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.     

Nonmetric tests of ratio vs. subtractive theories of stimulus comparison

Theories of stimulus comparison were tested by examining ordinal properties of data obtained with six scaling tasks. Subjects judged simple “ratios” or “differences” of stimulus pairs constructed from a factorial design. In four additional tasks, the same judges also compared relations between pairs of stimulus pairs, judging “ratios of ratios,” “ratios of differences,” “differences of ratios,” and “differences of differences.” The data were consistent with a subtractive theory, which asserts that two stimuli are compared by subtraction, regardless of the task, but that judges can compare two stimulus differences by either a ratio or a difference. All six tasks could be related by the subtractive theory using a single set of scale values. Other simple theories, including the theory that “ratio” judgments can be represented by a ratio model, could not reproduce the six rank orders (of the six sets of data) using a single set of scale values.     

Ordinal properties of perceived average duration: simultaneous and sequential presentations

When a subject evaluates the duration of two simultaneous events, the perceived durations are combined in a nonlinear manner, whereas comparable evaluations of successive events yield linear combinations. Fifty-four subjects rated average durations of pairs of time intervals ranging from 0.5 s to 10.0 s. The intervals making up a pair were presented successively and simultaneously on separate occasions within the same presentation sequence. The order of data was consistent with models previously proposed for perceived average duration. A nonmetric analysis of the combined ordinal data from both conditions yielded a single set of measures of perceived duration with ratio-scale properties. The common scale for the two conditions is consistent with differences in results from simultaneous and successive monitoring of time intervals, stemming from differences in the way duration information is combined rather than how it is perceived. the derived scale is related to physical time by a power function with a 1.06 exponent.     

A technique for the nonmetric analysis of paired comparisons of psychological intervals

A nonmetric coordinate adjustment technique is developed which determines scale values for objects whose interobject intervals (differences in subjective value) have been directly compared. In Monte Carlo simulations, the degree of metric determinancy of the scale values is shown to be quite high even when the amount of error is relatively high. This robustness under high-error conditions permitted the analysis of individual subject data in experiments on the direct comparison of loudness differences and loudness ratios where only one judgment per interval comparison was obtained per subject.This research was supported by a grant from the National Research Council of Canada.     

Weight of evidence supports one operation for "ratios" and "differences" of heaviness

This paper investigates an apparent contradiction between recent studies of "ratios" and "differences" of heaviness. Birnbaum and Veit (1974) found a single rank order for judgments in the two tasks, whereas Rule, Curtis, and Mullin (1981), who used a different stimulus set, procedure, and experimental design, reported two orders. To investigate the cause of this discrepancy, the present study manipulated the experimental design using the same stimuli and procedure as Rule et al. (1981). In one experiment (within-subject designs), each subject judged all combinations of the standard and comparison stimulus; in the other experiment (between-subjects designs) each subject received only one standard, and different groups of subjects were given different standards. "Ratios" and "differences" of heaviness were monotonically related for the majority of subjects who judged all combinations of standards and comparisons. Variations in the modulus and response examples did not affect the rank order of "ratios" within subjects. These results suggest that the contradiction in results is due to the difference in experimental design rather than differences in stimuli or procedure. In the between-subjects designs, the rank order of the "ratio" judgments depended on the standards and examples. Both previous and present results are consistent with the theory that subjects use one operation, subtraction, for both tasks and that the judgment function varies with between-subjects manipulations of the standard, examples, and modulus.     

Comparison of two theories of "ratio" and "difference" judgments

This article examines the hypothesis that judges compare stimuli by ratio and subtractive operations when instructed to judge" "ratios" and "differences." Rule and Curtis hold that magnitude estimations are a power function of subjective values, with an exponent between 1.1 and 2.1. Accordingly, the two-operation model tested assumes magnitude estimations of "ratios" are a comparable power function of subjective ratios. In contrast, Birnbaum and Veit theorize that judges compare two stimuli by subraction for both "ratio" and "difference" instructions and that magnitude estimations of "ratios" are approximately an exponential function of subjective differences. Three tests were used to compare the theory of one operation with the two-operation theory for the data of nine experiments. The results strongly favor the theory that observers use the same operation for both instructions.     

The need for process research on psychophysical judgment: comments on "Ratio and subtractive processes in psychophysical judgment" by Veit

This article is a commentary on Veit's article "Ratio and Subtractive Processes in Psychophysical Judgment." Veit's article makes an important contribution to the area of psychophysical judgment by providing a systematic approach that combines measurement and psychological theory. Using multi-factor designs and a cross-task scale-invariance criterion, Veit shows how to concurrently examine the integration rule, response-transformation function, and psychophysical function for judgment tasks. The need to expand this methodology to further understand the operations and processes underlying psychophysical judgment is stressed in the present article, and an illustration involving feedback mechanisms is provided.     

