Estimation of the Coefficient of Variation with Minimum Risk: A Sequential Method for Minimizing Sampling Error and Study Cost

The coefficient of variation is an effect size measure with many potential uses in psychology and related disciplines. We propose a general theory for a sequential estimation of the population coefficient of variation that considers both the sampling error and the study cost, importantly without specific distributional assumptions. Fixed sample size planning methods, commonly used in psychology and related fields, cannot simultaneously minimize both the sampling error and the study cost. The sequential procedure we develop is the first sequential sampling procedure developed for estimating the coefficient of variation. We first present a method of planning a pilot sample size after the research goals are specified by the researcher. Then, after collecting a sample size as large as the estimated pilot sample size, a check is performed to assess whether the conditions necessary to stop the data collection have been satisfied. If not an additional observation is collected and the check is performed again. This process continues, sequentially, until a stopping rule involving a risk function is satisfied. Our method ensures that the sampling error and the study costs are considered simultaneously so that the cost is not higher than necessary for the tolerable sampling error. We also demonstrate a variety of properties of the distribution of the final sample size for five different distributions under a variety of conditions with a Monte Carlo simulation study. In addition, we provide freely available functions via the MBESS package in R to implement the methods discussed.     

Cognitive mediation of putting: Use of a think-aloud measure and implications for studies of golf-putting in the laboratory

ObjectivesWhereas accounts of skilled performance based on automaticity (Beilock & Carr, 2001; Fitts & Posner, 1967) emphasize reduced cognitive involvement in advanced skill, other accounts propose that skilled performance relies on increased cognitive control (Ericsson & Kintsch, 1995). The objective of this study was to test predictions differentiating the automaticity and cognitive control accounts by assessing thinking during golf putting.DesignThe cognitive processes of less-skilled and more-skilled golfers were examined during putting using concurrent, think-aloud verbal reports. The design included putting conditions that differed in complexity and thus the need to adapt the putt to the particular conditions.MethodPutting complexity was manipulated via changes to putt length and perceived stress during putting. Putts were executed from two starting locations (i.e., the same starting location as the previous putt or a new starting location).ResultsThe analysis showed that, during putting: more thoughts were verbalized overall by more-skilled golfers than less-skilled golfers; both groups verbalized more thoughts overall during higher-complexity putts (i.e., longer distance putts, and putts under higher stress when executed from a new starting location) than lower-complexity putts; and the two groups did not differ significantly in the number of thoughts related to motor mechanics.ConclusionsThe results of this study provide support for a cognitive control account of skilled performance and suggest that the path to skilled performance involves the acquisition of more refined higher-level cognitive representations mediating planning and analysis.     

Effects of self-generated versus experimenter-provided cues on the representation of future events

Most experimental studies of prospection focused on episodic forms of future events prompted by means of verbal cues. However, there is evidence suggesting that future events differ considerably according to whether they are produced in response to external, experimenter-provided verbal cues or they are self-generated. In the present study, we compared the quality, the phenomenal characteristics, the temporal distribution, and the content of imagined events prompted by experimenter-provided cues (i.e., cue-words and short verbal sentences) or elicited by means of verbal cues that were self-generated in an autobiographical fluency task. The results showed that future events prompted by means of self-generated cues contained fewer event-specific details than future events prompted by experimenter-provided cues. However, future events elicited by means of self-generated and by experimenter-provided cues did not differ with respect to their phenomenal characteristics. The temporal distribution and the thematic content of future representations were also affected by the type of cue used to elicit prospection. These results offer a holistic view of the properties of future thinking and suggest that the content and the characteristics of envisioned future events may be affected by the method used to elicit prospection.     

Flexible representations in visual working memory and interactions with long‐term learning: Commentary on the special issue

This special issue of the British Journal of Psychology brings together cutting edge research on a range of topics in visual working memory (VWM). In this commentary, we attempt to summarize common themes in current VWM research exemplified in this issue. The articles include several reviews of important topics as well as empirical papers covering three main themes. The first concerns the nature of mental representations of memoranda in the commonly used delayed estimation task, where both fine‐grained and broad categorical details appear to be represented, and their susceptibility to interference. The second concerns interactions between VWM representations, both those that produce individuation of representations and those that create an overarching ensemble structure. Finally, the third main topic concerns the use of VWM during visual search and in the learning of repeated configurations in search displays. The work presented here, and other work in the field, points to a rich interplay between representations in VWM but also between VWM and information in long‐term memory. Opportunities for further investigation are highlighted throughout.     

The influence of number line estimation precision and numeracy on risky financial decision making

This study examined whether different aspects of mathematical proficiency influence one's ability to make adaptive financial decisions. “Numeracy” refers to the ability to process numerical and probabilistic information and is commonly reported as an important factor which contributes to financial decision‐making ability. The precision of mental number representation (MNR), measured with the number line estimation (NLE) task has been reported to be another critical factor. This study aimed to examine the contribution of these mathematical proficiencies while controlling for the influence of fluid intelligence, math anxiety and personality factors. In our decision‐making task, participants chose between two options offering probabilistic monetary gain or loss. Sensitivity to expected value was measured as an index for the ability to discriminate between optimal versus suboptimal options. Partial correlation and hierarchical regression analyses revealed that NLE precision better explained EV sensitivity compared to numeracy, after controlling for all covariates. These results suggest that individuals with more precise MNR are capable of making more rational financial decisions. We also propose that the measurement of “numeracy,” which is commonly used interchangeably with general mathematical proficiency, should include more diverse aspects of mathematical cognition including basic understanding of number magnitude.     

