Memory for psychophysical scaling judgments

In three experiments, we examined memory for responses and stimuli experienced in a single direct psychophysical scaling session in which subjects made absolute magnitude estimations of the loudnesses of pure tones. Recall of scaling responses was found to be accurate for the softest and loudest stimuli, but systematically greater than actual judgments for the intermediate stimulus amplitudes, yielding distorted psychophysical functions for the recall data which nonetheless had the same power function exponent as that for the judged stimuli. Also, memory for the range of stimulus amplitudes was fairly accurate, but subjects could not distinguish between judged and nonjudged amplitudes within that range. The results are consistent with the role of extreme stimuli as anchors for judgment, and indicate that memories for these stimuli and responses made to them can be expected to influence future scaling judgments. These results also are consistent with the uncertainty hypothesis of mnemophysics. The present research was supported by a grant from the Natural Sciences and Engineering Research Council of Canada to L.M.W. Thanks to the reviewers for insightful critiques.     

On the psychophysical law and estimation procedures in psychophysical scaling

A general formulation of the power law is presented which has two special features: (1) negative exponents are admissible; and (2) the log law is a special limiting case. Estimation procedures, which provide joint estimates of the exponent and the absolute threshold, are derived for the direct ratio scaling methods. A solution is provided for theaveraging problem for ratio production and bisection scaling, two methods generating observations on the physical scale, and Monte Carlo methods are used to evaluate the resulting estimators.     

Sensory scaling and the psychophysical law

Sensory scaling is analysed as a sensori-motor task for which two relations must be determined, the first, S = f(I), being the relation between I, the stimulus intensity, and S, a measure of the neural effect of the stimulus, and the second being the relation between the subject's response, R, and S. It is shown that for any scaling procedure the relation between R and S can be arbitrarily specified, and according to the choice made S = f(I) will be found to be either a power function or a logarithmic function; these two “psycho- physical laws” do not reflect empirical differences between scaling procedures but conventional differences in the assumptions made when interpreting these procedures. A model is then elaborated in which S = f(I) is fixed and the relation between R and S depends on the demands of the psychophysical task and the effects of previous learning. With this more complex model the empirical implications of the power function and log function differ; it is shown that if the latter is accepted explanations can be given for two major problems in scaling theory, the disparity between the functions given by category scaling and the direct methods, and the difference between prothetic and metathetic continua.     

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.     

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.     

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.     

Multidimensional scaling of form: A psychophysical analysis

Both metric and nonmetric multidimensional scaling methods were used to analyze similarity estimates when random polygons were used as stimulus patterns. Three dimensions, dispersion, jaggedness, and elongation were obtained with both analyses and were related to physical measures of the patterns.     

On the use of bisection procedures in animal psychophysical scaling

The ability of bisection procedures to specify the form of the psychophysical scale depends upon the precision of the technique. It is demonstrated that the precision of bisection techniques is a function of the stimulus interval bisected. Consequently, the choice of stimuli in a bisection experiment may predispose the ability of the experiment to distinguish between alternative psychophysical scales. The testing of interval scale properties of derived scales and the assessment of context effects in bisection experiments was also discussed.This material has been reviewed by the Walter Reed Army Institute of Research, and there is no objection to its presentation and/or publication. The opinions or assertions contained herein are the private views of the author and are not to be construed as official or as reflecting the view of the Department of the Army or the Department of Defense.     

Mixed-modality psychophysical scaling: Sequential dependencies and other properties

J. C. Stevens and Marks’s (1980) method of magnitude matching and a derivative, category matching, are examined in two experiments. Category matching produces highly similar matching functions to those of magnitude matching. The two methods are both subject to significant sequential dependencies, which, however, should not affect exponents of matching functions. Such mixed-modality scaling methods are also useful for theory testing. In the present case, responses were assimilated to the immediately previous response (different modality stimulus) but contrasted with the stimulus (same modality) two trials back in the sequence. The dependency of the response-response dependency on Sn-S_n-k was independent of stimulus modality. However, the usual dependency of the coefficient of variation of ratios of successive responses on Sn-S_n-k was not found. These results support the class of theories in which assimilative response-response dependencies and contrastive response-stimulus dependencies arise from different mechanisms, and disconfirm those in which both effects arise in a linked fashion from a single mechanism.     

Direct psychophysical scaling of the olfactory pleasantness of diluted n-amyl acetate

A category and two magnitude scales were constructed from observations of 12 Os who judged the pleasantness of a geometric dilution series of n-amyl acetate. Pleasantness varied inversely with concentration and had a short subjective range for a fairly typical range of stimulus concentrations. Scales resembled power functions with negative exponents of .110 to .126. A concave upward relationship between the two types of scales, which was also found in previous experiments involving hedonic and oiliness attributes, suggests a nonprothetic continuum, although evidence was mixed.     

Auditory psychophysical scaling exposure effects: magnitude estimation and cross-modal matching

The purpose of the present study was to investigate possible effects of exposure upon suprathreshold psychological responses when auditory magnitude estimation and cross-modal matching with audition as the standard are conducted within the same experiment. Four groups of 10 subjects each whose over-all age range was 18 to 23 yr. were employed. During the cross-modal matching task the Groups 1 and 2 subjects adjusted a vibrotactile stimulus presented to the dorsal surface of the tongue and the Groups 3 and 4 subjects adjusted a vibrotactile stimulus presented to the thenar eminence of the right hand to match binaurally presented auditory stimuli. The magnitude-estimation task was conducted before the cross-modal matching task for Groups 1 and 3 and the cross-modal matching task was conducted before the magnitude-estimation task for Groups 2 and 4. The psychophysical methods of magnitude estimation and cross-modal matching showed no effect of one upon the other when used in the same experiment.     

Memory and the experience of duration in retrospect

Two experiments investigated the relationship between long-term memory for events occurring during an interval and the experience of duration of the interval in retrospect. In both, Ss attended to a sequence consisting of a standard, an experimental, and a second standard interval. Then unexpected comparative duration and memory judgments were requested. In Experiment I, either 30 or 60 unrelated words occurred during the 180-see experimental interval. When more words had occurred, judgments of duration of the experimental interval, judgments of number of words presented, and number of words recognized all increased, but free recall of words was unaffected. In Experiment II, 80 categorized words occurred during the 160-see experimental interval, with category instances in either blocked or random order. When words were blocked by category, judgments of duration of the experimental interval, free recall, and recognition all increased, but judgments of number of words were unaffected. Results were discussed in terms of Ornstein’s (1969) “storage size” hypothesis.     

Constrained scaling: the effect of learned psychophysical scales on idiosyncratic response bias

We report seven experiments in which subjects were trained to respond with numbers to the loudness of 1000-Hz pure tones according to power functions with exponents of 0.60, 0.30, and 0.90. Subjects were then presented with stimuli from other continua (65-Hz pure tones or 565-nm lights varying in amplitude) and were asked to judge the subjective magnitude of these stimuli on the same numerical scale. Stimuli from the training continuum were presented, with feedback, on every other trial in order to maintain the trained scale. Except for the 0.90 scale, subjects readily learned the predetermined scales and were able to use them to judge the non-training stimuli with group results consistent with those usually reported. Also, in contrast to the usual magnitude estimation results, these results produced extremely low levels of intersubject variability. We argue that such learned scales can be used as "rulers" for measuring perceived magnitudes, according to a common unit.     

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.