Biasing power law exponents by magnitude estimation instructions

This study investigates the influence of attention loading on the established intersensory effects of passive bodily rotation on choice reaction time (RT) to visual motion. Subjects sat at the center of rotation in an enclosed rotating chamber and observed an oscilloscope on which were, in the center, a tracking display and, 10° left of center, a RT line. Three tracking tasks and a no-tracking control condition were presented to all subjects in combination with the RT task, which occurred with and without concurrent cab rotations. Choice RT to. line motions was inhibited (p < .001) both when there was simultaneous vestibular stimulation and when there was a tracking task; response latencies lengthened progressively with increased similarity between the RT and tracking tasks. However, the attention conditions did not affect the intersensory effect; the significance of this for the nature of the sensory interaction is discussed.     

Perceived numerosity: A comparison of magnitude production,magnitude estimation,and discrimination judgments

In previous studies, modalities with a higher Weber fraction have tended to have a lower power-function exponent. Within a modality, however, the Weber fraction and power-function exponent for individual subjects were unrelated, and the present study largely confirms this finding for the numerosity dimension. More important than discriminability in the judgment of numerosity were cognitive factors. A single feedback trial considerably reduced intersubject variability on the magnitude-estimation exponent, although it failed to eliminate individual differences completely (precue and postcue exponents correlated signigicantly, r=+.50). Intrasubject variability, by contrast, seemingly did not involve the underlying exponent. As in previous studies, numerosity generally was underestimated and the power-function exponent was 1.08 for magnitude production and .80 for precue magnitude estimation. Contrary to previous results, however, males and females did not differ in exponent, perhaps because the present procedure allowed self-selection of individuals more interested in numerosity tasks.     

Effect of distance instructions on size judgments

The proposition that in a reduced-cue setting subjects could use cognitive information about an object's distance to make accurate judgments of its size was tested. An improved paradigm was used to determine the effects of distance instructions per se. This paradigm also allowed independent tests of the effectiveness of cue reduction. The data indicated that cue reduction was successful and that the specific distance tendency governed size judgments when there were no distance instructions. When distance instructions were given, they produced size judgments in precisely the ratio predicted by the size-distance invariance hypothesis. However, there was a large constant error, which reflects a tendency of college students to overestimate the amount of distance signified by a verbal instruction. Hence, cognitive information in the form of verbal distance instructions has precise effects on size judgments, but the latter are not veridical, even in the absence of anchor effects from the specific distance tendency and residual perceptual cues.     

Effects of aging on the magnitude and accuracy of quality-of-encoding judgments

Age invariance in monitoring associative learning has been the norm in numerous investigations concerning how accurately people predict future recall, predictions that are based partly on people's beliefs about forgetting. In this study, we obtained a measure of monitoring that is minimally influenced by beliefs about forgetting. Participants made quality-of-encoding (QUE) judgments by rating how well each item had been encoded. In 2 experiments, older and younger adults studied 60 paired-associate items; immediately after studying each one, they made a QUE judgment. Each item was presented at a 4-s or 8-s presentation rate. QUEs from both age groups were sensitive to the production of different strategies, presentation rate, and item characteristics. Reliable age differences in the correlation of QUEs and subsequent recall were found for related items but not for unrelated items. The outcomes indicate similar processes for generating QUE judgments by older and younger adults, but they also suggest the possibility of an age-related deficit in the accuracy of monitoring encoding in some experimental conditions.     

Effects of exposure to psychophysical scaling on lingual vibrotactile magnitude estimation and magnitude production

The purpose of the present study was to determine if the results obtained by the scaling methods of magnitude estimation and magnitude production could be influenced by providing subjects with prior exposure to psychophysical scaling in the form of magnitude estimation or magnitude production. Group 1 (n = 10, Mage = 21.1 yr.) performed lingual vibrotactile-magnitude estimation followed by lingual vibrotactile magnitude production. Group 2 (n = 10, Mage = 19.7 yr.) performed lingual vibrotactile-magnitude production (using the magnitude-estimation responses provided by Group 1), followed by lingual vibrotactile-magnitude estimation. For the magnitude estimations there was no over-all statistically significant difference between the two groups, but there was for the magnitude-production values. Magnitude-estimation scaling was apparently not influenced by prior exposure to magnitude production, while magnitude-production scaling was influenced by prior exposure to magnitude estimation. The results are discussed in terms of how subjective scaling behavior in psychophysical experimentation may be influenced by the interaction between an absolute internal scaling mechanism and parameters set by the experimenter, such as scaling method and range of stimulus intensity.     