多维项目反应理论补偿性模型参数估计:基于广义回归神经网络集合

运用广义回归神经网络(GRNN)方法对小样本多维项目反应理论(MIRT)补偿性模型的项目参数进行估计,尝试解决传统参数估计方法样本数量要求较大的问题。MIRT双参数Logistic补偿模型被设置为二级计分的二维模型。首先,模拟二维能力参数、项目参数值与考生作答矩阵。其次,把通过主成分分析得到的前两个因子在每个题目上的载荷作为区分度的初始值以及题目通过率作为难度的初始值,这两个指标的初始值作为神经网络的输入。集成100个神经网络,其输出值的均值作为MIRT的项目参数估计值。最后,设置2×2种(能力相关水平:0.3和0.7; 两种估计方法:GRNN和MCMC方法)实验处理,对GRNN和MCMC估计方法的返真性进行比较。结果表明,小样本的情况下,基于GRNN集成方法的参数估计结果优于MCMC方法。     

Are situation awareness and decision-making in driving totally conscious processes? Results of a hazard prediction task

Detecting danger in the driving environment is an indispensable task to guarantee safety which depends on the driver’s ability to predict upcoming hazards. But does correct prediction lead to an appropriate response? This study advances hazard perception research by investigating the link between successful prediction and response selection. Three groups of drivers (learners, novices and experienced drivers) were recruited, with novice and experienced drivers further split into offender and non-offender groups. Specifically, this works aims to develop an improved Spanish Hazard Prediction Test and to explore the differences in Situation Awareness, (SA: perception, comprehension and prediction) and Decision-Making (DM) among learners, younger inexperienced and experienced drivers and between driving offenders and non-offenders. The contribution of the current work is not only theoretical; the Hazard Prediction Test is also a valid way to test Hazard Perception. The test, as well as being useful as part of the test for a driving license, could also serve a purpose in the renewal of licenses after a ban or as a way of training drivers. A sample of 121 participants watched a series of driving video clips that ended with a sudden occlusion prior to a hazard. They then answered questions to assess their SA (“What is the hazard?” “Where is it located?” “What happens next?”) and DM (“What would you do in this situation?”). This alternative to the Hazard Perception Test demonstrates a satisfactory internal consistency (Alpha = 0.750), with eleven videos achieving discrimination indices above 0.30. Learners performed significantly worse than experienced drivers when required to identify and locate the hazard. Interestingly, drivers were more accurate in answering the DM question than questions regarding SA, suggesting that drivers can choose an appropriate response manoeuvre without a totally conscious knowledge of the exact hazard.     

A Hierarchical Rater Model for Longitudinal Data

Research studies in psychology and education often seek to detect changes or growth in an outcome over a duration of time. This research provides a solution to those interested in estimating latent traits from psychological measures that rely on human raters. Rater effects potentially degrade the quality of scores in constructed response and performance assessments. We develop an extension of the hierarchical rater model (HRM), which yields estimates of latent traits that have been corrected for individual rater bias and variability, for ratings that come from longitudinal designs. The parameterization, called the longitudinal HRM (L-HRM), includes an autoregressive time series process to permit serial dependence between latent traits at adjacent timepoints, as well as a parameter for overall growth. We evaluate and demonstrate the feasibility and performance of the L-HRM using simulation studies. Parameter recovery results reveal predictable amounts and patterns of bias and error for most parameters across conditions. An application to ratings from a study of character strength demonstrates the model. We discuss limitations and future research directions to improve the L-HRM.     

Dealing with Big Numbers: Representation and Understanding of Magnitudes Outside of Human Experience

Being able to estimate quantity is important in everyday life and for success in the STEM disciplines. However, people have difficulty reasoning about magnitudes outside of human perception (e.g., nanoseconds, geologic time). This study examines patterns of estimation errors across temporal and spatial magnitudes at large scales. We evaluated the effectiveness of hierarchical alignment in improving estimations, and transfer across dimensions. The activity was successful in increasing accuracy for temporal and spatial magnitudes, and learning transferred to the estimation of numeric magnitudes associated with events and objects. However, there were also a number of informative differences in performance on temporal, spatial, and numeric magnitude measures, suggesting that participants possess different categorical information for these scales. Educational implications are discussed.     

Language facilitates introspection: Verbal mind-wandering has privileged access to consciousness

Introspection and language are the cognitive prides of humankind, but their interactions in healthy cognition remain unclear. Episodes of mind-wandering, where personal thoughts often go unnoticed for some time before being introspected, offer a unique opportunity to study the role of language in introspection. In this paper, we show that inner speech facilitates awareness of mind-wandering. In two experiments, we either interfered with verbal working memory, via articulatory suppression (Exp. 1), or entrained it, via presentation of verbal material (Exp. 2), and measured the resulting awareness of mind-wandering. Articulatory suppression decreased the likelihood to spontaneously notice mind-wandering, whereas verbal material increased retrospective awareness of mind-wandering. In addition, an ecological study using smartphones confirmed that inner speech vividness positively predicted mind-wandering awareness (Exp. 3). Together, these findings support the view that inner speech facilitates introspection of one’s thoughts, and therefore provides empirical evidence for a positive relation between language and consciousness.