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.     

Links between self-reported and laboratory behavioral impulsivity

Havik, M., Jakobson, A., Tamm, M., Paaver, M., Konstabel, K., Uusberg, A., Allik, J., Ööpik, V. & Kreegipuu, K. (2012). Links between self‐reported and laboratory behavioral impulsivity. Scandinavian Journal of Psychology 53, 216–223. A major problem in the research considering impulsivity is the lack of mutual understanding on how to measure and define impulsivity. Our study examined the relationship between self‐reported impulsivity, behavioral excitatory and inhibitory processes and time perception. Impulsivity – fast, premature, thoughtless or disinhibited behavior – was assessed in 58 normal, healthy participants (30 men, mean age 21.9 years). Self‐reported impulsivity as measured by Adaptive and Maladaptive Impulsivity Scale (AMIS) and behavioral excitatory and inhibitory processes as measured by Stop Signal Task were not directly related. Time perception, measured by the retrospective Time Estimation Task, was related to both. The length of the perceived time interval was positively correlated to AMIS Disinhibition subscale and negatively to several Stop Signal Task parameters. The longer subjects perceived the duration to last, the higher was their score on Disinhibition scale and the faster were their reactive responses in the Stop Signal Task. In summary our findings support the idea of cognitive tempo as a possible mechanism underlying impulsive behavior.     

Age-related changes in children's executive functions and strategy selection: A study in computational estimation

Third, fifth, and seventh graders selected the best strategy (rounding up or rounding down) for estimating answers to two-digit addition problems. Executive function measures were collected for each individual. Data showed that (a) children's skill at both strategy selection and execution improved with age and (b) increased efficiency in executive functions contributed significantly to age-related improvement in children's strategy selection skill. These findings have implications for understanding of age-related differences in computational estimation, strategy selection processes, and mechanisms of strategic development in children.     

Individual differences in children's mathematical competence are related to the intentional but not automatic processing of Arabic numerals

In recent years, there has been an increasing focus on the role played by basic numerical magnitude processing in the typical and atypical development of mathematical skills. In this context, tasks measuring both the intentional and automatic processing of numerical magnitude have been employed to characterize how children’s representation and processing of numerical magnitude changes over developmental time. To date, however, there has been little effort to differentiate between different measures of ‘number sense’. The aim of the present study was to examine the relationship between automatic and intentional measures of magnitude processing as well as their relationships to individual differences in children’s mathematical achievement. A group of 119 children in 1st and 2nd grade were tested on the physical size congruity paradigm (automatic processing) as well as the number comparison paradigm to measure the ratio effect (intentional processing). The results reveal that measures of intentional and automatic processing are uncorrelated with one another, suggesting that these tasks tap into different levels of numerical magnitude processing in children. Furthermore, while children’s performance on the number comparison paradigm was found to correlate with their mathematical achievement scores, no such correlations could be obtained for any of the measures typically derived from the physical size congruity task. These findings therefore suggest that different tasks measuring ‘number sense’ tap into different levels of numerical magnitude representation that may be unrelated to one another and have differential predictive power for individual differences in mathematical achievement.     

儿童数字线表征的发展——心理长度的影响

探讨儿童在数字线估计任务中心理长度的发展及其对数量表征模式的影响.选取7~9岁儿童共109名进行数字线估计任务测试,设置了10cm和20cm两种长度条件,要求儿童完成根据位置判断数字任务(position to number,PN任务).结果表明儿童在数字线PN任务中存在心理长度,且7岁儿童心理长度的范围超过10,随着儿童年龄的增长,他们的心理长度范围不断缩小;心理长度范围影响儿童的表征模式,随着心理长度范围的缩小,儿童的数字线表征出现从指数模式到线性模式的变化趋势;与表征模式的发展趋势一致,儿童估计的精确性随年龄增长逐渐提高.     

A fast numerical algorithm for the estimation of diffusion model parameters

In this paper, we describe a new algorithmic approach for parameter estimation in Ratcliff's [(1978). A theory of memory retrieval. Psychological Review, 85 (2), 59-108] diffusion model. This problem, especially if inter-trial variabilities of parameters are included in the model, is computationally very expensive; the parameter estimation procedure often takes a long time even with today's high-speed computers. The algorithm described here makes the calculation of the cumulative distribution functions for predicted process durations computationally much less expensive. This improvement is achieved by solving the Kolmogorov backward equation numerically instead of employing the previously used closed form solution. Additionally, the algorithm can determine the optimum fit for one of the model parameters (the starting point z) directly, thereby reducing the dimension of the parameter search space by one. The resulting method is shown to be notably faster than the standard (closed-form solution) method for parameter estimation.     

How to, and how not to, bridge computational cognitive neuroscience and Husserlian phenomenology of time consciousness

A number of recent attempts to bridge Husserlian phenomenology of time consciousness and contemporary tools and results from cognitive science or computational neuroscience are described and critiqued. An alternate proposal is outlined that lacks the weaknesses of existing accounts.     

Are unsupervised neural networks ignorant? Sizing the effect of environmental distributions on unsupervised learning

Learning environmental biases is a rational behavior: by using prior odds, Bayesian networks rapidly became a benchmark in machine learning. Moreover, a growing body of evidence now suggests that humans are using base rate information. Unsupervised connectionist networks are used in computer science for machine learning and in psychology to model human cognition, but it is unclear whether they are sensitive to prior odds. In this paper, we show that hard competitive learners are unable to use environmental biases while recurrent associative memories use frequency of exemplars and categories independently. Hence, it is concluded that recurrent associative memories are more useful than hard competitive networks to model human cognition and have a higher potential in machine learning.     

An electro-physiological temporal principal component analysis of processing stages of number comparison in developmental dyscalculia

Developmental dyscalculia (DD) still lacks a generally accepted definition. A major problem is that the cognitive component processes contributing to arithmetic performance are still poorly defined. By a reanalysis of our previous event-related brain potential (ERP) data (Soltész et al., 2007) here our objective was to identify and compare cognitive processes in adolescents with DD and in matched control participants in one-digit number comparison. To this end we used temporal principal component analysis (PCA) on ERP data. First, PCA has identified four major components explaining the 85.8% of the variance in number comparison. Second, the ERP correlate of the most frequently used marker of the so-called magnitude representation, the numerical distance effect, was intact in DD during all processing stages identified by PCA. Third, hemispheric differences in the first temporal component and group differences in the second temporal component suggest executive control differences between DD and controls.     

Item difficulty parameter estimation using the idea of the graded response model and computerized adaptive testing

Abstract:  In test operations using IRT (item response theory), items are included in a test before being used to rate subjects and the response data is used to estimate their item parameters. However, this method of test operation may lead to item content leakage and an adequate test operation can become difficult. To address this problem, Ozaki and Toyoda (2005, 2006 ) developed item difficulty parameter estimation methods that use paired comparison data from the perspective of the difficulty of items as judged by raters familiar with the field. In the present paper, an improved method of item difficulty parameter estimation is developed. In this new method, an item for which the difficulty parameter is to be estimated is compared with multiple items simultaneously, from the perspective of their difficulty. This is not a one-to-one comparison but a one-to-many comparison. In the comparisons, raters are informed that items selected from an item pool are ordered according to difficulty. The order will provide insight to improve the accuracy of judgment.