Errors in subtractions: judged and observed frequencies

In a first study 10 adults, aged 24-44 years, solved all 105 subtraction problems in the form M - N = , where 0 < or = M < or = 13, 0 < or = N < or = 13 and N < or = M. Each participant solved every problem 10 times and in total there were 10 500 answers. Answers, response latencies and errors were registered. Retrospective verbal reports were also given, indicating how a solution was reached: (1) via a (conscious) reconstructive cognitive process or (2) via an (unconscious) reproductive (retrieval) process. The participants made 291 errors (2.8%) when solving the subtractions in study 1. The rate of self-correction was very high, 92%. In a second study 27 undergraduate students estimated overall error rates, including self-corrected errors for the 105 subtraction problems used in the first study. Judged and actual error rates were compared. The participants systematically underestimated error rates for error prone problems and overestimated error rates for error free problems. The participants were fairly accurate when they predicted problems that were most error prone, with a hit rate of 0.67 for the (18) problems predicted as the most error prone ones. In contrast, predictions of which problems were error free were very poor with a hit rate of only 0.20 of the problems predicted as error free really having no errors in study 1. The correlation between judged error rates and frequencies for actually made errors was 0.69 for answers belonging to reconstructive solutions. In contrast, there was no significant correlation between judged and actual error rates at all for retrieved solutions, possibly reflecting the inaccessibility to consciousness of quick retrieval processes.     

Is the link between forebrain size and feeding innovations caused by confounding variables? A study of Australian and North American birds

The short notes of ornithology journals feature new and unusual feeding behaviours, which, when systematically collated, could provide a quantitative estimate of behavioural flexibility in different bird groups. Previous studies suggest that taxonomic variation in the frequency of new behaviours (innovations) is correlated with variation in relative forebrain size. Recent work on primates shows, however, that observer bias can affect innovation frequency. We assess this possibility in birds via three estimates in North America and Australia: the number of full-length papers in academic journals, the frequency of photographs in birding magazines and a questionnaire on reporting bias given to ornithologists at a meeting. We also look at sampling effects due to single journal sources by doing a split-half analysis of our North American database (The Wilson Bulletin vs. six other journals) and adding three new Australian journals to the one we had used previously. In multiple regressions that also included species number per taxon, none of the potential biases could account for the correlation between forebrain size and innovation frequency. Species number was the best predictor of full-length paper frequency, which was the best predictor of photograph numbers. Ornithologists are not preferentially interested in innovative, large-brained taxa, suggesting that the correlation between innovations and neural substrate size is not a spurious effect of the biases examined here. Accepted after revision: 27 July 2001 Electronic Publication     

心理学研究方法中“质”与“量”的整合

心理学研究方法中“质”与“量”的分歧由来已久。虽然“质”与“量”的研究方法各有其优势,但是也不可避免地存在一些弱点。如果将质与量的方法进行整合,使之进行优势互补,从而更大可能地揭示心理现象发生和发展的规律是我们所面临的课题。要对质的研究方法与量的研究方法进行整合,首先必须“去范式”,将研究的重点聚焦于研究问题,而非范式;其次必须将质性的资料与定量的资料放在同一个层面上进行比较。该文通过一个案例,向读者介绍如何进行“质”与“量”的研究方法的整合     

Skull size and intelligence, and King Robert Bruce's IQ

An estimate of someone's IQ is a potentially informative personal datum. This study examines the association between external skull measurements and IQ scores, and uses the resulting regression equation to provide an estimate of the IQ of King Robert I of Scotland (Robert Bruce, 1274–1329). Participants were 48 relatively healthy Caucasian men (age 71–76 years) resident in Scotland. Using magnetic resonance imaging data, intracranial volume estimated from external skull length and width correlated greater than .5 (p < .001) with measured intracranial area, which correlates very highly with brain volume. IQ scores estimated from the National Adult Reading Test (NART) correlated .56 (p < .001) with measured intracranial area, and .49 (p < .01) with estimated intracranial volume based on external skull width and length. The partial correlation coefficient of this latter association was .25 (p = .09) after adjustment for measured intracranial area. Thus, actual intracranial area accounts for about 74% of the variance shared by NART and estimated intracranial volume. A cast of the skull of Robert Bruce was measured and its intracranial volume estimated. A regression equation between IQ and estimated intracranial volume, based on data from the 48 subjects, estimated the IQ of Robert Bruce at about 128 (95% confidence interval 106 to  130), i.e. almost two standard deviations above the mean. NART scores show a ceiling effect, so this estimated IQ might be an underestimate. Robert Bruce's estimated high IQ is congruent with his military, political and other intellectual achievements.     

