UNCERTAINTY OF COMPARATIVE JUDGEMENTS AND MULTIDIMENSIONAL STRUCTURE

An analysis of preferences with respect to silhouette drawings of nude females is presented. Systematic intransitivities were discovered. The dispersions of differences (comparatal dispersions) were shown to reflect the multidimensional structure of the stimuli, a finding expected on the basis of prior work. Difference ratings of these stimuli were analyzed by the TORSCA and INDSCAL procedures. The three stimulus dimensions all appeared in the multidimensional analyses.     

Completely nonmetric multidimensional scaling

Most of the distance models underlying multidimensional scaling assume that if a stimulus y is between the stimuli x and z on each dimension, then x and z should be the farthest apart of the three stimuli. An iterative algorithm is described that uses only this betweenness prediction to infer the ordering of a set of stimuli on each of one or two dimensions. Applied to previously published semantic similarity data, this algorithm produced two-dimensional configurations that were similar in appearance to Euclidean configurations but generally involved fewer violations of the betweenness prediction.     

Improving the efficiency and effectiveness of interactively selected MDS data designs

Two revisions of interactive MDS data selection procedures are presented. One revision improves the estimates of the MDS parameters by adding an analysis of the volume of the spatial coordinates of stimuli. Frames of stimuli augmented by an analysis of volume should more nearly surround the swarm of stimulus points. The second revision, based on randomly ordering the list of stimuli, permits more efficient data designs to be selected by reducing the number of judgments collected but never analyzed.This investigation was supported in part by a Research Scientist Development Award (KO2-DA00017), research grants (DA01070 and MH24149) from the U.S. Public Health Service, and a research and instruction award (IUC 2-47622-1990) from the University of California.     

不同手指表征方式对数量表征能力的影响

采用距离启动范式,考察中国文化背景下不同手指表征方式对数量表征能力的影响。实验首先验证单手表征中不同手指数量表征方式对小数字（1～5）认知表征的影响;实验2则进一步采用中国人特有的单手手指表征,考察其对大数字（5～9）认知表征的影响。结果表明,小数字中出现了标准手指表征方式语义层面的位置编码、非标准手指表征方式知觉层面总和编码的激活;但大数字中两种手指表征方式均出现了语义层面位置编码的激活。此结果与计算模型理论一致,说明当手指数量从少到多变化时,标准手指表征方式为语义性的符号数量表征;而非标准手指表征方式由知觉性的非符号向语义性符号数量表征过渡。     

Detection theory,micromatching, and the constant-ratio rule

The conformance of detection theory and micromatching with the constant-ratio rule (CRR) was determined by calculations for sets of three stimuli and subsets of two stimuli. For an arbitrary selection of sets, the CRR would be expected to hold quite well if either detection theory or micromatching lay behind the responses. For specific stimulus configurations, however, detection theory and micromatching differ considerably from one another and from the CRR. These configurations are found particularly for the univariate distributions, and this corresponds to empirical findings that the CRR holds better for multidimensional than for unidimensional stimuli. It is shown how the differences between the three theories in the implied constancies of ratios can be used in diagnosis of the basis ofempirical confusion matrices.     

Prior categorization can produce more efficient ordering

We hypothesized that prior categorization of an attribute might sometimes facilitate the ordering of stimuli, particularly when the number of stimuli is relatively large or some of them need to be remembered. In four experiments, participants were required to rank order either numbers or line lengths either using a selection sort or following prior categorization. The results indicated that prior categorization produced faster sorting when the number of stimuli to be ordered was relatively large and when the stimuli were not continuously visible.     

