in guiding goal-directed behavior, we test the hypothesis that individual differences in boredom and self-control differentiate high from low exercisers. The role of boredom as a non-adaptive disposition is of particular interest, because research on boredom in sports is scarce. Here, we investigate the role of such individual differences in self-reported weekly exercise behavior (in minutes) in a sample of N = 507 participants (n = 200 female, M_age = 36.43 (±9.54)). We used the robust variant of Mahalanobis distance to detect and remove n = 51 multivariate outliers and then performed latent profile analysis to assess if boredom (boredom proneness; exercise-related boredom) and self-control (trait self-control; if-then planning) combine into identifiable latent profiles. In line with theoretical considerations, the Bayesian Information Criterion favored a solution with two latent profiles. One profile was characterized by higher-than-average exercise-related boredom and boredom proneness and lower-than-average self-control and if-then planning values. This pattern was reversed for the second profile. A one-sided Bayesian two-sample t-test supported the hypothesis that the first profile is associated with less exercise behavior than the second profile, BF = 16.93. Our results foster the notion of self-control and if-then planning as adaptive dispositions. More importantly, they point to an important role of boredom in the exercise setting: exercise-related boredom and getting easily bored in general are associated with less exercise activity. This is in line with recent theorizing on boredoms' and self-controls’ function in guiding goal-directed behavior.     

Misunderstandings and omissions in textbook accounts of effect sizes

There have been frequent attempts in psychology to reduce the reliance on null hypothesis significance testing (NHST) as the criterion for establishing the importance of results. Many authorities now recommend the reporting of effect sizes (ESs) as a supplement or alternative to NHST. However, there is extensive specialist literature highlighting problems associated with the use and interpretation of ESs. A review of the coverage of ESs in over 100 textbooks on statistical analysis in behavioural science revealed widespread neglect of ESs and the relevant critical issues that have widespread coverage in the more specialist literature. For example, many textbooks claim that ESs should be interpreted as a simple measure of the practical real-world importance of a result despite the fact that ESs are profoundly influenced by features of design and analysis strategy. We seek to highlight areas of misunderstanding about ESs found in the pedagogical literature in the light of the more specialist literature and make recommendations to researchers for the appropriate use and interpretation of ESs. This is critical as statistics textbooks have a crucial role in the education of researchers.     

A unified approach to exploratory factor analysis with missing data,nonnormal data,and in the presence of outliers

Factor analysis is regularly used for analyzing survey data. Missing data, data with outliers and consequently nonnormal data are very common for data obtained through questionnaires. Based on covariance matrix estimates for such nonstandard samples, a unified approach for factor analysis is developed. By generalizing the approach of maximum likelihood under constraints, statistical properties of the estimates for factor loadings and error variances are obtained. A rescaled Bartlett-corrected statistic is proposed for evaluating the number of factors. Equivariance and invariance of parameter estimates and their standard errors for canonical, varimax, and normalized varimax rotations are discussed. Numerical results illustrate the sensitivity of classical methods and advantages of the proposed procedures.This project was supported by a University of North Texas Faculty Research Grant, Grant #R49/CCR610528 for Disease Control and Prevention from the National Center for Injury Prevention and Control, and Grant DA01070 from the National Institute on Drug Abuse. The results do not necessarily represent the official view of the funding agencies. The authors are grateful to three reviewers for suggestions that improved the presentation of this paper.     

Measuring religious affiliation in Great Britain: the 2011 census in historical and methodological context

Abstract

The British religious census of 2011 is located in its broader historical and methodological context. The principal developments in the measurement of religious affiliation (proxy-assigned or self-assigned) in Britain are traced from the Reformation to the present day, charting the relative contribution of the Churches, the State and empirical social science. The key statistics which have emerged from their respective efforts are summarised, with nominal religious affiliation universal until the time of the French Revolution and preponderant until as late as the 1980s. For recent decades, when the profession of faith has been rejected by large numbers of Britons, particular attention is paid to the variant results from different question-wording. Depending upon what is asked, the proportion of the population currently making sense of their lives without asserting a confessional religious identity ranges from one-quarter to one-half. The difficulties of trying to construct a religious barometer through a single, unitary indicator are thus illuminated.