Repeated magnitude estimations with a variable standard: Sequential effects and other properties

Twelve Ss made magnitude estimations of the loudness of each one of a sequence of pure tones according to the rule R(N) = R(N - 1) · [S(N)/S(N - 1)], where R(N) is the response on Trial N, R(N - 1) is the response on Trial N - 1, and S(N)/S(N - 1) is the judged ratio of the “loudness” of the pure tone presented on Trial N to that of the pure tone presented on Trial N - 1. It was found that these magnitude estimations were assimilated toward the immediately preceding stimuli as far as five trials back in the sequence of stimuli. In addition, ratio judgments were consistently asymmetric and the data displayed a form of “time order error.” In all cases, there are similar effects displayed in category judgment data. These and other data imply that at least some kinds of magnitude estimations may involve a judgment of the “difference” or “distance” between pairs of stimuli as a first step in the production of the response required by the judgment situation.     

Isolating the effects of symbolic distance,and semantic congruity in comparative judgments: An additive-factors analysis

The time needed to compare two symbols increases as the cognitive distance between them on the relevant dimension increases (symbolic distance effect). Furthermore, when subjects are told to choose either the larger or the smaller of two stimuli, the response time is shorter if the instruction is congruent with the overall size of the stimuli (semantic congruity effect). Three experiments were conducted to determine the locus of these effects in terms of a sequence of processing stages. The developmental aspects of these effects were also evaluated, as the subjects were from kindergarten, first grade, third grade, fifth grade, and college. By varying the visual quality of the stimulus in each experiment, it was determined that the distance effect resides in a comparison stage, whereas the congruity effect is an encoding phenomenon. Both distance and congruity effects were present at all grade levels, but they decreased in magnitude as grade increased. The results were interpreted relative to recent models of comparative judgments.     

Perceptual encoding in comparative judgments of race

Ss made comparative judgments along the black-white racial dimension using opposite response sets (“Which is blacker?” or “Which is whiter?”). Three classes of pictures were used: B (black),W (white), and M (racially mixed). I or the BM judgments. “Which is whiter?” took significantly longer. The MW and BW judgments showed no difference between response instructions. Analysis of the stimuli showed that skin tone was not the primary perceptual attribute used in racial encoding. The observation of a funnel effect in the judgment latencies is shown to be consistent with other research demonstrating the effect of response set in comparative judgments Further. the results support sociological observations about the cultural use of the linguistic labels “black” and “white”     

Direct and indirect perception of size

Three experiments, using a reaction time paradigm, examine the direct (stimulus bound) and indirect (mediational inference) approaches to size perception. Subjects determine which of two stimuli is the larger when the two can be at different egocentric distances. The effects of two variables on reaction times are examined—distal ratio, the ratio of physical sizes of the stimuli, and proximal ratio, the ratio of the angular projections of the stimuli on the retina. In Experiment 1, both ratios are found to affect reaction times, with the proximal ratios yielding the larger effect, more in line with the predictions of the indirect approach. But the results of Experiments 2 and 3 indicate that distance is taken into greater account, the more similar the distal sizes of the stimuli. In one stimulus condition, distance appears not to affect reaction times. It is suggested that direct size perception occurs for large stimulus differences, indirect size perception for smaller differences. The identical results of the two experiments, one with and one without texture, point to some variable other than texture occlusion or interception as the stimulus for direct size perception. Some aspect of distance from the eye-level plane is suggested as an alternative.     

“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.     

Oculomotor adjustments and size-distance perception

The relationship between perceived size and distance and oculomotor adjustments were assessed in two experiments. In both experiments, Ss were required to make scalar linear size, angular size, and distance judgments of stimuli subtending a constant retinal image size at different levels of convergence. The results of the first experiment indicate that the perceived linear size, angular size, and distance of the stimulus decreased with increased convergence, the decrease in perceived linear size being greater than that of perceived angular size. While again showing a decrease in perceived linear and angular size, the results of the second experiment also show that there was a smaller decrease in perceived distance with increased convergence when Ss continued to view the stimulus as convergence was changed than when they did not view the stimulus as convergence was changed. The implications these results have for size and distance perception are discussed.     

