A reanalysis of Lord’s statistical treatment of football numbers

Stevens’ theory of admissible statistics [Stevens, S. S. (1946). On the theory of scales of measurement. Science, 103, 677680] states that measurement levels should guide the choice of statistical test, such that the truth value of statements based on a statistical analysis remains invariant under admissible transformations of the data. Lord [Lord, F. M. (1953). On the statistical treatment of football numbers. American Psychologist, 8, 750-751] challenged this theory. In a thought experiment, a parametric test is performed on football numbers (identifying players: a nominal representation) to decide whether a sample from the machine issuing these numbers should be considered non-random. This is an apparently illegal test, since its outcomes are not invariant under admissible transformations for the nominal measurement level. Nevertheless, it results in a sensible conclusion: the number-issuing machine was tampered with. In the ensuing measurement-statistics debate Lord’s contribution has been influential, but has also led to much confusion. The present aim is to show that the thought experiment contains a serious flaw. First it is shown that the implicit assumption that the numbers are nominal is false. This disqualifies Lord’s argument as a valid counterexample to Stevens’ dictum. Second, it is argued that the football numbers do not represent just the nominal property of non-identity of the players; they also represent the amount of bias in the machine. It is a question about this property-not a property that relates to the identity of the football players-that the statistical test is concerned with. Therefore, only this property is relevant to Lord’s argument. We argue that the level of bias in the machine, indicated by the population mean, conforms to a bisymmetric structure, which means that it lies on an interval scale. In this light, Lord’s thought experiment-interpreted by many as a problematic counterexample to Stevens’ theory of admissible statistics-conforms perfectly to Stevens’ dictum.     

医学科研或论文中常见的统计学问题

医学统计学在医学科研中占有重要地位,统计方法正确使用与否直接影响论文的结果和质量,但是具体使用过程中统计学方法或指标常常被混淆或使用不妥。本文就科研设计、数据描述、推演结论等方面容易混淆的统计学常见问题进行简要阐述,并举例分析可能出现误用的指标和方法,提高医务工作者对医学统计学的认识。     

Characterizing Human Expertise Using Computational Metrics of Feature Diagnosticity in a Pattern Matching Task

Forensic evidence often involves an evaluation of whether two impressions were made by the same source, such as whether a fingerprint from a crime scene has detail in agreement with an impression taken from a suspect. Human experts currently outperform computer‐based comparison systems, but the strength of the evidence exemplified by the observed detail in agreement must be evaluated against the possibility that some other individual may have created the crime scene impression. Therefore, the strongest evidence comes from features in agreement that are also not shared with other impressions from other individuals. We characterize the nature of human expertise by applying two extant metrics to the images used in a fingerprint recognition task and use eye gaze data from experts to both tune and validate the models. The Attention via Information Maximization (AIM) model (Bruce & Tsotsos, 2009) quantifies the rarity of regions in the fingerprints to determine diagnosticity for purposes of excluding alternative sources. The CoVar model (Karklin & Lewicki, 2009) captures relationships between low‐level features, mimicking properties of the early visual system. Both models produced classification and generalization performance in the 75%–80% range when classifying where experts tend to look. A validation study using regions identified by the AIM model as diagnostic demonstrates that human experts perform better when given regions of high diagnosticity. The computational nature of the metrics may help guard against wrongful convictions, as well as provide a quantitative measure of the strength of evidence in casework.     