Multilevel Modeling with Correlated Effects

When there exist omitted effects, measurement error, and/or simultaneity in multilevel models, explanatory variables may be correlated with random components, and standard estimation methods do not provide consistent estimates of model parameters. This paper introduces estimators that are consistent under such conditions. By employing generalized method of moments (GMM) estimation techniques in multilevel modeling, the authors present a series of estimators along a robust to efficient continuum. This continuum depends on the assumptions that the analyst makes regarding the extent of the correlated effects. It is shown that the GMM approach provides an overarching framework that encompasses well-known estimators such as fixed and random effects estimators and also provides more options. These GMM estimators can be expressed as instrumental variable (IV) estimators which enhances their interpretability. Moreover, by exploiting the hierarchical structure of the data, the current technique does not require additional variables unlike traditional IV methods. Further, statistical tests are developed to compare the different estimators. A simulation study examines the finite sample properties of the estimators and tests and confirms the theoretical order of the estimators with respect to their robustness and efficiency. It further shows that not only are regression coefficients biased, but variance components may be severely underestimated in the presence of correlated effects. Empirical standard errors are employed as they are less sensitive to correlated effects when compared to model-based standard errors. An example using student achievement data shows that GMM estimators can be effectively used in a search for the most efficient among unbiased estimators. This research was supported by the National Academy of Education/Spencer Foundation and the National Science Foundation, grant number SES-0436274. We thank the editor, associate editor, and referees for detailed feedback that helped improve the paper.     

A Unified Approach to Power Calculation and Sample Size Determination for Random Regression Models

The underlying statistical models for multiple regression analysis are typically attributed to two types of modeling: fixed and random. The procedures for calculating power and sample size under the fixed regression models are well known. However, the literature on random regression models is limited and has been confined to the case of all variables having a joint multivariate normal distribution. This paper presents a unified approach to determining power and sample size for random regression models with arbitrary distribution configurations for explanatory variables. Numerical examples are provided to illustrate the usefulness of the proposed method and Monte Carlo simulation studies are also conducted to assess the accuracy. The results show that the proposed method performs well for various model specifications and explanatory variable distributions. The author would like to thank the editor, the associate editor, and the referees for drawing attention to pertinent references that led to improved presentation. This research was partially supported by National Science Council grant NSC-94-2118-M-009-004.     

A Pearson-Type-VII item response model for assessing person fluctuation

Using Lumsden’s Thurstonian fluctuation model as a starting point, this paper attempts to develop a unidimensional item response theory model intended for binary personality items. Under some additional assumptions, a new model is obtained in which the item characteristic curves are defined by a cumulative Pearson-Type-VII distribution, and the person response curves are two-parameter normal ogives. Procedures for fitting the new model are proposed. Furthermore, the relations between individual fluctuation and scalability are discussed, and a scalability index based on the new model is proposed. All the developments in this paper are illustrated using two empirical examples.     

注意在短时距估计中的作用

注意一直是时间知觉研究的一个重要问题。本文综述了研究已经取得一些较为一致的结果：在双任务程序中对时间任务的注意越多,时距估计越准确;在单一任务中对目标刺激的时间属性注意越多,对该刺激的持续时距估计越准确;在时间导向任务中,个体可以有效地、主动把注意导向未来的某段时距,那么将对出现在那个时刻的刺激做出更好的反应。最后,讨论了现有研究中存在的、以及今后研究中需要着重考虑的问题。     

Representational change and children's numerical estimation

We applied overlapping waves theory and microgenetic methods to examine how children improve their estimation proficiency, and in particular how they shift from reliance on immature to mature representations of numerical magnitude. We also tested the theoretical prediction that feedback on problems on which the discrepancy between two representations is greatest will cause the greatest representational change. Second graders who initially were assessed as relying on an immature representation were presented feedback that varied in degree of discrepancy between the predictions of the mature and immature representations. The most discrepant feedback produced the greatest representational change. The change was strikingly abrupt, often occurring after a single feedback trial, and impressively broad, affecting estimates over the entire range of numbers from 0 to 1000. The findings indicated that cognitive change can occur at the level of an entire representation, rather than always involving a sequence of local repairs.     

European starlings are capable of discriminating subtle size asymmetries in paired stimuli

Small deviations from bilateral symmetry (fluctuating asymmetries) are cues to fitness differences in some animals. Therefore, researchers have considered whether animals use these small asymmetries as visual cues to determine appropriate behavioral responses (e.g., mate preferences). However, there have been few systematic studies of animals' abilities to visually discriminate such minor asymmetries. If the asymmetries cannot be discriminated, fluctuating asymmetry can not be a visual cue. Here, we report an investigation of European starlings' (Sturnus vulgaris) abilities to discriminate small size asymmetries. We trained starlings, through operant conditioning in a free-flight aviary, to discriminate achromatic, symmetric paired stimuli from size-matched asymmetric stimuli. By starting the learning process with a large asymmetry and progressing through sequential trials of decreasing asymmetry, we elucidated a behavioral limit to asymmetry discrimination. We found that starlings are capable of discriminating a 10% size asymmetry. There was weaker evidence for discrimination of 5% asymmetry but no evidence for signal discrimination at 2.5% size asymmetry. This level of asymmetry discrimination suggests that many size asymmetry cues in nature can be discriminated by birds. At each level of asymmetry discrimination, we also tested whether starlings could generalize their learned symmetry preference to unreinforced novel images. Consistent with previous findings, we found that starlings could generalize their symmetry preferences.