Range and regression effects in magnitude scaling

The relation between power law exponents obtained by magnitude estimation and magnitude production was studied for both loudness and perceived distance. While the results confirm the usual finding of higher values for production for relatively large stimulus ranges, just the opposite occurs when the stimulus range is short, necessitating a revision of the Stevens-Greenbaum regression principle. The relation between range and exponent was explored, both for the case in which several intensities are presented for judgment and for the simpler case of only two intensities. In both cases, a power relation was described relating stimulus ratios to judgmental ratios, with exponents containing both range-dependent and range-independent components.     

A multidimensional scaling analysis of judged similarity of complex forms from two task situations

Ss provided judgments of pairwise stimulus similarities for 21 12-turn random forms in two experimental tasks: a scaling task, involving a variant of the method of graded dichotomies, and a sorting task, which simply required Ss to categorize the forms. The grouped data from both tasks, when analyzed using nonmetric multidimensional scaling techniques, yielded five-dimensional configurations with euclidean distances. The correspondence of these two spaces, assessed using canonical correlations, was extremely good. The psychological dimensions derived from both tasks were related to two sets of physical measures on the forms: the factor space suggested by Brown and Owen and a set of more basic physical measures. Physical cues of greatest importance involved size, dispersion, angularity, and rotation measures. The value of the tasks and the utility of the Brown and Owen measures were discussed.     

Models for ordinal hierarchical classes analysis

This paper proposes an ordinal generalization of the hierarchical classes model originally proposed by De Boeck and Rosenberg (1998). Any hierarchical classes model implies a decomposition of a two-way two-mode binary arrayM into two component matrices, called bundle matrices, which represent the association relation and the set-theoretical relations among the elements of both modes inM. Whereas the original model restricts the bundle matrices to be binary, the ordinal hierarchical classes model assumes that the bundles are ordinal variables with a prespecified number of values. This generalization results in a classification model with classes ordered along ordinal dimensions. The ordinal hierarchical classes model is shown to subsume Coombs and Kao's (1955) model for nonmetric factor analysis. An algorithm is described to fit the model to a given data set and is subsequently evaluated in an extensive simulation study. An application of the model to student housing data is discussed.     

视觉空间关系判断的分离与协同

采用任务表征相互影响范式,通过三个实验探讨了类别空间关系判断和数量空间关系判断的加工特性和相互关系.结果表明:(1)先行类别关系启动有利于数量空间关系判断,对类别空间关系判断没有影响;先行数量关系启动对两个判断任务均无影响.(2)先行类别关系干扰降低两个空间关系判断的绩效,先行数量关系干扰对两个空间关系判断没有影响.(3)先行类别关系对空间关系判断的启动和干扰效应不局限于特定条件,具有普遍性.研究提示,右脑为优势半球的数量关系加工以左脑为优势半球的类别关系加工为基础,支持视觉空间认知加工既分离又协同的观点.     

Selection of strategies for narrowing choice options: Antecedents and consequences

This study investigates the antecedents (task and decision maker characteristics) and consequences (set size and decision quality) of prescreening strategy selection. In Experiment 1 we investigated which strategy, inclusion or exclusion, is more natural for narrowing choices in tasks with a single correct answer; about 70% of the participants selected exclusion. Experiment 2 directly contrasted correct answer tasks with personal judgment tasks, using the same foils for the two tasks. Participants were more likely to use exclusion for items with a correct answer than for personal judgments. In Experiment 3, participants could choose different strategies for different items and rated the difficulty of each item. The greater the perceived difficulty of an item, the more likely participants were to choose an exclusion strategy. In all three experiments exclusion led to larger set sizes, across task type and experimental design. There were no differences in decision quality as a function of strategy selection after correcting for set size. Individual differences based on personality inventories were not found to be good predictors of strategy selection, but had moderate effects on set size for personal judgment tasks. Results are discussed in terms of a status quo bias for adding or deleting options from an initial reference frame.     

The Rokeach Value Survey: Underlying Structure and Multidimensional Scaling

Studies have demonstrated that the ordinal, ipsative data provided by the Rokeach Value Survey (RVS; Rokeach 1973) are not suited to factor analysis. In this study, nonmetric multidimensional scaling (MDS) was used with a sorting task to identify the underlying subset of values. American college students were the participants, and the results indicate that individualism-achievement and collectivism-affiliation are the underlying dimensions of the RVS for both the terminal and the instrumental values. Observed variation in the use of MDS space was predicted, based on participants' developmental differences as measured by the Maslowian Assessment Survey (Williams & Page, 1989). Gender differences in the use of MDS space by participants were not observed. Analysis of angular variance was used to test both hypotheses.     

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.     

Inverse cross-modality matching: A test of ratio judgment consistency for group and individual data

Direct and inverse cross-modality matches made by 20 subjects were assessed for ratio judgment consistency. Each subject matched apparent duration to loudness, and vice versa, in both a directly and an inversely proportional manner. All four tasks were repeated twice so that individual differences could be examined using interrepetition correlations. Group data exhibited the appropriate inverse relationship indicative of consistency, although the inverse matches were slightly curvilinear and resembled earlier studies with inverse attribute scales. Some individuals showed a high degree of consistency but many departed widely from inverse proportionality. Individual differences in exponents, which occurred for both types of tasks, were not removed by S. S. Stevens’ (1971) regression balance procedure. However, interrepetition correlations for the differences in the absolute values of the direct and inverse exponents of individuals were nonsignificant, suggesting that when subjects’ exponents differed for the two types of tasks they did so on a random basis. The latter finding implies that subjects would give inversely proportional matches were it not for random factors. The findings were discussed in relation to other types of ratio consistency.     