The fit between Strong-Campbell Interest Inventory General Occupational Themes and Holland's hexagonal model

Using a multidimensional scaling procedure, the present study examined the fit of Holland's RIASEC hexagon model to the internal relationships among the Strong-Campbell Interest Inventory (SCII) General Occupational Theme scales. SCII intercorrelation matrices for both sexes as reported in the SCII Manual were submitted, separately for each sex, to TORSCA 9 nonmetric scaling analysis. The Wakefield and Doughtie procedure was used to compare obtained TORSCA coordinates with expectations from Holland's hexagonal model. As a comparison, identical analyses were performed on Vocational Preference Inventory (VPI) scale intercorrelation matrices, these data having originally served as the basis for advancing the utility of the hexagon model. For females, the SCII-hexagon fit was not good, with a near reversal of the Social and Enterprising scales. For males, the SCII-hexagon fit was good. For either SCII or VPI scales, the female data met expectations from Holland's model less often than the male data. A replication study on SCII data for 305 female clients of a vocational assessment clinic confirmed the previously observed sex differences. Sex differences in the structure of vocational preferences are discussed.     

Effects of rank ordering stimuli on magnitude ratings of these and other stimuli

Five experiments investigated the effects of rank ordering stimuli on subsequent magnitude ratings of these and other stimuli. In Experiments 1 and 2, subjects first rank ordered environmental issues in terms of their importance. Ranking stimuli from “most” to “least” led to more extreme ratings than ranking them from “least” to “most,” regardless of whether the rating criterion was the same as or diametrically opposite to the ranking criterion. (For example, subjects who had previously ranked them beginning with the most important issue subsequently rated these issues not only as more important, but also as more trivial, than did subjects who had ranked them beginning with the least important.) These effects generalized to stimuli other than those that had previously been ranked, and generalized over stimulus domains. (For example, ratings of environmental issues were also affected by ranking the importance of attributes of a marriage partner.) Other experiments in the series circumscribed the conditions in which these effects occur. Results suggested that rank ordering stimuli leads subjects to adopt comparative standards, the use of which generalizes to subsequent magnitude rating tasks and produces an anchoring bias similar to that identified by A. Tversky and D. Kahneman (1974, Science (Washington, D.C.), 185, 1124–1131). Implications of these results for the cognitive processes that underlie social judgment are discussed.     

Space-Time Counterfactuals

A definition is proposed to give precise meaning to the counterfactual statements that often appear in discussions of the implications of quantum mechanics. Of particular interest are counterfactual statements which involve events occurring at space-like separated points, which do not have an absolute time ordering. Some consequences of this definition are discussed. This revised version was published online in June 2006 with corrections to the Cover Date.     

A note on the use of triads for paired comparisons

When scaling a large number of stimuli from comparative judgments, considerable savings in time and labor may be realized if stimuli are presented in triad form rather than in pairs. If, forN stimuli, the proper configuration of triads can be assembled so that all possible pairs appear once, the paired judgment matrix may be reproduced with one-third fewer judgments and two-thirds fewer presentations than would be required with complete pairing. A simple procedure is described for enumerating triad configurations for whichN is an odd multiple of three.     

Dissimilarity cumulation as a procedure correcting for violations of triangle inequality

Dissimilarity on a finite set is a function that assigns to every pair of points (stimuli) a nonnengative number vanishing if and only if the two points are identical. For any two points in a finite set, the minimum of the length of all finite chains connecting these points is a quasimetric (i.e., it satisfies all metric axioms except for symmetry). The computation of the quasimetric from a dissimilarity can be viewed as a data-analytic procedure of “correcting” dissimilarities into (quasi)distances, an alternative to nonmetric Multidimensional Scaling: the procedure simply replaces the dissimilarity between any two points with the shortest length across all chains of points connecting them. It is shown in this paper that this procedure can be equivalently described as a series of recursive corrections for violations of the triangle inequality across all triples of points considered in an arbitrary order.     

Automated assembly of optimally spaced and balanced paired comparisons: Controlling order effects

To control order effects in questionnaires containing paired comparisons, Ross (1934) described an optimal ordering of the pairings. The pairs can also be balanced so that every stimulus appears equal numbers of times as the first and the second member of a pair. First, we describe and illustrate the optimally spaced, balanced ordering of pairings. Then we show how the optimally spaced, balanced order can be used to implement a matrix-sampling design or a fully incomplete design when the number of stimuli n is so large that respondents cannot reasonably be expected to judge all n(n - 1)/2 pairs. The algorithm for balancing and optimally spacing the list of pairs is described.     

