Commentary on ‘mentoring and the impact of the research climate’

Conclusions First of all, I would like to commend Roberts and colleagues for taking on a difficult but very important topic. It would be valuable if someone could follow up with a broader sample of universities and laboratories — paying careful attention to possible sampling and non-sampling errors. In general, I recommend that mentors explicitly both learn and teach ethical theory and practice within the context of their scientist development programs. Finally, while it is important to emphasize sound and ethical research standards and processes in mentoring programs, this should not be at the expense of an appropriate emphasis on skills essential to professional competitiveness, such as responsible, effective publication, grant winning, and demonstrably strong performance on the grants won. Dr. Gardenier is a survey statistician at the National Center for Health Statistics of the Centers for Disease Control and Prevention. The views presented are his personal opinions only.     

A Bayesian approach to the evolution of perceptual and cognitive systems

We describe a formal framework for analyzing how statistical properties of natural environments and the process of natural selection interact to determine the design of perceptual and cognitive systems. The framework consists of two parts: a Bayesian ideal observer with a utility function appropriate for natural selection, and a Bayesian formulation of Darwin's theory of natural selection. Simulations of Bayesian natural selection were found to yield new insights, for example, into the co‐evolution of camouflage, color vision, and decision criteria. The Bayesian framework captures and generalizes, in a formal way, many of the important ideas of other approaches to perception and cognition.     

The role of causal models in multiple judgments under uncertainty

Two studies examined a novel prediction of the causal Bayes net approach to judgments under uncertainty, namely that causal knowledge affects the interpretation of statistical evidence obtained over multiple observations. Participants estimated the conditional probability of an uncertain event (breast cancer) given information about the base rate, hit rate (probability of a positive mammogram given cancer) and false positive rate (probability of a positive mammogram in the absence of cancer). Conditional probability estimates were made after observing one or two positive mammograms. Participants exhibited a causal stability effect: there was a smaller increase in estimates of the probability of cancer over multiple positive mammograms when a causal explanation of false positives was provided. This was the case when the judgments were made by different participants (Experiment 1) or by the same participants (Experiment 2). These results show that identical patterns of observed events can lead to different estimates of event probability depending on beliefs about the generative causes of the observations.     

Minority religions in the census: the case of British Muslims

Abstract

This article considers the impact of census data on British Muslims, as well as the potential consequences of changes to the UK census beyond 2011 for minority religions. Focusing on the Muslim case, it reflects on data generated in previous censuses and the ways in which they have been used. The discussion explores the perceived need for social statistics on religion, particularly in relation to the increased identification of ‘Muslim’ as a religious rather than ethnic classification. It gives an overview of insights gained as a result of having data on religion in addition to ethnicity, notably: the high levels of socioeconomic disadvantage experienced by British Muslims and the ability to access information on Muslims that was hitherto hidden. Finally, the article provides a brief summary of proposed changes to the new census format and considers the likely outcomes for British Muslims if the scope of data collected on religion is reduced.     

Are summary statistics enough? Evidence for the importance of shape in guiding visual search

Peripheral vision outside the focus of attention may rely on summary statistics. We used a gaze-contingent paradigm to directly test this assumption by asking whether search performance differed between targets and statistically-matched visualizations of the same targets. Four-object search displays included one statistically-matched object that was replaced by an unaltered version of the object during the first eye movement. Targets were designated by previews, which were never altered. Two types of statistically-matched objects were tested: One that maintained global shape and one that did not. Differences in guidance were found between targets and statistically-matched objects when shape was not preserved, suggesting that they were not informationally equivalent. Responses were also slower after target fixation when shape was not preserved, suggesting an extrafoveal processing of the target that again used shape information. We conclude that summary statistics must include some global shape information to approximate the peripheral information used during search.     

Calibrated Bayes Factors Should Not Be Used: A Reply to Hoijtink,van Kooten,and Hulsker