A monte carlo investigation of the statistical significance of Kruskal's nonmetric scaling procedure

Recent advances in computer based psychometric techniques have yielded a collection of powerful tools for analyzing nonmetric data. These tools, although particularly well suited to the behavioral sciences, have several potential pitfalls. Among other things, there is no statistical test for evaluating the significance of the results. This paper provides estimates of the statistical significance of results yielded by Kruskal's nonmetric multidimensional scaling. The estimates, obtained from attempts to scale many randomly generated sets of data, reveal the relative frequency with which apparent structure is erroneously found in unstructured data. For a small number of points (i.e., six or seven) it is very likely that a good fit will be obtained in two or more dimensions when in fact the data are generated by a random process. The estimates presented here can be used as a bench mark against which to evaluate the significance of the results obtained from empirically based nonmetric multidimensional scaling.A preliminary version of this paper was presented at the International Federation for Information Processing Congress 68 in Edinburgh, Scotland, August 5–10, 1968.     

“Ratios” and “differences” in perceived sweetness intensity

For a number of perceptual continua, it has been shown in previous studies that subjects use only one quantitative comparison between two sensory impressions of a pair of stimuli, irrespective of whether they are instructed to judge “ratios” or “differences”. This comparison can be described by algebraic subtraction. The present study was designed to investigate whether this one-operation theory for psychophysical judgment also applied to the sensory continuum of sweetness. Subjects were presented with pairs of fructose solutions, and judged “ratios” of, or “differences" in, perceived sweetness intensities. The pairs were constructed on the basis of a factorial judgment design. The results showed that the reported “differences” could be adequately described by a difference response model, and that the reported “ratios” could be adequately described by a ratio response model. However, the reported “ratios” and reported “differences” were monotonically related, and the marginal means of the log-transformed response matrix of “ratios” were a linear function of the marginal means of the response matrix of “differences”. These results are incompatible with the notion that subjects judged differences when instructed to judge “differences”, but ratios when instructed to judge “ratios”. The consistency of the ratio response model with “ratio” judgments is probably caused by a comparative operation based on “differences” in combination with an exponential response output function. It may be concluded that subjects judge only “differences”, and not “ratios”, between perceived sweetness intensities.     

Assembling a task space: global determination of local shift costs

Most theorizing on the origin of the costs that are associated with task shifts focuses on local transitions between individual trials. In the present article we argue that this emphasis has resulted in a neglect of more global representational structures, which also determinate shift costs. To substantiate this claim, we employed a set of four tasks that results from a factorial combination of two types of judgment and two judgment-to-response mappings. From previous work it is known that this kind of task combination is associated with a characteristic profile of shift costs as a function of the relation between successive tasks. Previously we have interpreted this profile as an indication of a hierarchically ordered dimensional representation of the two types of judgment and the two judgment-to-response mappings. Such a representation can only be expected to emerge when the two task features, judgment and mapping, vary independently of each other within the same situation. It is shown that the characteristic shift cost profile can indeed only be observed when the performance of any of the four tasks is required in a block of trials. In contrast, with only two tasks occurring in each block of trials, shift costs do not reflect the relation between successive tasks. This finding confirms the importance of global representational structures as a determinant of shift costs beyond local transitions between individual trials.     

4岁儿童对他人记忆的评判与错误信念理解的关系

从观点采择的角度考察儿童对他人记忆的评判及其与错误信念理解的关系。与他人分享记忆时,个体需要同时处理自我与他人对过去的表征和看法;而要顺利完成错误信念任务,个体需要同时加工自我的真实信念与他人的错误信念。因此个体对他人记忆的评判能力可能会与其对错误信念的理解相关。40名4岁儿童完成一系列错误信念任务和评判他人记忆是否正确任务,情境包括视觉、意图解释和情绪解释。结果表明,控制年龄、语言和记忆能力等因素后,被试评判他人记忆的成绩仍然可以预测其对错误信念的理解。这些结果为幼儿在回忆叙述中谈及他人越多,其心理理论越好提供了进一步的证据和可能的解释     

Individual differences in perceived similarity and preference for visual art: A multidimensional scaling analysis

Previous studies have shown that individuals may attend to different dimensions in making an overall judgment of similarity between complex stimuli. The present study investigated the nature of differences in the perceived similarity of reproductions of paintings by the use of multidimensional scaling techniques. Using the INDSCAL model, a group of art-trained students are shown to differ significantly from a group of nonart students in terms of their differential weighing of a set of common dimensions. The same subjects’ preferences are examined in relation to these differences by use of the PREFMAP hierarchy of models. While the simplest (vector) model was found to be appropriate for almost all subjects, large differences in vector direction and average subject ideal-point location are found. Implications for future studies of responses to art are discussed.