How do people order stimuli?

People may find it easier to construct an order after first representing stimuli on a scale or categorizing them, particularly when the number of stimuli to be ordered is large or when some of them must be remembered. Five experiments tested this hypothesis. In two of these experiments (1 and 3), we asked participants to rank line lengths or to rank photographs by artistic value. The participants provided evidence of how they performed these tasks, and this evidence indicated that they often made use of some preliminary representation—either a metric or a categorization. Two further experiments (2 and 4) indicated that people rarely produced rankings when given a choice of assessment measures for either the length of lines or the artistic value of photographs. In Experiment 5, when the number of lines was larger or lines were only visible one at a time, participants were faster at estimating line lengths as a percentage of the card covered than at rank ordering the lengths. Overall, the results indicate that ordering stimuli is not an easy or natural process when the number of stimuli is large or when the stimuli are not all perceptible at once. An implication is that the psychological measures available to individuals are not likely to be purely ordinal when many of the elements being measured must be recalled.     

Nonparametric polytomous IRT models for invariant item ordering, with results for parametric models

It is often considered desirable to have the same ordering of the items by difficulty across different levels of the trait or ability. Such an ordering is an invariant item ordering (IIO). An IIO facilitates the interpretation of test results. For dichotomously scored items, earlier research surveyed the theory and methods of an invariant ordering in a nonparametric IRT context. Here the focus is on polytomously scored items, and both nonparametric and parametric IRT models are considered.The absence of the IIO property in twononparametric polytomous IRT models is discussed, and two nonparametric models are discussed that imply an IIO. A method is proposed that can be used to investigate whether empirical data imply an IIO. Furthermore, only twoparametric polytomous IRT models are found to imply an IIO. These are the rating scale model (Andrich, 1978) and a restricted rating scale version of the graded response model (Muraki, 1990). Well-known models, such as the partial credit model (Masters, 1982) and the graded response model (Samejima, 1969), do no imply an IIO.     

Evaluating the importance of the convex hull in solving the Euclidean version of the traveling salesperson problem: reply to Lee and Vickers (2000)

Lee and Vickers (2000) suggest that the results of MacGregor and Ormerod (1996), showing that the response uncertainty to traveling salesperson problems (TSPs) increases with increasing numbers of nonboundary points, may have resulted as an artifact of constraints imposed in the construction of stimuli. The fact that similar patterns of results have been obtained for our "constrained" stimuli, for a stimulus constructed under different constraints, for 13 randomly generated stimuli, and for random and patterned 48-point problems provides empirical evidence that the results are not artifactual. Lee and Vickers further suggest that, even if not artifactual, the results are in principle limited to arrays of fewer than 50 points and that, beyond this, the total number of points and number of nonboundary points are "diagnostically equivalent." This claim seems to us incorrect, since arrays of any size can be constructed that will permit experimental tests of whether problem difficulty is influenced by the number of nonboundary points, or the total number of points, or both. We present a reanalysis of our original data using hierarchical regression analysis which indicates that both factors may influence problem complexity.     

Collecting paired-comparison data with a sorting algorithm

Monte Carlo techniques were used to evaluate the performance of an on-line paired-comparisons data collection procedure that makes use of a common computer sorting algorithm. The results revealed that the sorting method can reduce the number of trials per subject substantially even when a considerable amount of random error is present. While a complete paired-comparisons design requires N(N?1)/2 trials (where N is the number of objects), the sorting procedure requires a theoretical minimum of N(log₂N) trials. The savings in the number of trials consequently increases with N. Furthermore, the negative effect of random error on the final ordering of the data from the sorting method is small and decreases with the number of stimuli. The data from a small empirical study reinforces the Monte Carlo observations. It is recommended that the sorting method be used in place of the complete paired-comparisons procedure whenever a substantial number of stimuli are included in the design.     

