Effects of class-interval size upon certain frequency distributions of interresponse times

Inter-response time distributions with class intervals of 0.05 and 0.04 sec revealed characteristics not observable with class intervals of 0.5 sec or greater. Bimodalities were clearly evident in the inter-response time distributions for two out of three pigeons. These modes seemed to correspond to two discrete response topographies.     

A hierarchical model for estimating response time distributions

We present a statistical model for inference with response time (RT) distributions. The model has the following features. First, it provides a means of estimating the shape, scale, and location (shift) of RT distributions. Second, it is hierarchical and models between-subjects and within-subjects variability simultaneously. Third, inference with the model is Bayesian and provides a principled and efficient means of pooling information across disparate data from different individuals. Because the model efficiently pools information across individuals, it is particularly well suited for those common cases in which the researcher collects a limited number of observations from several participants. Monte Carlo simulations reveal that the hierarchical Bayesian model provides more accurate estimates than several popular competitors do. We illustrate the model by providing an analysis of the symbolic distance effect in which participants can more quickly ascertain the relationship between nonadjacent digits than that between adjacent digits.     

A mixture model for distributions of correlation coefficients

An old problem in personnel psychology is to characterize distributions of test validity correlation coefficients. The proposed model views histograms of correlation coefficients as observations from a mixture distribution which, for a fixed sample sizen, is a conditional mixture distributionh(r|n) = _{j j} h(r; _j ,n), whereR is the correlation coefficient, _j are population correlation coefficients and _j are the mixing weights. The associated marginal distribution ofR is regarded as the parent distribution underlying histograms of empirical correlation coefficients. Maximum likelihood estimates of the parameters _j and _j can be obtained with an EM algorithm solution and tests for the number of componentst are achieved after the (one-component) density ofR is replaced with a tractable modeling densityh(r; _j ,n). Two illustrative examples are provided.     

Illusions of brightness, length, and now size: comparable effects derived from the Craik-O'Brien-Cornsweet distributions

Analogous illusions of brightness, line length, and object size occur when stimulus distributions follow the Mach function. Similarly, analogous illusions of brightness and length are produced by stimulus distributions that follow the Craik-O'Brien-Cornsweet function. In Exp. 1, object size is studied using Craik-O'Brien-Cornsweet stimuli composed of 12 clip-art representations of candles, swords, forks, screwdrivers, or pens. Despite their equal dimensions, the three objects next to the taller gradient were judged larger than the three adjacent to the shorter gradient. In Exp. 2, variations of the sword and screwdriver figures having three separations of their constituent objects were used. The illusion produced in Exp. 1 was replicated and, for the figures composed of screwdrivers, increasing separation reduced the hypothesized mis-estimations. The relationship of these Craik-O'Brien-Cornsweet size illusions to their brightness and length counterparts mirrors the relationships previously reported for Mach stimuli; moreover, these findings converge to suggest that the visual system registers size of objects with a frequency code and that illusions of size appear when interactions among neurons disrupt this code.     

Novel fabrication of bulk Al with gradient grain size distributions via powder metallurgy

We describe a novel approach to synthesize gradient microstructures, defined hereafter as containing a broad but continuous distribution of grain sizes. These microstructures extend the concept of a bimodal grain size distribution and the ability to design with multiple length scales. We demonstrate the proposed approach via experiments involving cryogenic ball milling of Al–4.5Mg–0.4Mn–0.05Fe and Al–50Mg powder followed by subsequent consolidation. Our results reveal that the grains in the consolidated powder present a gradient size distribution ranging from <100 nm to >3 μm. Moreover, phase composition analysis revealed a unique “interfingered” structure where the two starting phases were intermixed in a complex three-dimensional mesh. Hardness studies of this gradient microstructure show average Vickers hardness values of 200 ± 2.6, 204 ± 4.3 and 266 ± 50 for macrohardness, microhardness and nanoindentation, respectively. The standard deviation values highlight that the gradient microstructure is disordered locally, but homogenous macroscopically.     