Size-distance paradox with accommodative micropsia

Two experiments tested the hypothesis that the paradoxical relative distance judgment associated with the size-distance paradox is due to the visual system’s assuming equal linear size and perceiving a smaller angular size for the closer stimulus equal in visual angle. In Experiment I, two different sized coins were presented successively, and 16 Ss were asked to give ordinal judgments of apparent distance and apparent size. When the two coins depicted the same figures, the closer stimulus was judged to be farther and smaller, more frequently, than when two coins depicted different figures. In Experiment II, 48 Ss were asked to give ratio judgments of apparent distance, apparent linear size, and apparent angular size for two stimuli which were presented successively. When the stimuli were of equal shape, the mean ratios of the far stimulus to the near stimulus were smaller for the apparent distance but larger for the apparent linear size and angular size than when the stimuli were of different shape. The obtained distance judgments were consistent with the hypothesis but the obtained judgments of linear size and angular size were not.     

The role of instructions and familiar size in absolute judgments of size and distance.

The effects of familiar size and instructions (apparent, objective) on direct reports of size and distance were evaluated. Subjects estimated the size and distance of two different-sized playing cards or two unfamiliar stimuli under either apparent or objective instructions. The stimuli were presented successively at a distance of 5.48 m under reduced-cue conditions. The form of the instructions selectively influenced the effect of familiar size on absolute judgments of size and distance, with apparent instructions minimizing, and objective instructions promoting, familiar-size effects. The ratio of the distance judgments of the first to the second presented stimuli approximated the relative retinal sizes of the two objects under both apparent and objective instructions, while the ratio of size judgments tended to be either influenced by or independent of the object's relative retinal sizes under apparent and objective instructions, respectively. These results are consistent with Gogel's theory of off-size perception and, in particular, with the claim that, in comparison with apparent instructions, objective instructions are more likely to direct observers to base their judgments on cognitive, as opposed to perceptual, sources of spatial information.     

反应选项对时序知觉重复启动效应的影响

先前研究采用两项反应任务发现了时序知觉重复启动效应, 这可能是反应选项导致的虚假效应, 本研究采用三项反应任务对此进行了检验。实验1运用三项判断任务以消除缺乏中间选项所致的反应偏向, 结果发现重复启动显著影响“哪个图形先出现”和“两个图形同时出现”的时序判断; 实验2在实验1的基础上对“同时出现”反应选项进行两种指导语操作, 实验结果不仅与实验1一致, 而且“有把握时判断为同时出现”和“有无把握都判断为同时出现”之间没有显著差异, 说明被试能够识别时序加以判断, 不支持反应偏向的前提条件。因此, 时序知觉重复启动效应不是反应选项产生的反应偏向引发的虚假效应, 重复启动对“系列性”和“同时性”时序知觉都存在显著影响。     

Size scaling in two-dimensional pictorial arrays

The study examined effects of instructional sets (objective, phenomenal, projective, and retinal) on the judged sizes of blocks placed at various “distances” in a pictorial array. Magnitude estimations of size were consistent with previous studies of size constancy in three-dimensional arrays. Chronometric analyses indicated that reaction time increased with distal size, but was not affected by perceived distance. The results suggested that size was scaled relative to a perceptual unit. Instructions affected the nature of the scale unit (proximal vs. distal), but not the scaling process itself.     

数量对时间知觉的影响-来自抽象数量和实际数量的证据

本研究采用抽象数量和实际数量叠加的方式呈现刺激,进一步探讨数量对时间知觉的影响。两个实验都运用时间的系列比较任务,以抽象数量和实际数量这两种数量的一致和不一致为条件,将阿拉伯数字和其字体大小叠加及阿拉伯数字和其呈现个数叠加的方式系列呈现在屏幕中央,要求被试比较判断刺激呈现的时间长短。结果显示被试均依靠实际数量的大小判断时间长短,而似乎忽略了抽象数量的存在。这一结果表明实际数量对时间知觉的影响要比抽象数量大,支持并扩展了数量理论。     

Nested models of relative judgment: Applications to a similarity averaging model

A theoretical analysis of the Eisler and Ekman (1959) model of similarity judgments for unidimensional continua is presented, based on a general model of relative judgment. This general model assumes that judgments are mediated by perceived relations of pairs of stimuli, that there exists a transformation of the judgmental response that is a function of the sensory ratio of the two stimuli, and that response bias operates in a multiplicative manner. Three structural conditions are presented, each imposing constraints on the structure of observed judgments. The structural conditions define threenested models of relative judgment, with the second a weakened version of the first, and the third a weakened version of the second. The special virtue of the general model is that it is applicable to a variety of judgmental tasks (e.g., ratio estimation, similarity, pair comparison), the key being derivation of theresponse transformation conforming to the structural conditions. The structural conditions thus constitute necessary conditions for several different judgmental models. The theory was first applied with success to ratio estimation judgments (Fagot, 1978), and this paper applies the general model to the Eisler and Ekman similarity “averaging” model. Empirical tests were carried out on published data for pitch, darkness, visual area, and heaviness judgments. Although the strong form of the model presented by Eisler and Ekman was rejected, weakened versions were generally supported by the data. These results were similar to those obtained for ratio estimation (Fagot, 1978), and are interpreted to be very promising for the general model of relative judgment.     

