Inferring accuracy for judges and items: Choice of unit of analysis reverses the conclusions

This study explores the relationship between the precision and the accuracy of forecasts using either judge or item as the unit of analysis. Participants in five experiments answered general-knowledge questions by indicating intervals that were likely to include the correct answer. Results indicate that the precision of an interval estimate is not a straightforward cue to the likelihood that such an interval includes the truth (hit rate). Whereas judges who state more precise estimates (i.e. who provide narrower interval estimates) have lower hit rates, questions for which the average judgment is more precise have higher hit rates. Thus, the relation between precision and accuracy depends on whether one ‘slices’ the data by judge or by question. We offer an explanation for this seemingly paradoxical effect and implement it as a computer simulation to demonstrate its validity. © 1997 John Wiley & Sons, Ltd.     

Precision and accuracy of judgmental estimation

Whereas probabilistic calibration has been a central normative concept of accuracy in previous research on interval estimates, we suggest here that normative approaches for the evaluation of judgmental estimates should consider the communicative interaction between the individuals who produce the judgments and those who receive or use them for making decisions. We analyze precision and error in judgment and consider the role of the accuracy–informativeness trade-off (Yaniv and Foster, 1995) in the communication of estimates. The results shed light on puzzling findings reported earlier in the literature concerning the calibration of subjective confidence intervals. © 1997 John Wiley & Sons, Ltd.     

An evaluation of estimation data collection to trial‐by trial data collection during discrete trial teaching

There are many data collection procedures used during discrete trial teaching including first‐trial data collection, probe data, trial‐by‐trial data collection, and estimation data. Continuous, or trial‐by‐trial data collection, consists of the interventionist collecting data on learner behavior on each trial. Estimation data consists of the interventionist estimating learner performance after a teaching session using a rating scale. The purpose of the present study was to compare trial‐by‐trial data collection to estimation data collection during discrete trial teaching to teach children expressive labels. The data collection procedures were examined in terms of accuracy of data collection, efficiency of teaching (i.e., number of trials delivered per session), and rate of child acquisition of targets. Results of the adapted alternating treatment design replicated across three participants and multiple targets found estimation data collection to be as accurate as trial‐by‐trial data collection in determining mastery of targets. Estimation data collected by the interventionist was also found to be accurate when compared to the actual trial‐by‐trial data collected after the study concluded.     

The relation between subitizable symbolic and non‐symbolic number processing over the kindergarten school year

A long‐standing debate in the field of numerical cognition concerns the degree to which symbolic and non‐symbolic processing are related over the course of development. Of particular interest is the possibility that this link depends on the range of quantities in question. Behavioral and neuroimaging research with adults suggests that symbolic and non‐symbolic quantities may be processed more similarly within, relative to outside of, the subitizing range. However, it remains unclear whether this unique link exists in young children at the outset of formal education. Further, no study has yet taken numerical size into account when investigating the longitudinal influence of these skills. To address these questions, we investigated the relation between symbolic and non‐symbolic processing inside versus outside the subitizing range, both cross‐sectionally and longitudinally, in 540 kindergarteners. Cross‐sectionally, we found a consistently stronger relation between symbolic and non‐symbolic number processing within versus outside the subitizing range at both the beginning and end of kindergarten. We also show evidence for a bidirectional relation over the course of kindergarten between formats within the subitizing range, and a unidirectional relation (symbolic → non‐symbolic) for quantities outside of the subitizing range. These findings extend current theories on symbolic and non‐symbolic magnitude development by suggesting that non‐symbolic processing may in fact play a role in the development of symbolic number abilities, but that this influence may be limited to quantities within the subitizing range.     

对威胁刺激的碰撞时间估计

对靠近运动刺激的碰撞时间(time-to-collision, TTC)估计具有重要的进化意义。为了解释个体如何进行TTC估计, 研究者提出了结构主义理论、生态光学理论和tau理论等, 也考察了影响TTC估计的部分因素。近年的研究通过比较个体对威胁刺激和非威胁刺激的TTC估计, 考察了刺激的情绪相关属性对TTC估计的影响。结果表明, 相比于自然非威胁刺激(如兔子等图片), 个体会低估自然威胁刺激(如蛇等图片)的TTC, 但这种TTC的低估在社会威胁刺激(如愤怒面孔图片)上有时很小甚至不显著。个体低估TTC可能存在三种原因：(1)个体对威胁刺激具有特异性反应; (2)威胁刺激具有较高的情绪唤醒度; (3)个体对威胁刺激具有心理距离更近和运动速度更快的知觉偏差。未来研究可以进一步考察在社会威胁刺激上表现出的TTC低估效应不稳定的原因; 探索威胁刺激TTC估计中的自主生理反应和神经机制; 采用虚拟现实技术进行威胁刺激TTC估计的研究; 在实验设计中考虑性别和人格特质等个体因素的影响。     

