Intensity resolution and subjective magnitude in psychophysical scaling

Several successful theories of psychophysical judgment imply that exponents of power functions in scaling tasks should covary with measures of intensity resolution such asd’ in the same tasks, whereas the prevailing metatheory of ideal psychophysical scaling asserts the independence of the two. In a direct test of this relationship, three prominent psychophysical scaling paradigms were studied: category judgment without an identification function, absolute magnitude estimation, and cross-modality matching with light intensity as the response continuum. Separate groups of subjects for each scaling paradigm made repeated judgments of the loudnesses of the pure tones that constituted each of two stimulus ensembles. The narrow- and wide-range ensembles shared six identical stimulus intensities in the middle of each set. Intensity resolution, as measured byd’-like distances, of these physically identical stimuli was significantly worse for the wide-range set for all three methods. Exponents of power functions fitted to geometric mean responses, and in magnitude estimation and cross-modality matching the geometric mean responses themselves, were also significantly smaller in the wide-range condition. The variation of power function exponents, and of psychophysical scale values, for stimulus intensities that were identical in the two stimulus sets with the intensities of other members of the ensembles is inconsistent with the metatheory on which modern psychophysical scaling practice is based, although it is consistent with other useful approaches to measurement of psychological magnitudes.     

On the “absoluteness” of category and magnitude scales of pain

The concept of “absolute scaling” (Zwislocki & Goodman, 1980) implies that direct judgments of sensory magnitude not only reflect the relative positions of the stimuli being judged, but also permit us to assess level differences in sensation. In order to explore this notion for different scaling methods, in the present investigation we compared magnitude estimation with category partitioning, a verbally anchored categorization procedure, in scaling painful pressure stimuli covering different intensity ranges. The results indicate that when the same stimulus range was presented after 1 week, both methods appeared to be highly reliable, with category partitioning faring somewhat better than magnitude estimation. When the stimulus range was unobtrusively changed between sessions, both methods reflected the within-subjects shift in absolute level. When two different sets of subjects judged the slightly different stimulus ranges, both methods resulted in scale values consistent with absolute scaling, though only category partitioning was sensitive enough to differentiate the two stimulus ranges. The results are discussed in the context of different possibilities of anchoring direct scaling methods in order to obtain “absolute” level information.     

On the "absoluteness" of category and magnitude scales of pain

The concept of "absolute scaling" (Zwislocki & Goodman, 1980) implies that direct judgments of sensory magnitude not only reflect the relative positions of the stimuli being judged, but also permit us to assess level differences in sensation. In order to explore this notion for different scaling methods, in the present investigation we compared magnitude estimation with category partitioning, a verbally anchored categorization procedure, in scaling painful pressure stimuli covering different intensity ranges. The results indicate that when the same stimulus range was presented after 1 week, both methods appeared to be highly reliable, with category partitioning faring somewhat better than magnitude estimation. When the stimulus range was unobtrusively changed between sessions, both methods reflected the within-subjects shift in absolute level. When two different sets of subjects judged the slightly different stimulus ranges, both methods resulted in scale values consistent with absolute scaling, though only category partitioning was sensitive enough to differentiate the two stimulus ranges. The results are discussed in the context of different possibilities of anchoring direct scaling methods in order to obtain "absolute" level information.     

Remembrance of sounds past: memory and psychophysical scaling

What is the role of long-term memories of previous stimulus-response mappings, and of previous sensory and perceptual experiences generally, in psychophysical scaling judgments? I conducted four experiments in an attempt to provide some preliminary answers to this question. In each experiment, subjects made judgments of the loudness of sounds on 3 successive days. Stimulus intensities were drawn randomly from the same set on Days 1 and 3 but from a different set, either all 12 dB higher or all 12 dB lower, on Day 2. Four different types of psychophysical scaling judgments were studied: category judgment without an experimenter-induced identification function, ratio magnitude estimation with a variable standard, absolute magnitude estimation, and cross-modality matching. The first two methods required completely relative judgment, the last two completely absolute judgment. Data from all methods reveal profound effects of stimulus-response mappings experienced on previous days (long-term memory) and immediately previous stimuli and responses (short-term memory) on responses to current stimuli. Responses were typically a compromise between absolute and relative judgment. Individual differences were dramatic.     