Metacognition in psychophysical judgment: An unfolding view of comparative judgments of mental workload

An experiment is reported in which it was found that when subjects were required to indicate which of two visual extents was more difficult to categorize as “long” or “short,” they executed these categorizations and then measured the distance of the representation of each stimulus from the long-short category boundary; the stimulus nearer the boundary was judged to be the more difficult. When they were requested to indicate which was easier to categorize, they selected the alternative that was farther. Coombs’s theory of data (1952, 1964) and his unfolding theory of preferential choice (1950, 1964) provided the conceptualization of metacognition in this psychophysical task context. Strong support for the probabilisitic version of unfolding theory was obtained from the observed selective effects of laterality on the levels of stochastic transitivity attained for various classes of triples and the reliably longer times for comparisons with bilateral pairs than with unilateral pairs. The semantic congruity effects obtained, together with the changes in the form of the relationship between probability and response time as a function of practice, can be best accounted for by an evidence accrual theory in which the distances from the active reference point are measured and compared with a criterion on each evidence accrual. No support is provided for the view that propositionally based semantic “ease”- “difficulty” codes serve as the basis for these metacognitive comparative judgments of ease and difficulty.     

Distance discrimination and observer strategy in judgments of relative size

Six paid Ss participated in an experiment designed to assess the effects of observer strategy and the detectability of a distance cue on judgments of relative size. Ss viewed stimulus pairs through a 21-in. tunnel at one end of an 8-ft table. The Standard stimulus, 94 in. from S, was individually paired with three larger and two smaller comparison stimuli 96 in. from S. A slit of light on the table 95 in. from S and 90 deg to his line of sight served as distance cue. Increases in distance detection improved accuracy of relative size judgments when the comparison stimulus was larger than the Standard stimulus, but decreased accuracy when the comparison stimulus was smaller. Magnitude of this effect varied directly with Ss’ post-experimental reports of judgmental strategy. These findings confirm the importance of distance discrimination in judgments of actual size and the necessity to control perceiver characteristics in the study of size-distance relationships.     

Measuring the visual angle of the mind's eye

People in these experiments claimed to be able to imagine moving only a given distance toward some imaged object before it seemed to “overflow,” not remaining all visible at once in their mental images. In addition, the larger the imaged object, the further away it seemed at the point of overflow. Although the angle subtended by the imaged objects at the point of overflow did not vary systematically with the size of the object, it did vary with different stimuli and instructions. These disparities in the size of the angle estimated seemed partly due to differences in criterion of “overflow”: Images seem to fade off gradually toward the periphery and not to occur in a spatial medium with sharply defined edges. When subjects were given a relatively strict definition of “overflow,” similar estimates of the “visual angle of the mind's eye” were obtained with three distinct methods: (1) Asking subjects to estimate the apparent distance at which an imaged horizontal ruler began to overflow; (2) Measuring how much time subjects required to scan across each degree of an imaged line, and then inferring the maximal angle from the time required to scan an image of a longest nonoverflowing line; and, (3) Simply asking subjects to hold up their hands to indicate the subjective size of an image of the longest possible nonoverflowing line. Finally, the maximal subjective size of images seemed related to the scope of “focal” vision, and images tended to be constructed spontaneously at about the maximal size.     

Identification and categorization in visual search

Seven experiments were addressed to the general question of whether the identification of letters and numbers is a more rapid process than the categorization of such stimuli. Subjects were required to make a single response if a target stimulus specified by name (e.g., “A,” “2”) or designated by category class alone (e.g., “letter,” “number”) was presented in a trial. The principal findings were: (1) identification reaction times (RTs) were faster than categorization RTs: (2) RTs for targets shown without a context were faster than RTs for targets shown in the context of other stimuli; (3) identification RTs for targets shown in the context of stimuli from a different conceptual-taxonomic category were faster than RTs for targets shown in the context of stimuli from the same category only when target-context stimulus discriminability differencet were optimized. The results were interpreted in terms of a two-stage processing model in which context face,ors affect the duration of an initial encoding-scanning stage and search instruction (effective memory size) factors affect the duration of the memory comparison stage.     