Scaling clinical judgments of symptom pathology by means of the psychophysiological method of magnitude estimation

Summing scores across heterogeneous symptom items without consideration of their differing psychopathological significance has been criticized as producing an inadequate picture of an individual's clinical status. The purpose of this study was to derive symptom item weights representing clinically judged seriousness of each symptom through the application of Stevens's psychophysical method of magnitude estimation. A nationwide sample of 129 clinicians rated the pathological significance of 221 symptom items in a design such that every rater rated 121 items, 21 of which were rated by all raters and 100 of which were rated only by the A or B subgroup to which each rater was randomly assigned. Each item was rated as to the seriousness of the pathology it would represent if manifested by either a boy child, girl child, boy adolescent, or girl adolescent, with one-fourth of the raters assigned to each condition. The results of 211 two-way analyses of variance revealed that age and age and sex in interaction, but not sex alone, significantly influenced the clinical ratings. The resulting magnitude estimation ratings of symptom pathology ranged from 1.0 to 9.9. They were demonstrated to have satisfactory reliability and convergent validity and to have the psychophysical characteristics of a prothetic continuum.A preliminary version of this paper was presented at the 85th Annual Convention of the American Psychological Association, San Francisco, August 1977. The research was supported by HEW grant MH24886. The authors wish to express appreciation to Walter W. Wengel for his work in developing the median quotient ratings used in the study, to Terrance Auger for making available unpublished raw data, and to Merton S. Krause for helpful suggestions regarding the interpretation of results.     

Conditional probability judgments: Effects of imagining vs experiencing the conditioning event

Applications of Bayesian conditionalization often involve two temporal aspects: a probability judgment is based on knowledge at a point in time and is revised over time in light of added information. Let t, t′, and t″ designate three chronological points in time. E designates a target event which occurs or not at t″, and C designates a conditioning event which occurs or not at t′. Suppose that an individual judges P(EC) at t. If C occurs, Bayesian conditionalization requires that a judgment of P(E) at t′ is equal to the earlier judgment of P(EC). However, inconsistencies may result because a judgment of P(EC) at t is based on imagining C, while a judgment of P(E) at t′ is based on experiencing C. This study examines two sources of such inconsistencies. First, C normally is an abstraction of what might happen between t and t′. What actually happens may differ, such that an individual observes extraconditional information which affects a judgment of P(E) at t′. Second, experiencing C may change an individual's affective state, leading to greater optimism or pessimism about the occurrence of E. We report an experiment which documents both effects.     

Cognitive reference points in judgments of symbolic magnitude

Research on speeded symbolic magnitude comparisons indicates that decisions are made more quickly when the magnitudes of the stimuli being compared are relatively close to an explicit or implicit reference point. Alternative explanations of this phenomenon are tested by seeking similar effects in nonspeeded rating tasks. In accord with the predictions of discriminability models, rated magnitude differences between stimuli in the vicinity of a reference point are expanded relative to differences between stimuli far from it. The inferred locations of cities along a west-east axis varies systematically depending on which coast, Pacific or Atlantic, is specified as the reference point. Scales derived from the rating data are correlated with the pattern of reaction times obtained in a comparable speeded comparison task. In addition, the distance between the cities nearest the locale of our subjects is subjectively stretched. Reference point effects are also observed when the form of the comparative specifies an implicit reference point at either end of a continuum of subjective size; however, these effects are very small and do not clearly support a discriminability interpretation. Stronger evidence for discriminability effects is obtained when an explicit reference point is established at an arbitrary size value. An implicit scaling model, related to range-frequency theory, is proposed to account for the influence of reference points on relative discriminability of stimulus magnitudes. The implicit scaling model is used to develop an account of how symbolic magnitudes may be learned and of how habitual reference points can produce asymmetries in distance judgments.     

Aging and judgments of duration: Effects of task complexity and method of estimation

The effects of aging on judgments of short temporal durations were explored using the prospective paradigm and the methods of verbal estimation and production. Younger and older adults performed a perceptual judgment task at five levels of complexity for periods of 30, 60, and 120 sec. Participants either continued to perform the task for a specified interval (production) or were stopped and then verbally estimated the interval. Older adults gave shorter verbal estimates and longer productions than did younger adults. The methods of verbal estimation and production yielded approximately equal duration judgment ratios once range effects were taken into account. Task complexity had little effect. The major conclusion is that duration judgment ratios decrease from younger to older adults when the intervals are filled with a mental task.     

Effect of reference number on magnitude estimation

The psychophysical function obtained by the method of magnitude estimation was influenced by the reference number (modulus) assigned to a “standard” line and the position of this standard in the range of comparison stimuli. Data from two experiments with judgments of apparent length of lines show how both variables systematically affect the slope of the power function. AllowingO to choose his own reference numbers, even though these numbers varied among as, tended to produce less variability in slope than ifE imposed fixed reference numbers forO to use.     