Dimensional and metric structures in multidimensional stimuli

The present experiments investigated two characteristics of subjects’ multidimensional representations: their dimensional organization and metric structure, for both analyzable and integral stimuli. In Experiment 1, subjects judged the dissimilarity between all pairs of stimuli differing in brightness and size (analyzable stimuli), while in Experiment 2, subjects made dissimilarity judgments for stimuli varying in width height, and area shape (integral stimuli). For the brightness size stimuli, the findings that (a) brightness judgments were independent of size (and vice versa) and (b) the best fitting scaling solution was one that depicted an orthogonal structure are strong evidence that subjects perceived brightness size as a dimensionally organized structure. In contrast, for the rectangle stimuli, neither width height nor area shape contributed additively to overall dissimilarity. The results of the metric fitting were more equivocal. For all stimulus sets, the Euclidean metric yielded scaling solutions with lower stress values than the city block metric. When bidimensional ratings were regressed on unidimensional ratings, the city block metric yielded a slightly higher correlation coefficient than the Euclidean metric for brightness size stimuli. The two rules of combination were equivalent for the width-height stimuli, but the Euclidean metric provided a better approximation for the area shape stimuli. The results were discussed in terms of how subjects integrate physical dimensions for the case of integral stimuli and the superiority of dimensional vs. metric structure as an indicator of stimulus analyzability.     

Stimulus context and absolute magnitude estimation: a study of individual differences

The effect of stimulus context on absolute-magnitude-estimation (AME) judgments was examined by determining whether the loudness judgment of a tone is influenced by the intensities of other tones presented within the session. A group of 18 subjects was tested in separate sessions in which they judged stimuli within either a low (10-60 dB SL) or a high (40-90 dB SL) range of intensities. Examination of the results of individual subjects revealed that judgments of stimuli common to the two ranges were, in most subjects, unaffected or only slightly affected by the position of the range. The judgments of 2 subjects who failed to follow the instructions, however, showed very large context effects due to changing the stimulus range. The results of a second experiment, in which 22 subjects judged the loudness of tones within either a narrow (35-65 dB SL) or a wide (20-80 dB SL) range, revealed that, in all but 1 subject, the width of the range had no systematic effect on the loudness judgments of stimuli common to both ranges. This was also true 1 month later when 16 of the subjects returned to the laboratory to judge the loudness of tones within an even wider range of 10-90 dB SL. It was concluded that AME judgments are relatively insensitive to the potential biasing influences of stimulus context.     

Categorical perception of tonal intervais: Musicians can’t tellsharp fromflat

Six musicians with relative pitch judged 13 tonal intervals in a magnitude estimation task. Stimuli were spaced in .2-semitone increments over a range of three standard musical categories (fourth, tritone, fifth,). The judged magnitude of the intervals did not increase regularly with stimulus magnitude. Rather, the psychophysical functions showed three discrete steps cor-responding to the musically defined intervals. Although all six subjects had identified in-tune intervals with >95% accuracy, all were very poor at differentiating within a musical category— they could not reliably tell “sharp” from “flat.” After the experiment, they judged 63% of the stimuli to be “in tune,” but in fact only 23% were musically accurate. In a subsequent labeling task, subjects produced identification functions with sharply defined boundaries between each of the three musical categories. Our results parallel those associated with the identification and scaling of speech sounds, and we interpret them as evidence for categorical perception of music.     

Mixed-method mixed-modality psychophysical scaling

Four experiments are reported in which the direct psychophysical scaling methods of magnitude estimation, category judgment, and cross-modality matching were mixed in the same series of trials, both with a single stimulus modality and in a mixed-modality situation. The mixed-method scaling situation gave results consistent with those obtained when methods are used alone, and it has several advantages. Interactions between the methods were consistent with the idea that judgments made under all three are mediated by a primitive process of categorization that is influenced by heuristics used to achieve a single category identity for each stimulus.     

Unmasking the magnitude estimation response

The fuzzy judgement model of Ward (1979) predicts an inverse relation between the amount of stimulus information available to subjects and the magnitude of sequential dependencies on previous stimuli and responses in psychophysical scaling tasks. Ward confirmed this prediction for magnitude estimations of interdot distance for previous responses but not for previous stimuli, although the inverse relation has been repeatedly reported for both the previous stimuli and responses in absolute identification (e.g., Mori, 1989). This paper further explores this seemingly puzzling contradiction. A magnitude estimation of loudness experiment was conducted in which the amount of stimulus information available to subjects was manipulated by a modified version of informational masking (Watson, 1987). An absolute-identification-with-feedback experiment was also conducted to check the effectiveness of the informational masking in reducing the amount of stimulus information. The results of the magnitude estimation experiment show a striking similarity with those of Ward and generalize the failure of sequential dependencies on previous stimuli to vary inversely with stimulus information. An additional assumption that judgement strategies are altered under low-information conditions is necessary to explain this result.     

