儿童数字估计中的心理长度

从儿童对数字属性的认识角度探讨一年级儿童在不同数字范围中采用不同表征形式的根本原因。两个实验均采用数字线估计任务,实验一测量一年级儿童在15cm数字线长度下0～100与0～1000两种范围上的数字估计;实验二测量一年级儿童对0～1000范围10cm和20cm数字线长度的估计。结果显示,无论在不同的数字范围还是在不同的数字线长度下,儿童对低端数字的估计均存在心理长度,即儿童倾向于将低端数字与固定的线段长度对应起来,且这种对应关系不随数字范围与数字线长度的变化而变化。心理长度的存在是儿童在不同数字范围和不同数字线长度中采用不同数字表征形式的根本原因,也是儿童对数概念的认识发展到等距水平时出现的一种独特特点。     

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.     

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.     

Initial judgment task and delay of the final validity-rating task moderate the truth effect

Repeatedly seen or heard statements are typically judged to be more valid than statements one has never encountered before. This phenomenon has been referred to as the truth effect. We conducted two experiments to assess the plasticity of the truth effect under different contextual conditions. Surprisingly, we did not find a truth effect in the typical judgment design when using a ten minutes interval between statement repetitions. However, we replicated the truth effect when changing the judgment task at initial statement exposure or when using an interval of one week rather than ten minutes. Because none of the current truth effect theories can fully account for these context effects, we conclude that the cognitive processes underlying truth judgments are more complex than has hitherto been assumed. To close the theoretical gap, we propose a revised fluency attribution hypothesis as a possible explanation of our findings.     

Step changes in the intertrial interval in the midsession reversal task: Predicting pigeons' performance with the learning-to-time model

Our goal was to assess the role of timing in pigeons' performance in the midsession reversal task. In discrete-trial sessions, pigeons learned to discriminate between 2 stimuli, S1 and S2. Choices of S1 were reinforced only in the first half of the session and choices of S2 were reinforced only in the second half. Typically, pigeons choose S2 before the contingency reverses (anticipatory errors) and S1 after (perseverative errors), suggesting that they time the interval from the beginning of the session to the contingency reversal. To test this hypothesis, we exposed pigeons to a midsession reversal task and, depending on the group, either increased or decreased the ITI duration. We then contrasted the pigeons' performance with the predictions of the Learning-to-Time (LeT) model: In both conditions, preference was expected to reverse at the same time as in the previous sessions. When the ITI was doubled, pigeons' preference reversal occurred at half the trial number but at the same time as in the previous sessions. When the ITI was halved, pigeons' preference reversal occurred at a later trial but at an earlier time than in the previous sessions. Hence, pigeons' performance was only partially consistent with the predictions of LeT, suggesting that besides timing, other sources of control, such as the outcome of previous trials, seem to influence choice.     

"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