Odor magnitude: Coarse vs. fine grain

Despite a dismal reputation, olfaction’s resolving power actually appears to be keen, especially when the contaminating influence of noise in the stimulus is discounted from psychophysical performance. In a previous investigation, subjects were able to resolve a change of 4% in the concentration of butyl alcohol. In the present experiment, these same subjects resolved a change of 9% in the concentration of amyl butyrate. The data imply that resolving power varies among odorants. The growth of odor intensity assessed by magnitude estimations of easily discriminable (i.e., grossly different) concentrations also varies among odorants. These observations prompt the question: Does an odorant for which resolution is relatively difficult lead to slower growth of perceived intensity with concentration than an odorant for which resolution is easy? In a scaling experiment, amyl butyrate indeed led to slower growth of intensity than butyl alcohol. Nevertheless, amyl alcohol, which permitted poorer resolution than butyl alcohol, led to approximately the same rate of growth as butyl alcohol. Accordingly, growth of odor intensity with concentration may correlate only weakly with resolving power.     

Cross- vs. within-racial judgments of attractiveness

Subjects from two pairs of ethnic groups (Chinese and White in Experiment 1, Black and White in Experiment 2) judged the attractiveness of faces in yearbook pictures of persons that belonged to their own or to the other ethnic group. This was to see whether: (1) a given group would perceive more variation in the attractiveness of faces belonging to its own vs. the other ethnic group, as suggested by the cross-racial literature, for example, Malpass and Kravitz (1969), and (2) the two groups would use the same or different rules to define attractiveness. There were essentially no differences in perceived variation for cross- vs. within-racial judgments, but there were differences in the criteria used to define attractiveness. As expected, Black and White aesthetic criteria were more like one another than were Chinese and White criteria. Discussion centered around reconciling these findings with the recognition literature.     

The effects of angle-arm length on judgments of angle magnitude and orientation contrast

Acute angles frequently are overestimated, an effect that has been attributed to lateral inhibitory mechanisms. It can be derived from such theories that lengthening the arms of an angle should either reduce or not affect its judged subtense. However, in Experiments 1 and 2, it was found that angles with longer arms were judged larger. In Experiment 3, direct measures of anglearm orientation indicated that orientation contrast does not increase with angle-arm length, that it decreases with distance from the angle vertex, and that these effects are not averaged along the entire length of the arm. It follows that inhibitory mechanisms alone cannot explain why longer armed angles appear larger or why angle arms appear straight rather than bowed. It is suggested that a distinction is required between the orientation and the angular domains and that the latter judgments depend, at least partially, on the space or area within an angle. The fact that angles appear unbowed may reflect the fact that perceived orientation differences occur along an angle’s arm only when matches are made to small segments of the arm.     

Memory for numbers: Nominal vs. magnitude information

Across three paired associate learning experiments, the recall of four-digit number responses to word stimuli favored the most significant digit over the least significant (magnitude encoding rather than exhibiting typical bowed serial position functions (nominal encoding). Only with instructions emphasizing exact recall of each individual digit did recall functions revert to bowed curves. The results are interpreted as evidence for two kinds of number coding in semantic memory.     

Pervasiveness and magnitude of context effects: evidence for the relativity of absolute magnitude estimation

To test the assertion that absolute magnitude estimation serves to minimize context effects, two experiments were conducted in which area stimuli were judged under differing conditions. In Experiment 1, four groups of subjects made magnitude estimations of triangles ranging in area from 1.5 to 3,072 cm2. No standard or modulus was used, and instructions were similar to those used in absolute magnitude estimation experiments. Each group first judged a different subrange of the stimuli (1.5-24; 48-768; 6-96; or 192-3,072 cm2) before making judgments of the remaining stimuli. In Experiment 2, two groups of subjects made magnitude estimations of triangles ranging in area from 1.5 to 12,288 cm2, with each group first judging a different subrange of stimuli (1.5-24 cm2 or 768-12,288 cm2). The design and instructions were virtually identical to those used in absolute magnitude estimation experiments. Our results indicate that the wording of the instructions is not crucial and that judgments are influenced in two ways that are not predicted by proponents of absolute magnitude estimation. First, the power functions fit to the initially presented subranges (e.g., 1.5-24 cm2), which were judged without contextual effects produced by previously presented stimuli, were inconsistent with one another. Second, judgments of the remaining stimuli were influenced by the subrange of stimuli judged initially. The prevalence of context effects in both experiments, in spite of instructional differences, suggests that although one should avoid using a standard and modulus, there is little else to be gained by adopting the absolute magnitude estimation procedure.