Mental measurement of line length: the role of the standard

Reaction times were examined for magnitude estimates of line length. In the first two experiments, reaction times increased linearly with judged length. This result is consistent with the hypothesis the judgments are made by laying off a mental image of the standard along the line to be judged. The slope of the function relating judged length to reaction time was not affected by the length of the standard line, suggesting that the rate at which the image of the standard is laid off is not a function of the length of the standard. Reaction time also increased linearly with judged length when subjects judged line length when the standard of 1 in. was suggested but not provided as well as when no standard was suggested. The hypothesized laying-off process was compared to other cognitive manipulations, such as mental rotation and size scaling. Equivalence of judgments based on the representation of the standard in perceptual memory and in imagination is discussed.     

The role of perception in the mislocalization of the final position of a moving target

The judged final position of a moving stimulus has been suggested to be shifted in the direction of motion because of mental extrapolation (representational momentum). However, a perceptual explanation is possible: The eyes overshoot the final position of the target, and because of a foveal bias, the judged position is shifted in the direction of motion. To test this hypothesis, the authors replicated previous studies, but instead of having participants indicate where the target vanished, the authors probed participants' perceptual focus by presenting probe stimuli close to the vanishing point. Identification of probes in the direction of target motion was more accurate immediately after target offset than it was with a delay. Another experiment demonstrated that judgments of the final position of a moving target are affected by whether the eyes maintain fixation or follow the target. The results are more consistent with a perceptual explanation than with a memory account.     

Effects of similarity and repetition on memory: registration without learning?

We investigated judgments of the frequency of test items (Y) that were highly similar to studied items (X) to test a prediction made by several memory models: that the judged frequency of Y should be proportional to the judged frequency of X. Whether stimuli were pictures or words, judged frequency of Y was bimodally distributed with 1 mode at zero, suggesting that frequency judgments involve a 2-stage process in which a zero judgment is made if there is a mismatch between retrieved information and the test item. Nonzero judgements, taken by themselves, were consistent with the prediction of proportionality. In 2 experiments, the percentage of zero judgments made to Y increased with repetition of X, but in 2 others the percentage did not change beyond frequency = 1. The percentage of "new" judgments in recognition memory followed this same pattern. Because the judged frequency of X increased even as X-Y discrimination showed no improvement, we characterize the result as "registration without learning."     

Dimensional dominance and stimulus discriminability.

The relationship between the discriminability of scaling stimuli and assessed dimensional dominance was investigated in three studies. Sixty kindergarten children were assessed using a psychophysical scaling method to determine JND values for the size, brightness, and orientation dimensions. Thirty of the same subjects were then assessed for dimensional dominance using stimuli of two levels of known discriminability, based on the obtained JND values. In a third experiment, the remaining 30 subjects were assessed for dimensional dominance using stimuli that systematically emphasized the values of one dimension relative to the other two dimensions, again based on obtained JND values.The results indicated that (1) kindergarten children were able to perform consistently during psychophysical scaling, and there was little variability between children in their judgments of stimuli, (2) the overall level of discriminability affects dimensional dominance scaling behavior, with subjects more likely to exhibit dominance for one dimension when all the values of scaling stimuli are high in discriminability, and (3) some support for the hypothesis that dimensional dominance scaling behavior can be manipulated by manipulating the relative discriminability of scaling stimuli was found, though the trend was not clear.The relative discriminability of scaling stimuli appears to have some effects on dimensional dominance scaling behavior of young children. However, some pre-experimental bias to attend to a particular dimension seems to remain even when the values of all dimensions present are of equal and known discriminability. Dimensional dominance is a function of an interaction between discriminability of scaling stimuli and the experiential bias or perceptual set of the subject.     

Revelation effects in remembering,forecasting, and perspective taking

The revelation effect is a robust phenomenon in episodic memory whereby stimuli that immediately follow a simple cognitive task are more likely to garner positive responses on a variety of memory tests, including autobiographical memory judgments. Six experiments investigated the revelation effect for judgments of past and future events as well as judgments made from others’ perspectives. The purpose of this work was to determine whether these subjectively distinct judgments are subject to the same decision-making biases, as might be expected if they are governed by similar processes (e.g., Schacter, Addis, & Buckner 2007). College-aged participants were asked to rate a variety of life events according to whether the events had occurred during their childhoods or would occur during the next 10 years. Events that followed an anagram task were judged as more likely to have happened in the past and more likely to occur in the future. We also showed a revelation effect when participants were asked to adopt the perspective of others when making judgments about past and future events. When the task was reworded to be non-episodic (participants judged how common the events were during childhood and adulthood), no revelation effect was found for either past or future time frames, which suggests common boundary conditions for both types of judgments. The results are consistent with studies showing strong parallels between remembering and other forms of self-projection but not with semantic memory judgments.     