Display size effects in visual search: Analyses of reaction time distributions as mixtures

In a reanalysis of data from Cousineau and Shiffrin (2004) and two new visual search experiments, we used a likelihood ratio test to examine the full distributions of reaction time (RT) for evidence that the display size effect is a mixture-type effect that occurs on only a proportion of trials, leaving RT in the remaining trials unaffected, as is predicted by serial self-terminating search models. Experiment 1 was a reanalysis of Cousineau and Shiffrin's data, for which a mixture effect had previously been established by a bimodal distribution of RTs, and the results confirmed that the likelihood ratio test could also detect this mixture. Experiment 2 applied the likelihood ratio test within a more standard visual search task with a relatively easy target/distractor discrimination, and Experiment 3 applied it within a target identification search task within the same types of stimuli. Neither of these experiments provided any evidence for the mixture-type display size effect predicted by serial self-terminating search models. Overall, these results suggest that serial self-terminating search models may generally be applicable only with relatively difficult target/distractor discriminations, and then only for some participants. In addition, they further illustrate the utility of analysing full RT distributions in addition to mean RT.     

Using the linear mixed model to analyze nonnormal data distributions in longitudinal designs

Using a Monte Carlo simulation and the Kenward–Roger (KR) correction for degrees of freedom, in this article we analyzed the application of the linear mixed model (LMM) to a mixed repeated measures design. The LMM was first used to select the covariance structure with three types of data distribution: normal, exponential, and log-normal. This showed that, with homogeneous between-groups covariance and when the distribution was normal, the covariance structure with the best fit was the unstructured population matrix. However, with heterogeneous between-groups covariance and when the pairing between covariance matrices and group sizes was null, the best fit was shown by the between-subjects heterogeneous unstructured population matrix, which was the case for all of the distributions analyzed. By contrast, with positive or negative pairings, the within-subjects and between-subjects heterogeneous first-order autoregressive structure produced the best fit. In the second stage of the study, the robustness of the LMM was tested. This showed that the KR method provided adequate control of Type I error rates for the time effect with normally distributed data. However, as skewness increased—as occurs, for example, in the log-normal distribution—the robustness of KR was null, especially when the assumption of sphericity was violated. As regards the influence of kurtosis, the analysis showed that the degree of robustness increased in line with the amount of kurtosis.     

A model of contemporary feminine role change and family size

Through a review of existing theory and research a model was constructed which traces the restricting effect female employment has on family size through a discussion of intervening psychological variables. The model presents four psychological changes that are associated with paid employment of middle-class women in the United States: (1) increased self-orientation, (2) increased feelings of personal efficacy, (3) the increased belief that the spouse holds expectations for female autonomy, and (4) the increased belief that female employment outside the home is socially acceptable. It is suggested that these variables act to restrict family size through their effects on desired family size, perceived desired family size of the husband, expected family size, commitment to employment, and occupational satisfaction.     

基于两水平回归模型的调节效应分析及其效应量

使用多元回归法进行调节效应分析在社科领域已常有应用。简述了目前多元回归法的调节效应分析存在的不足,包括人为变换检验模型、自变量和调节变量区分不足、误差方差齐性的假设难以满足、调节效应量指标ΔR²没有直接测量调节变量对自变量与因变量关系的调节程度。比较好的方法是用两水平回归模型进行调节效应分析并使用相应的效应量指标。在介绍新方法和新效应量后,总结出一套调节效应的分析流程,通过一个例子来演示如何用Mplus软件进行两水平回归模型的调节效应及其效应量分析。最后讨论了两水平回归模型的调节效应分析的发展,包括稳健的调节效应分析、潜变量的调节效应分析、有调节的中介效应分析和有中介的调节效应分析等。     

A general linear model for estimating effect size in the presence of publication bias

When the process of publication favors studies with smallp-values, and hence large effect estimates, combined estimates from many studies may be biased. This paper describes a model for estimation of effect size when there is selection based on one-tailedp-values. The model employs the method of maximum likelihood in the context of a mixed (fixed and random) effects general linear model for effect sizes. It offers a test for the presence of publication bias, and corrected estimates of the parameters of the linear model for effect magnitude. The model is illustrated using a well-known data set on the benefits of psychotherapy.Authors' note: The contributions of the authors are considered equal, and the order of authorship was chosen to be reverse-alphabetical.     

Subjective sampling distributions and the additivity of estimates

Abstract.— Previous studies of sampling distributions have been conducted almost exclusively under the assumption that persons behave in accordance with the "fundamental convention" of probability, i.e. that the sum of all probability estimates will equal 1. When this assumption was tested by asking subjects to give "unrestricted" probability estimates of all possible outcomes of samples from a given population, a general tendency of overestimation made the sum of all probabilities exceed 1 to a considerable extent. The subjective sampling distributions appeared to be unaffected by sample size ( N=5 or 10) and number of outcomes, and were flatter than the corresponding "objective" sampling distributions.     