Point-biserial correlation: Interval estimation,hypothesis testing,meta-analysis,and sample size determination

The point-biserial correlation is a commonly used measure of effect size in two-group designs. New estimators of point-biserial correlation are derived from different forms of a standardized mean difference. Point-biserial correlations are defined for designs with either fixed or random group sample sizes and can accommodate unequal variances. Confidence intervals and standard errors for the point-biserial correlation estimators are derived from the sampling distributions for pooled-variance and separate-variance versions of a standardized mean difference. The proposed point-biserial confidence intervals can be used to conduct directional two-sided tests, equivalence tests, directional non-equivalence tests, and non-inferiority tests. A confidence interval for an average point-biserial correlation in meta-analysis applications performs substantially better than the currently used methods. Sample size formulas for estimating a point-biserial correlation with desired precision and testing a point-biserial correlation with desired power are proposed. R functions are provided that can be used to compute the proposed confidence intervals and sample size formulas.     

Marginalized maximum a posteriori estimation for the four-parameter logistic model under a mixture modelling framework

The four-parameter logistic model (4PLM) has recently attracted much interest in various applications. Motivated by recent studies that re-express the four-parameter model as a mixture model with two levels of latent variables, this paper develops a new expectation–maximization (EM) algorithm for marginalized maximum a posteriori estimation of the 4PLM parameters. The mixture modelling framework of the 4PLM not only makes the proposed EM algorithm easier to implement in practice, but also provides a natural connection with popular cognitive diagnosis models. Simulation studies were conducted to show the good performance of the proposed estimation method and to investigate the impact of the additional upper asymptote parameter on the estimation of other parameters. Moreover, a real data set was analysed using the 4PLM to show its improved performance over the three-parameter logistic model.     

"Constructive" enumeration by chimpanzees (Pan troglodytes) on a computerized task

Two chimpanzees used a joystick to collect dots, one at a time, on a computer monitor (see video-clip in the electronic supplementary material), and then ended a trial when the number of dots collected was equal to the Arabic numeral presented for the trial. Both chimpanzees performed substantially and reliably above chance in collecting a quantity of dots equal to the target numeral, one chimpanzee for the numerals 1–7, and the second chimpanzee for the numerals 1–6. Errors that were made were seldom discrepant from the target by more than one dot quantity, and the perceptual process subitization was ruled out as an explanation for the performance. Additionally, analyses of trial duration data indicated that the chimpanzees were responding based on the numerosity of the constructed set rather than on the basis of temporal cues. The chimpanzees' decreasing performance with successively larger target numerals, however, appeared to be based on a continuous representation of magnitude rather than a discrete representation of number. Therefore, chimpanzee counting in this type of experimental task may be a process that represents magnitudes with scalar variability in that the memory for magnitudes associated with each numeral is imperfect and the variability of responses increases as a function of the numeral's value. Accepted after revision: 11 June 2001 Electronic Publication     

A noniterative method of joint correspondence analysis

Correspondence analysis leads to a graphical representation of the associations between categories of the row and column variables of a contingency table. Greenacre's (1988) formulation of joint correspondence analysis is a multivariate extension which finds the optimal joint display of contingency tables between all pairs of variables in a set. Greenacre presented a discrepancy function and an alternating least squares algorithm for its minimization. Boik (1996) presented an alternative algorithm, also of the alternating least squares type, for minimizing the same discrepancy function. In this paper, a noniterative procedure, not based on the minimization of any discrepancy function, is described.     

Sample size requirements for estimating pearson, kendall and spearman correlations

Interval estimates of the Pearson, Kendall tau-a and Spearman correlations are reviewed and an improved standard error for the Spearman correlation is proposed. The sample size required to yield a confidence interval having the desired width is examined. A two-stage approximation to the sample size requirement is shown to give accurate results.