A COGNITIVE THEORY OF PSYCHOPHYSICS. I

The fundamental premise of this paper is that subjects deal with stimulus information when performing psychophysical judgments. The coding strategy employed to manipulate this information depends upon the particular experimental procedure, which leads to unique psychophysical functions. Different methods impose different memory constraints upon the subject, thus producing a variety of sensitivity measures for the same stimulus attribute.     

Perceiving the centroid of configurations on a rolling wheel

Undergraduates observed configurations of point-lights undergoing wheel-generated motions and judged how wheel-like the movement of each stimulus appeared on a 7-point scale. Viewer judgments were predicted by a metric defining the variable parameters for the motion path of each configuration’s geometric center—the centroid. The effects on judgments of eye movement and the stimulus characteristics of rotation, translation, and configuration were explored in six experiments. First, a strain operation on the dynamic stimuli did not affect the ability of the metric to predict perceptual judgments. Second, the predictive strength of the metric did not interact with the type of eye movements used in viewing the stimuli, though judged wheel-likeness was greater under pursuit vision than under static fixation. Third, variations in the extent of translation yielded little, if any, effect on observers’ judgments, nor did translation in a circular path. Finally, for stimuli having two lights extremely close together in the configuration, the metric’s predictive value was slightly lessened but only at the limits of visual acuity. Thus, within a wide range of presentation conditions, and for a wide variety of configurations, a metric that defined the variable parameters for the motion path of the centroid was an accurate predictor of observers’ judgments of goodness of perceived rotary motion.     

Effect of stimulus pulse duration and interstimulus interval on cross-modal matching of auditory and lingual vibrotactile stimuli

Cross-modal matching functions for eight intensity levels of a 1000-Hz auditory stimulus and a 250-Hz lingual vibrotactile stimulus were obtained for two groups of subjects. Group 1 adjusted the vibrotactile stimulus to match the auditory stimulus, and Group 2 adjusted the auditory stimulus to match the vibrotactile stimulus. Stimulus-pulse durations and interstimulus intervals were varied over six experimental conditions for both groups. The variations in stimulus-pulse durations and interstimulus intervals had no appreciable effect on mean matching-function exponents for the two groups. A possible regression effect consistent with data from other psychophysical scaling studies was noted for matching functions of the two stimuli.     

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.     

Both perceptual and conceptual factors influence taste-odor and taste-taste interactions

Observers are often asked to make intensity judgments for a sensory attribute of a stimulus that is embedded in a background of “irrelevant” stimulusdimensions. Under some circumstances, these background dimensions of the stimulus can influence intensity judgments for the target attribute. For example, judgments of sweetness can be influenced by the other taste or-odor qualities of a solution (Frank & Byram, 1988; Kamen et al., 1961). Experiments 1 and 2 assessed the influence of stimulus context, instructional set, and reference stimuli on cross-quality interactions in mixtures of chemosensory stimuli. Experiment 1 demonstrated that odor-induced changes in sweetness judgments were dramatically influenced when subjects rated multiple attributes of the stimulus as compared with when they judged sweetness alone. Several odorants enhanced sweetness when sweetness alone was judged, while sweetness was suppressed for these same stimuli when total-intensity ratings were broken down into ratings for the sweetness, saltiness, sourness, bitterness, and fruitiness of each solution. Experiment 2 demonstrated a similar pattern of results when bitterness was the target taste. In addition, Experiment 2 showed that the instructional effects applied to both taste-odorand taste-taste mixtures. It was concluded that the taste enhancement and suppression observed for taste-odor and taste-taste mixtures are influenced by (1) instructional sets which influence subjects’ concepts of attribute categories, and (2) the perceptual similarities among the quality dimensions of the stimulus.     

The influence of category membership of stimuli on sequential effects in magnitude judgment

The present study addresses the problem of whether range effects and sequential dependencies are affected by stimulus category membership in the same way. Two sets of squares differing in color were presented to subjects. The subjects were asked to judge them according to size, under two instructions. The separation instruction required them to judge each square solely in relation to its own category. The integration instruction required them to ignore category membership. The results indicated that, under the separation instruction, the range effects, as well as the sequence effects, confined themselves to stimuli of the same category. Under the integration instruction, however, the squares were judged in relation to the range of all the stimuli, and sequential effects were independent of the stimulus category. This parallel trend in the category-specific effects of range and preceding stimuli was found for judgments, as well as for reaction times. The findings are discussed with regard to models of sequential effects.