Response time distributions and the Stroop Task: a test of the Cohen, Dunbar, and McClelland (1990) model.

Cohen, Dunbar, and McClelland's (1990) model was tested for Strooplike interference tasks by studying the shape of the distribution of response latencies produced by Ss and by the model. The model correctly anticipates changes in mean response latency (M(RT)) across congruent and incongruent conditions. It does not, however, correctly anticipate changes in the shape of the distributions, even though changes in the shape of the distributions underlie the changes in M(RT). Thus the model predicts M(RT) successfully but for the wrong reason. It is concluded that the model is not an adequate account of Ss' performance in the Stroop task.     

Skewness and asymmetry of distributions

The ‘skewness’ of a distribution, a poorly-defined term, is conventionally deemed to be invariant under linear transformations. A comparison is made of three criteria of it: the sign of odd central moments; the several relationships of the mean, the median and the mode; and asymmetry proper which is the set of ratios of the probability densities of all pairs of points equidistant above and below some arbitrary point, usually the principal mode. Some useful general relationships are discussed. The skeness of convolutions is briefly discussed. A class of distributions is identified for which the skewness of the minimum ofk competing processes is independent ofk. It has importance in the parametric study of survivorship.     

Beyond the two-strategy model of skilled spelling: Effects of consistency, grain size, and orthographic redundancy

Most models of spelling assume that people rely on two procedures when engaging in spelling: a lexical look-up procedure that retrieves spellings in their entirety, and a nonlexical procedure that constructs spellings with a set of phoneme-grapheme rules. In the present research, we investigated whether larger sized subsyllabic relationships also play a role in spelling, and how they compare to small-sized phoneme-grapheme relationships. In addition, we investigated whether purely orthographic units can explain some of the variance typically attributed to the mapping between sound and spelling. To do this, we ran five spelling experiments, two using real words and three using nonwords. Results from the experiments showed that there were independent contributions of both phoneme-grapheme and larger sized subsyllabic sound-spelling relationships, although the effect of phoneme-grapheme-sized relationships was always stronger and more reliable than larger sized subsyllabic sound-spelling relationships. Purely orthographic effects were also shown to affect word spelling, but no significant effects were found with nonword spelling. Together, the results support the hypothesis that a major constraint on spelling comes from phoneme-grapheme-sized relationships.     

Predicting the size of individual and

An a priori test of the difference engine model (Myerson, Hale, Zheng, Jenkins, & Widaman, 2003) was conducted using a large, diverse sample of individuals who performed three speeded verbal tasks and three speeded visuospatial tasks. Results demonstrated that, as predicted by the model, the group standard deviation (SD) on any task was proportional to the amount of processing required by that task. Both individual performances as well as those of fast and slow subgroups could be accurately predicted by the model using no free parameters, just an individual or subgroup’s mean z-score and the values of theoretical constructs estimated from fits to the group SDs. Taken together, these results are consistent with post hoc analyses reported by Myerson et al. and provide even stronger supporting evidence. In particular, the ability to make quantitative predictions without using any free parameters provides the clearest demonstration to date of the power of an analytic approach on the basis of the difference engine.     

On the asymptotic distributions of two statistics for two-level covariance structure models within the class of elliptical distributions

Since data in social and behavioral sciences are often hierarchically organized, special statistical procedures for covariance structure models have been developed to reflect such hierarchical structures. Most of these developments are based on a multivariate normality distribution assumption, which may not be realistic for practical data. It is of interest to know whether normal theory-based inference can still be valid with violations of the distribution condition. Various interesting results have been obtained for conventional covariance structure analysis based on the class of elliptical distributions. This paper shows that similar results still hold for 2-level covariance structure models. Specifically, when both the level-1 (within cluster) and level-2 (between cluster) random components follow the same elliptical distribution, the rescaled statistic recently developed by Yuan and Bentler asymptotically follows a chi-square distribution. When level-1 and level-2 have different elliptical distributions, an additional rescaled statistic can be constructed that also asymptotically follows a chi-square distribution. Our results provide a rationale for applying these rescaled statistics to general non-normal distributions, and also provide insight into issues related to level-1 and level-2 sample sizes. The authors thank an associate editor and three referees for their constructive comments, which led to an improved version of the paper. This research was supported by grants DA01070 and DA00017 from the National Institute on Drug Abuse and a University of Notre Dame faculty research grant.