Judgments of average lightness and darkness: A further consideration of inverse attributes

Twenty subjects judged the average lightness and darkness of paired Munsell gray papers according to magnitude estimation and category rating instructions. The data from category rating were approximately consistent with an averaging model but those from magnitude estimation were not. An analysis in terms of a two-stage model suggested that category ratings and magnitude estimates of each attribute were produced on the basis of the same composition rule, but implicated different output transformations. In judging darkness, subjects appeared to have reversed the scales employed in judging lightness, by a linear transformation in the case of category rating and by a reciprocal transformation in the case of magnitude estimation. However, differences between the input parameters obtained from judgments of lightness and darkness suggested that the scales of these attributes constructed from judgments of average magnitude may be biased.     

Averaging: An empirical validity criterion for magnitude estimation

Ss judged grayness of neutral value Munsell chips under two response conditions: magnitude estimation and graphic rating. In addition, they judged average grayness of pairs of chips under the same two response modes. The averaging data were evaluated in terms of a simple model for subjective averaging. The graphic rating data fitted the model, but the magnitude estimates showed consistent discrepancy. It was concluded that the Ss were averaging, but that magnitude estimation distorted their judgments.     

The Wisdom of Many in One Mind: Improving Individual Judgments With Dialectical Bootstrapping

ABSTRACT— The "wisdom of crowds" in making judgments about the future or other unknown events is well established. The average quantitative estimate of a group of individuals is consistently more accurate than the typical estimate, and is sometimes even the best estimate. Although individuals' estimates may be riddled with errors, averaging them boosts accuracy because both systematic and random errors tend to cancel out across individuals. We propose exploiting the power of averaging to improve estimates generated by a single person by using an approach we call dialectical bootstrapping . Specifically, it should be possible to reduce a person's error by averaging his or her first estimate with a second one that harks back to somewhat different knowledge. We derive conditions under which dialectical bootstrapping fosters accuracy and provide an empirical demonstration that its benefits go beyond reliability gains. A single mind can thus simulate the wisdom of many.     

Direct quantitative judgments of sums and a two-stage model for psychophysical judgments

Judged magnitudes of differences between stimuli have previously been shown to support a two-stage interpretation of magnitude estimation, in which input transformations and output transformations are each describable as power functions. In an effort to provide support for the model independent of the difference estimation procedure. the present investigation employed two additional judgment tasks. We obtained magnitude judgments and category judgments of the combined magnitudes (sums) of paired weights from two groups of Ss. Values of the inferred input exponent k calculated from the two sets of data were very similar and were also remarkably similar to the exponent previously calculated from magnitude estimations of differences between weights. The output exponent calculated from magnitude judgments of sums described a concave upward function; however. the similar function describing category judgments was essentially linear. These results show that the inferred input exponent is not the result of the difference estimation task, and in addition provides support for the contention that the interval scale may be a less biased sensory measure than the magnitude scale. The introduction of an additive constant to the model improved its fit to the data but the rule by which it was introduced made very little difference.     

Global-scale location and distance estimates: common representations and strategies in absolute and relative judgments

The authors examined whether absolute and relative judgments about global-scale locations and distances were generated from common representations. At the end of a 10-week class on the regional geography of the United States, participants estimated the latitudes of 16 North American cities and all possible pairwise distances between them. Although participants were relative experts, their latitude estimates revealed the presence of psychologically based regions with large gaps between them and a tendency to stretch North America southward toward the equator. The distance estimates revealed the same properties in the representation recovered via multidimensional scaling. Though the aggregated within- and between-regions distance estimates were fitted by Stevens's law (S. S. Stevens, 1957), this was an averaging artifact: The appropriateness of a power function to describe distance estimates depended on the regional membership of the cities. The authors conclude that plausible reasoning strategies, combined with regionalized representations and beliefs about the location of these relative to global landmarks, underlie global-scale latitude and distance judgments.     

运动员的生活满意感:个人自尊与集体自尊的贡献

评估了个人自尊与集体自尊在预测运动员的一般生活满意感和训练比赛满意感时的相对重要性。被试为139名中国运动员,男68名,女71名,平均年龄19．64岁。分层回归的结果发现,在控制了人口统计学变量、个人自尊和社会支持3类变量以后,集体自尊单独解释了训练比赛满意感总方差的13％。优势分析的结果表明,预测训练比赛满意感时,集体自尊最为重要,贡献了已解释方差的67％。这些结果提示,需要用不同的自尊来预测不同的满意感。     

Subjective ratios and differences in perceived heaviness

In previous studies, judgments of ratios and differences in subjective magnitude have yielded similar orders, consistent with a hypothesis that a single perceived relation underlies both judgment tasks. In the present research, 15 subjects estimated heaviness differences between 28 pairs of eight weights and each of 8 groups of 10 subjects evaluated heaviness ratios of eight variable stimuli with respect to a different standard stimulus. Presenting stimuli that were equally spaced on a cube-root scale of weight enhanced expected ordinal discrepancies between ratio and difference estimates, and employing independent groups for each standard stimulus in ratio estimation eliminated a possible bias due to varying standards within the presentation sequence. Differences in orders of ratio and difference estimates together with differences in scales obtained from non-metric analyses in terms of a difference model indicated that the judgments were based on two perceived relations that are ordinally consistent with arithmetic operations of ratios and differences. A ratio scale of heaviness was derived from the combined orders of subjective ratios and differences.     