Hoijtink, Kooten, and Hulsker (2016 Hoijtink, H., van Kooten, P., &; Hulsker, K. (2016). Why Bayesian psychologists should change the way they use the Bayes factor. Multivariate Behavioral Research, 51, 1--9. doi: 10.1080/00273171.2014.969364.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) present a method for choosing the prior distribution for an analysis with Bayes factor that is based on controlling error rates, which they advocate as an alternative to our more subjective methods (Morey &; Rouder, 2014 Morey, R.D., &; Rouder, J.N. (2014). Bayesfactor: Computation of Bayes factors for common designs. R package version 0.9.9. Retrieved from http://CRAN.R-project.org/package=BayesFactor [Google Scholar]; Rouder, Speckman, Sun, Morey, &; Iverson, 2009 Rouder, J.N., Speckman, P.L., Sun, D., Morey, R.D., &; Iverson, G. (2009). Bayesian t-tests for accepting and rejecting the null hypothesis. Psychonomic Bulletin and Review, 16, 225–237. doi: 10.3758/PBR.16.2.225[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]; Wagenmakers, Wetzels, Borsboom, &; van der Maas, 2011 Wagenmakers, E.-J., Wetzels, R., Borsboom, D., &; van der Maas, H. (2011). Why psychologists must change the way they analyze their data: The case of psi. A comment on Bem (2011). Journal of Personality and Social Psychology, 100, 426–432. doi: 10.1037/a0022790[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). We show that the method they advocate amounts to a simple significance test, and that the resulting Bayes factors are not interpretable. Additionally, their method fails in common circumstances, and has the potential to yield arbitrarily high Type II error rates. After critiquing their method, we outline the position on subjectivity that underlies our advocacy of Bayes factors.     

Sidman or statistics?

Murray Sidman's statements regarding variability, experimental control, and generality are interwoven with examples from the literature on conditional discrimination. Sidman's position was that statistical inferences from group studies produce no information about the behavior of individual subjects and that statistical treatment of individual subject data masks variability which may represent conditions that are not controlled. Sidman's work on conditional discrimination provides excellent examples of how complex discriminations should be examined in detail with accuracy levels obtained for each type of discrimination within an experiment. Sidman made important contributions to the foundation of behavior analysis with extensive basic research as well as applications of methods and principles to clinical and educational settings.     

非参数认知诊断方法下诊断结果的概率化表征

非参数认知诊断分类方法非常适合课堂评估,其诊断结果采用0-1形式而缺乏概率化表征,不能精细地区分被试属性掌握程度的差异或变化,还缺乏可用于评价真实测验分类结果的信度和效度指标。要刻画被试属性掌握程度的差异,首要的问题是要为非参数认知诊断方法提供一种可以量化属性掌握概率的方法。针对此问题,基于二项分布和玻尔兹曼分布提出非参数认知诊断方法下诊断结果的概率化表征方法,并用于构建分类准确性和分类一致性指标。模拟研究与实测数据分析结果显示：概率化表征方法与非参数认知诊断方法的分类结果高度一致;概率化表征方法与认知诊断模型所得的属性掌握概率十分接近;概率化表征方法所得的属性（模式）掌握概率可用于计算属性（模式）分类准确性和分类一致性指标,在实际测验情景下可作为信度和效度指标,评价诊断结果的重测一致率和判准率。     

On Judgments of Approximately Equal

Although precision is often important in quantitative judgment, sometimes, it is valuable to recognize that two quantities are roughly the same. Fuzzy‐trace theory suggests that approximately equal judgments rely on gist representations (i.e., meaningful fuzzy categories of quantity). We conducted three experiments to investigate approximately equal judgments with number pairs presented in different formats, both with and without semantic content (breast cancer statistics). In each study, the ratio of the smaller divided by larger number predicted approximately equal judgments. Experiment 1 also examined how knowledge of breast cancer, presentation format (frequencies vs. percentages), and differences in gist comprehension of breast cancer information influence fuzzy equality judgments. As predicted by the fuzzy‐trace theory concept of denominator neglect, approximately equal judgments were more sensitive, as measured by signal detection theory (SDT) analyses, when presented as percentages. In both experiments with breast cancer statistics, people were more likely to judge number pairs approximately equal when they were embedded in sentences about breast cancer, and breast cancer knowledge predicted increased perception of equality, when appropriately consistent with reliable sources, and increased judgment sensitivity. In Experiment 2, a simple intervention focusing on gist meaning increased source‐consistent approximately equal judgments, increased SDT judgment sensitivity, and decreased SDT response bias. In Experiment 3, using number pairs devoid of semantic context spanning four orders of magnitude, we further examined ratio similarity. Overall, more knowledgeable judges and those who better understood the gist of meaningful numbers were more likely to judge literally different numbers as “approximately equal” rather than make precise discriminations that were meaningless. Copyright © 2017 John Wiley & Sons, Ltd.     

Mediation analysis and categorical variables: Some further frontiers

Iacobucci (2012) provides a conceptually appealing, readily implemented measure to assess mediation for a far wider range of data type combinations than traditional OLS-based analyses permit. Here, we consider potential applications and extensions along several lines, particularly in terms of random utility models, simulation-based estimation, and potential nonlinearities, as well as some methodological and cultural impediments.