心理与教育测验中异常反应侦查新技术：变点分析法

变点分析法(change point analysis, CPA)近些年才引入心理与教育测量学, 相较于传统方法, CPA不仅可以侦查异常作答被试, 还能自动精确地定位变点位置, 高效清洗作答数据。其原理在于：判断作答序列中是否存在可将该序列划分为具有不同统计学属性两部分的点(即变点), 并且需使用被试拟合统计量(person-fit statistic, PFS)来量化两个子序列之间的差异。未来可将单变点分析拓展至多变点, 结合反应时等信息, 构建非参数化指标以及将现有指标拓展至多级计分或多维测验, 以提高CPA的适用广度及效力。     

“词语自由联想”视域下医护人员形象调查——公众与医护人员的认知态度比较

言语行为可以反映认知态度,利用心理学的“自由联想法”对公众与医护人员进行针对医护人员形象的调查,以获得他们心目中描述医护人员形象的词语.按照他们头脑中出现的顺序进行加权统计;计算积极、中性和消极词语的比例.调查发现,公众对医护人员形象的认知态度存在矛盾;同时医护人员对自身职业评价较低;二者通过联想获得贬义词分值较高,原因是医护人员普遍被认为劳动强度大、职业安全感小等.运用社会认知心理学的平衡理论进行分析以期获得提升认知态度,改善医患关系的新途径.     

Using a supervised machine learning algorithm for detecting faking good in a personality self‐report

We developed a supervised machine learning classifier to identify faking good by analyzing item response patterns of a Big Five personality self‐report. We used a between‐subject design, dividing participants (N = 548) into two groups and manipulated their faking behavior via instructions given prior to administering the self‐report. We implemented a simple classifier based on the Lie scale's cutoff score and several machine learning models fitted either to the personality scale scores or to the items response patterns. Results shown that the best machine learning classifier—based on the XGBoost algorithm and fitted to the item responses—was better at detecting faked profiles than the Lie scale classifier.     

基于一般线性模型框架的心理统计教学

心理统计学教学中,不同的统计方法常常是独立教学,致使学生不易理解各种方法之间的关系。事实上,t检验、方差分析和多元线性回归等方法都可以统一到一般线性模型的框架下,而结构方程是对这个框架的最一般化的描述,且结构方程路径图是呈现这个框架的形象工具。因此,本文尝试用路径图的方式来呈现心理学研究中最常用的统计方法,并将结构方程分析结果与传统分析结果进行对照,帮助学生建立一般线性模型上位概念,将以往孤立的统计方法联系起来。     

Calculate or wait: Is man an eager or a lazy intuitive statistician?

Research on people's ability to act as intuitive statisticians has mainly focused on the accuracy of estimates of central tendency and variability. In this paper, we investigate two hypothesised cognitive processes by which people make judgements of distribution shape. The first claims that people spontaneously induce abstract representations of distribution properties from experience, including about distribution shape. The second process claims that people construct beliefs about distribution properties post hoc by retrieval from long-term memory of small samples from the distribution, implying format dependence with accuracy that differs depending on judgement format. Results from two experiments confirm the predicted format dependence, suggesting that people are often constrained by the post hoc assessment of distribution properties by sampling from long-term memory. The results, however, also suggest that, although post hoc sampling from memory seems to be the default process, under certain predictable circumstances people do induce abstract representations of distribution shape.     

Collective Efficacy as a Mediator of the Trustworthiness – Performance Relationship in Computer-Mediated Team-based Contexts

The current study investigated the role of trustworthiness perceptions at the individual level and collective efficacy at the team level on team performance in computer-mediated teams using multi-level structural equation modeling (MSEM). It was hypothesized that trustworthiness perceptions and collective efficacy would predict team performance, and collective efficacy would partially mediate the trustworthiness – performance relationship in computer-mediated teams. Sixty-four teams (five participants each) engaged in a computer-mediated task across two experimental sessions. Trustworthiness measured after session 1, collective efficacy measured after sessions 1 and 2, and team performance measured of sessions 1 and 2 were used to build the MSEM. The half longitudinal model for assessing mediation was used to examine the influence of trustworthiness perceptions on performance through collective efficacy over time. Results demonstrated support for the hypothesized model, such that trustworthiness perceptions demonstrated indirect effects on performance through collective efficacy. These findings extend past research by identifying an emergent mechanism by which trustworthiness is important for team performance in computer-mediated teams.