Reaction times and error rates for “same”-“different” judgments of multidimensional stimull

Each S indicated whether two successively presented rows of letters were “same” or “different.” Reaction times of the “different” response seemed to indicate that S examined the stimulus letters in a serial, self-terminating manner. However, the reaction times of the “same” response were not consistent with this model. Consequently, it was proposed that S employs simultaneously two distinct processes for comparing stimuli. One process would generate the “different” responses; the other process would generate the “same” responses. Most false “same” responses occurred when the two rows of letters differed minimally. Thus, the false “same” responses appear to result from a failure to detect the difference between the two stimuli. However, when S made a false “same” response, he was aware that he had done so. Therefore, it was suggested that only one of the two comparison processes failed to detect the stimulus difference.     

The role of instructions and familiar size in absolute judgments of size and distance

The effects of familiar size and instructions (apparent, objective) on direct reports of size and distance were evaluated. Subjects estimated the size and distance of two different-sized playing cards or two unfamiliar stimuli under either apparent or objective instructions. The stimuli were presented successively at a distance of 5.48 m under reduced-cue conditions. The form of the instructions selectively influenced the effect of familiar size on absolute judgments of size and distance, with apparent instructions minimizing, and objective instructions promoting, familiar-size effects. The ratio of the distance judgments of the first to the second presented stimuli approximated the relative retinal sizes of the two objects under both apparent and objective instructions, while the ratio of size judgments tended to be either influenced by or independent of the object’s relative retinal sizes under apparent and objective instructions, respectively. These results are consistent with Gogel’s theory of off-size perception and, in particular, with the claim that, in comparison with apparent instructions, objective instructions are more likely to direct observers to base their judgments on cognitive, as opposed to perceptual, sources of spatial information.     

Selective attention in the speeded classification and comparison of multidimensional stimuli

Selective attention was studied when subjects were required to make either speeded classifications of single stimuli or comparisons of pairs of multidimensional stimuli. Experiment 1 established that subjects were able to attend selectively to form when the irrelevant dimension of size or shading varied in a speeded-classification (card-sorting) task. Experiment 2 confirmed this finding in a discrete-trials task. However, subjects werenot able to filter out irrelevant dimensional disparity in a comparably designed simultaneous-comparison (i.e., “same”-“different”) task. Mean “same” reaction time increased monotonically with increases in disparity between the two stimuli on the irrelevant dimension. Experiment 3 also revealed a monotonie increase in “same” RT as a function of irrelevant disparity in a successive-comparison task. These results were discussed in terms of a normalization model proposed by Dixon and Just (1978) in which it is assumed that a subject equates the two stimuli on the irrelevant dimension before deciding that they are the same along the relevant dimension. It was concluded that: (1) although subjects can efficiently filter out irrelevant disparity in a speeded-classification task, interference due to irrelevant disparity is obtained in the comparison tasks, (2) a common process such as normalization does not necessarily underlie performance in the speeded-classification and comparison tasks, (3) the ability to attend selectively to a stimulus dimension may be task determined as well as stimulus determined, and (4) contrary to the Dixon and Just proposal, normalization of irrelevant disparity occurs in a comparison task, even when the relevant dimension is represented as a separate encoding feature.     

Anchor effects using numerical estimates of simple dot patterns

Shifts due to anchor stimuli using absolute judgments have been ascribed to “semantic” and “scale modulus” changes. To test this explanation, random dot patterns of 10, 12, 14, 16 and 18 dots were exposed for 0.30 sec with anchors of 4, 13 or 32 dots preceding each of the stimuli. In the control only the series of stimuli were judged. It was found that numerical estimates of the number of dots increased with small anchor, decreased with large anchor, and were not significantly changed with anchor in the vicinity of AL. These results exactly parallel those found using methods of absolute and comparative ratings and hence cannot be ascribed to semantic shifts especially in view of the fact that independent groups of Ss served in the four anchor and control conditions. Since the anchor effects were significant but not so large that they can be ascribed to change of scale modulus this theory must also be rejected. The AL model seems to offer the simplest and most unitary explanation of these as well as many other results obtained with different types of stimuli and different methods of judging.