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.     

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.     

Some functional measurement procedures for determining the psychophysical law

Various statistical procedures are ieveloped for determining the psychophysical law within the context of a functional measurement approach to studying stimulus integration in perception. The specific results are limited to additive or multiplicative psychological laws, but the generalization to alternative cognitive algebras is evident. Estimation of parameters of the hypothesized psychophysical law and test of the hypothesis that the row psychophysical law is the same as the column psychophysical law in a two-factor stimulus design is considered for various possible psychophysicaldaws, including linear, polynomial, and power laws.     

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.     

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.     

Perceptual invariance and the psychophysical law

The psychophysical power law, demonstrated empirically by Stevens, is derivable from two postulates concerning (1) the tendency of perceptual organizations to model the environment and (2) the tendency for perceptual relations to remain constant. The two postulates appear to rule out logarithmic laws of the Fechner type. The theory is extendable to multidimensional perceptions such as those encountered in speech and color vision. The power transformations produced by the sense organs may be of such form that they produce a perceptual space in which subsequent transformations need be only linear.     

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.     

Concerning the psychophysical power law

It is fortunate that, despite our theorizings, most of our facts manage to stay stubbornly as they were. I am encouraged by that thought as it bears on a recent theoretical attempt by Treisman (1964) to do over the psychophysical law. I should like, more in explication than in rebuttal, to comment on three major points relating to the law in question.     

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.     

Adaptive procedures in psychophysical research

As research on sensation and perception has grown more sophisticated during the last century, new adaptive methodologies have been developed to increase efficiency and reliability of measurement. An experimental procedure is said to be adaptive if the physical characteristics of the stimuli on each trial are determined by the stimuli and responses that occurred in the previous trial or sequence of trials. In this paper, the general development of adaptive procedures is described, and three commonly used methods are reviewed. Typically, a threshold value is measured using these methods, and, in some cases, other characteristics of the psychometric function underlying perceptual performance, such as slope, may be developed. Results of simulations and experiments with human subjects are reviewed to evaluate the utility of these adaptive procedures and the special circumstances under which one might be superior to another.     

Memory mechanisms and the psychophysical scaling of duration

Two experiments were performed to examine the suggestion that underlying memory mechanisms may be revealed in the form of the psychophysical function for duration. In experiment 1 a broad range of durations, with fine spacing at the lower end, was employed to bring out any transition in function that might reflect a change from 'ionic' memory to short-term memory. Estimation in conventional time-units (Verbal Estimation) was also compared with unit-free estimation (Magnitude Estimation). In experiment 2 Verbal Estimation was compared with the Production method, for a different range of stimulus values, and with varying interval content. Contrary to earlier claims, memory mechanisms were not found to be reflected in the values of power exponents for subjective duration. The value of the search for such functions is questioned, as simple linear plots fit the data at least as well.     

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.     

Adaptive procedures in psychophysical research.

As research on sensation and perception has grown more sophisticated during the last century, new adaptive methodologies have been developed to increase efficiency and reliability of measurement. An experimental procedure is said to be adaptive if the physical characteristics of the stimuli on each trial are determined by the stimuli and responses that occurred in the previous trial or sequence of trials. In this paper, the general development of adaptive procedures is described, and three commonly used methods are reviewed. Typically, a threshold value is measured using these methods, and, in some cases, other characteristics of the psychometric function underlying perceptual performance, such as slope, may be developed. Results of simulations and experiments with human subjects are reviewed to evaluate the utility of these adaptive procedures and the special circumstances under which one might be superior to another.     

Exposure effects on the psychophysical scaling methods of magnitude estimation and cross-modal matching for vibrotactile stimulation of the tongue and hand

The purpose of the present study was to investigate possible effects of exposure upon psychophysical scaling responses when vibrotactile magnitude estimation and cross-modal matching are conducted within the same experiment. Four groups of 10 subjects each, with an over-all age range of 18-23 yr., were employed. Groups 1 and 2 performed magnitude estimation for lingual vibrotaction and cross-modal matching with the lingual vibrotactile stimulus as the standard. Group 1 received the magnitude-estimation task first and Group 2 received the cross-modal-matching task first. Groups 3 and 4 performed magnitude estimation for vibrotaction applied to the thenar eminence of the hand and cross-modal matching with the vibrotactile stimulus applied to the thenar eminence of the hand as the standard. Group 3 received the magnitude-estimation task first and Group 4 received the cross-modal-matching task first. The psychophysical scaling methods of magnitude estimation and cross-modal matching showed very little exposure effect of one upon the other when used in the same experiment. Also, magnitude scaling responses tended to increase more rapidly with increases in vibrotactile stimulus intensity when the test site was the thenar eminence of the hand as opposed to the dorsum of the tongue.     

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.     

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.     

Comparison among four psychophysical procedures used in lateralization

Psychometrie functions were obtained from two listeners in four psychophysical tasks. The tasks were lateralization procedures in which Os were asked to make discriminations of interaural temporal differences of a 250-Hz tone. The four tasks were: a single-interval yes-no task, a single-interval left-right task, a two-alternative forced-choice task, and a two-interval same-different task. The theory of signal detection provides predictions relating the performances obtained in these four procedures. These predictions could not be verified in this experiment when it was assumed that the Os were listening to changes in lateral position produced by the interaural temporal difference. The data were, however, consistent with the assumption that Os use lateral motion as a cue for detection in two-interval tasks and lateral position as a cue in single-interval tasks.     

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.