Deployment of attention to the configuration of features in facelike patterns by ten-week-old infants

Abstract

Three experiments were conducted to investigate the response of 10-week-old infants to the configuration of features in facelike patterns. In each experiment a series of preview trials was shown before. facelike patterns were presented on test trials. Preview stimuli were schematic drawings with non-facial configurations (Experiment 1), schematic drawings with facial configurations (Experiment 2), or photographs of men's and women's faces (Experiment 3). Test stimuli in all three experiments were facelike drawings that differed in the number and the configuration of their stimulus features.     

Localization of electrocutaneous stimuli on the fingers and forearm: Effects of electrode configuration and body axis

Four experiments were done on the effects of electrode configuration (concentric vs. unifocal) and body axis (longitudinal vs. transverse) on localization of electrocutaneous pulse stimuli at the fingers and forearm. Subjects pointed to the apparent location of current pulses. For the transverse placement of electrodes, pulses were localized correctly, whatever the configuration and the body site might be. In addition, intrasubject variability at the forearm was smaller for the transverse axis than for the longitudinal axis. For the longitudinal placement of electrodes, pulses were localized as a function of configuration and body site. At the fingers, concentric electrodes provided precise localization but unifocal electrodes provided a great mislocalization; and intrasubject variability of localization was larger for the unifocal electrodes than for the concentric electrodes. At the forearm, whatever the configuration might be, the pulses were localized more proximally than the stimulus site; and intrasubject variability of localization did not differ between the configurations. These results are related to Boring’s anchor theory, apparent distance between two points, and the localization of other somatosensory stimuli.     

Inhibition of return for faces

Inhibition of return (IOR) refers to slower reaction times when a target appears unpredictably in the same location as a preceding cue, rather than in a different location. In the present study, frontal images of human faces were presented intact as face configurations, were rearranged to produce scrambled-face configurations, or were pixilated and randomized to produce nonface configurations. In an orienting paradigm designed to elicit IOR, face and scrambled-face stimuli were used as cues (Experiment 1), as targets (Experiment 2), or along with pixilated nonface stimuli as both cues and targets (Experiment 3). The magnitude of IOR for subsequent localization targets was unaffected by cue configuration. Likewise, the magnitude of IOR was unaffected by target configuration. These results suggest that IOR is a "blind" mechanism that is unaffected by the mere occurrence of biologically relevant cue and target stimuli.     

Categorization behaviour in adults,adolescents, and attention-deficit/hyperactivity disorder adolescents: A comparative investigation

Although significant progress has been made with respect to our understanding of categorization and concept learning behaviour in adults, much less is known about how this key capacity plays out with respect to more restrictive populations. This is unfortunate because much may be revealed about the nature of concept learning by examining the limits exhibited by special populations. With this tenet in mind, in what follows, we investigated key aspects of concept learning in terms of the unexplored comparative performance of three populations—adults, adolescents, and adolescents with attention-deficit/hyperactivity disorder (ADHD). To do so, we employed a novel parainformative experimental task involving categorical stimuli with four objects defined over three dimensions. The learning difficulty ordering for these types of three-dimensional stimuli has proven robust and has been replicated by several researchers. Indeed, in our experiment, we observed the same concept learning ordering in adults and adolescents, but not in ADHD adolescents: For example, the latter group showed greatly impaired categorization performance on stimuli characterized by an “exclusive-or” rule. However, categorization performance on such type of stimuli indicated good reliability in discriminating between adolescents with and without ADHD (receiver-operating characteristic, ROC?=?.82). We accurately predicted and accounted for these results using generalized invariance structure theory (GIST; Vigo, 2013. The GIST of concepts. Cognition, 129, 138–162), which posits that organisms detect invariance patterns in stimuli that are necessary precursors to concept formation.