An Excel macro for transformed and weighted averaging

An Excel macro is presented for averaging spreadsheet data. The macro has several special features: (1) The data are weighted by the inverse variance of each datum to decrease the contribution-of noisy outliers. (2) There is a provision for a power or a log transform of the data before averaging. The rationale for transforming the data before averaging is discussed (3) The output includes the average value, its standard error, and the reduced chi-square that measures the goodness of fit (4) The standard error is corrected by a heterogeneity factor based on the reduced chi-square The averaging of data is rarely done properly, and the intent of this article is to clarify the issues and provide a tool that allows researchers to improve their averaging techniques.     

Ratio scale measurement of the perceived lengths of lines.

In Experiments 1 and 2, magnitude and category estimates of perceived line length difference were used to rank order 36 pairs of lines with respect to the psychological length difference between the lines forming a pair. In Experiment 3 magnitude estimates of line length ratios were used to order the same 36 pairs with respect to the psychological length ratio between the lines comprising a pair. A nonmetric analysis of the rank-order of the difference and ratio judgments was used to construct a ratio scale of perceived line length. Perceived line length was found to be a power function of physical line length with an exponent of .46. In Experiments 4 and 5, magnitude and category estimates of line length similarity were obtained. A nonmetric analysis of these data indicated that similarity judgments were monotonic inverses of judgments of psychological ratios.     

Incremental exercise, plasma concentrations of catecholamines, reaction time, and motor time during performance of a noncompatible choice response time task

The primary purpose was to examine the effect of incremental exercise on a noncompatible response time task. Participants (N=9) undertook a 4-choice noncompatible response time task under 3 conditions, following rest and during exercise at 70% and 100% of their maximum power output. Reaction and movement times were the dependent variables. Maximum power output had been previously established on an incremental test to exhaustion. A repeated-measures multivariate analysis of variance yielded a significant effect of exercise intensity on the task, observation of the separate univariate repeated-measures analyses of variance showed that only movement time was significantly affected. Post hoc Tukey tests indicated movement time during maximal intensity exercise was significantly faster than in the other two conditions. The secondary purpose of the study was to assess whether increases in plasma concentrations of adrenaline and nor-adrenaline during exercise and power output would act as predictor variables of reaction and movement times during exercise. Catecholamine concentrations were based on venous blood samples taken during the maximum power output test. None of the variables were significant predictors of reaction time. Only power output was a significant predictor of movement time (R2 = .24). There was little support for the notion that peripheral concentrations of catecholamines directly induce a central nervous system response.     

A test of a two-stage model of magnitude judgment

It has been suggested that the power law J = aⁿ, describing the relationship between numerical magnitude judgments and physical magnitudes, confounds a sensory or input function with an output function flawing to do with O’s use of numbers. Judged magnitudes of differences between stimuli offer some opportunity for separating these functions. We obtained magnitude judgments of differences between paired weights, as well as magnitude judgments of the weights making up the pairs. From the former we calculated simultaneously an input exponent and an output exponent, working upon Attneave’s assumption that both transformations are describable as power functions. The inferred input and output functions, in combination, closely predict the judgments of individual weights by the same Os. Although pooled data (geometric means of judgments) conform fairly well to a linear output function, individual data do not; i.e., individual Os deviate quite significantly fromlinearity and from one another in their use of numbers. Individual values of the inferred sensory exponent, k, show significantly better uniformity over Os than do values of the phenotypica! magnitude exponent previously found to describe interval judgments of weight.     

Tests of product and additive scaling axioms

A product axiom for ratio judgments and an additive axiom for difference judgments were tested for six Ss judging brightness. The product axiom was rejected for all six Ss whereas the additive axiom was accepted for two Ss. Power functions did not fit the data well, although somewhat better for difference judgments than ratio judgments. A two-stage model fitted somewhat better, but failed to satisfy one important implication of that model, previously confirmed for lifted weights. The data gave stronger support for a theory of brightness estimation based on an additive axiom for difference judgments than a product axiom based on ratio judgments.     

权力感对道德困境判断的影响：基于CNI模型的分析

采用道德困境判断的CNI（consequence, norm, inaction）模型,通过两个实验考察权力感对道德困境判断的影响。实验1探讨个人权力感对道德困境判断的影响,结果显示高个人权力感显著增加被试对规则的敏感,促使个体做出道义论的道德判断。实验2考察回忆任务启动的权力感对道德困境判断的影响,发现相对于低权力感启动的被试,高权力感启动的被试在进行判断时更关注行为的结果,对规则更不敏感,这说明启动的权力感促进功利主义的道德判断,抑制道义论的道德判断。结果表明,不同类型的权力感对道德困境判断的影响存在差异。     

Latent growth curve analysis with dichotomous items: Comparing four approaches

A Monte Carlo study was used to compare four approaches to growth curve analysis of subjects assessed repeatedly with the same set of dichotomous items: A two‐step procedure first estimating latent trait measures using MULTILOG and then using a hierarchical linear model to examine the changing trajectories with the estimated abilities as the outcome variable; a structural equation model using modified weighted least squares (WLSMV) estimation; and two approaches in the framework of multilevel item response models, including a hierarchical generalized linear model using Laplace estimation, and Bayesian analysis using Markov chain Monte Carlo (MCMC). These four methods have similar power in detecting the average linear slope across time. MCMC and Laplace estimates perform relatively better on the bias of the average linear slope and corresponding standard error, as well as the item location parameters. For the variance of the random intercept, and the covariance between the random intercept and slope, all estimates are biased in most conditions. For the random slope variance, only Laplace estimates are unbiased when there are eight time points.     

Strategy Flexibility: On Jausovec's Flexible Thinking: An Explanation for Individual Differences in Ability

We examined some of the factors that influence evaluations of improvised music. Using the Consensual Assessment Technique (CAT), 10 expert judges evaluated 16 pieces of music, improvised on an electronic keyboard. Overall evaluations of improvisations were associated with their perceived complexity, creativity, and technical goodness. These predictors accounted for 76% of the variance in preference judgments. The intrinsic motivation of improvisers was also assessed, and was correlated with overall evaluations. No support was found for a nonlinear relation between the perceived complexity of the music and its aesthetic appeal, as suggested by Berlyne's optimal-complexity model. We outline a model linking characteristics of improvisers and their improvisations to judges' overall liking for the music. The benefits of using the CAT to assess music are also discussed.     

Information Integration in Juror Decision Making

Research applying information integration theory to jury decision making has long assumed that people average informational scale values when making legal judgments. Although often consistent with research results, this hypothesis has never been tested in a legal context against a more general additive rule. The present paper describes two studies conducted as a critical test between these two models. Incriminating evidence and eyewitness confidence were varied in a full-factorial, within-subjects design involving a total of 131 subjects acting as mock jurors. Subject responses included eyewitness accuracy and defendant-guilt probability estimates, as well as final verdict decisions. Results strongly support an averaging model of legal decision making. Additional results concerning the influence of initial attitudes and the interrelationships between the variables considered are reported and their implications are discussed.     

Reanalysis of the equation for simple action

De Villiers and Herrnstein (1976) have shown that the equation for simple action, derived from the matching law, predicts change in behavioral output for some 40 experiments in which the value of a single source of reinforcement has been varied. Using only the positive-reinforcement studies they cite that used five or more different reinforcement values, we found the high percentage of variance they report accommodated by this equation (94%) is predicated on instances of averaging rates of behavioral output before making a least-squares fit of the equation. In our reanalysis, which minimizes rate averaging, only 78% of the data variance is accommodated. This diminished data-variance accommodation can be improved by adding parameters that permit the equation's scaling constant to change as a function of reinforcement. Although these parameters permit acceptable levels of accommodation of data variance, they correspond to no obvious psychological processes. These findings support the view that the equation for simple action is an inadequate model for behavioral output.     

RETR_PWR: An SAS macro for retrospective statistical power analysis

In contrast to prospective power analysis, retrospective power analysis provides an estimate of the statistical power of a hypothesis test after an investigation has been conducted rather than before. In this article, three approaches to obtaining point estimates of power and an interval estimation algorithm are delineated. Previous research on the bias and sampling error of these estimates is briefly reviewed. Finally, an SAS macro that calculates the point and interval estimates is described. The macro was developed to estimate the power of anF test (obtained from analysis of variance, multiple regression analysis, or any of several multivariate analyses), but it may be easily adapted for use with other statistics, such as chi-square tests ort tests.     

Psychological causality in the attribution of responsibility for rape

According to a legal model of the attribution of responsibility for rape, judgments of physical and psychological causality of an alleged rapist are combined into overall evaluations of attacker responsibility. It was hypothesized that observers evaluate psychological causality by reconstructing the thought patterns of the accused rapist and by classifying this mental activity along dimensions of responsibility. Subjects read crime briefs, rated dimensions of responsibility, and assigned sentences. Factor analysis and analyses of variance indicate that observers organize psychological causality of the rapist around dimensions of intended violence, and the extent to which the attacker's thoughts are attributable to the victim. Multivariate analysis of variance confirmed the expected effects of the attacker's thoughts on judgments of culpability.This research was supported by a St. Louis University Beaumont Grant. The authors wish to express their gratitude to Kevin Wayne for assisting in data collection and analysis. A special thank you is extended to Audrey Feldman, who reviewed an earlier draft of this paper.