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.     

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.     

Direct quantitative judgments of sums and a two-stage model for psychophysical judgments

Judged magnitudes of differences between stimuli have previously been shown to support a two-stage interpretation of magnitude estimation, in which input transformations and output transformations are each describable as power functions. In an effort to provide support for the model independent of the difference estimation procedure. the present investigation employed two additional judgment tasks. We obtained magnitude judgments and category judgments of the combined magnitudes (sums) of paired weights from two groups of Ss. Values of the inferred input exponent k calculated from the two sets of data were very similar and were also remarkably similar to the exponent previously calculated from magnitude estimations of differences between weights. The output exponent calculated from magnitude judgments of sums described a concave upward function; however. the similar function describing category judgments was essentially linear. These results show that the inferred input exponent is not the result of the difference estimation task, and in addition provides support for the contention that the interval scale may be a less biased sensory measure than the magnitude scale. The introduction of an additive constant to the model improved its fit to the data but the rule by which it was introduced made very little difference.     

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.     

Higher order sequential effects in psychophysical judgments

We found that the depth of sequential effects depends on the judgment task. An experiment with squares indicated that stimulus-response pairs up to two trials back were included in the judgment process when subjects were required to make category judgments of size, whereas only the immediately preceding event was incorporated when subjects were making magnitude estimations. In the case of category judgment, interactions between the current stimulus and prior stimuli as well as configural effects indicated that events one and two trials back meet an equivalent function in the judgment process and that these events may jointly operate in one trial. These findings can be explained by a class of models that assume that the position of preceding stimuli relative to the current stimulus is decisive in the judgment process. The multiple-standards model is a representative of this class according to which there are two types of standards: (1) the endpoints of the range as long-term standards and (2) traces of preceding stimuli as short-term standards.     

A new scaling technique for absolute judgments

The results of an experiment using the method of absolute judgments can be viewed as a matrix of conditional probabilities in which the rows represent stimuli and the columns responses. The cosine of the angle between two row vectors is a measure of the similarity of the corresponding stimuli. This cosine provides the basis for a method of scaling the stimuli. Unlike the method of paired comparisons, this new technique does not require arbitrary fixing of a unit of measurement. A numerical example is given.     

Sequential dependencies and regression in psychophysical judgments

A tendency for judgments of stimulus magnitude to be biased in the direction of the value of the immediately preceding stimulus is found in magnitude estimations of loudness. This produces a bias in the empirical psychophysical function that results in underestimation of the exponent of the unbiased function presumed to relate number and stimulus intensity, N = aSⁿ. The biased judgment can be represented as a power product of focal and preceding stimulus intensity, N_ij= aS ^m S_j ^b. A bias-free estimate of the correct exponent, n, can be obtained from the relation n = m + b.     

Higher order sequential effects in psychophysical judgments

We found that the depth of sequential effects depends on the judgment task. An experiment with squares indicated that stimulus-response pairs up to two trials back were included in the judgment process when subjects were required to make category judgments of size, whereas only the immediately preceding event was incorporated when subjects were making magnitude estimations. In the case of category judgment, interactions between the current stimulus and prior stimuli as well as configural effects indicated that events one and two trials back meet an equivalent function in the judgment process and that these events may jointly operate in one trial. These findings can be explained by a class of models that assume that the position of preceding stimuli relative to the current stimulus is decisive in the judgment process. The multiple-standards model is a representative of this class according to which there are two types of standards: (1) the endpoints of the range as long-term standards and (2) traces of preceding stimuli as short-term standards.     

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.     

Rats' lever-press durations as psychophysical judgments of time

Hungry rats received food following lever-press durations exceeding a minimum value, which ranged from 0 to 6.4 sec. When no intertrial intervals separated successive presses, modal press durations remained at very short values as the minimum value required for food was increased. This was particularly true immediately after a food presentation. When an 8-sec intertrial interval followed each lever release, modal press durations were always at or beyond the minimum value required for food, and outcome of the preceding press had no effect on press duration. Possible reasons for the effects of intertrial intervals included punishment of short presses, increased delay of reinforcement of short presses, and reduced density of reinforcement. In addition, functions relating discrete-trials lever-press duration to minimum duration required for food were found to be qualitatively and quantitatively similar to the power functions recently proposed by Catania (1970) for interresponse time and response latency. This similarity was taken as support for a general psychophysical law of temporal judgments.     

Multidimensional scaling models for reaction times and same-different judgments

A method for joint analysis of reaction times and same-different judgments is discussed. A set of stimuli is assumed to have some parametric representation which uniquely defines dissimilarities between the stimuli. Those dissimilarities are then related to the observed reaction times and same-different judgments through a model of psychological processes. Three representation models of dissimilarities are considered, the Minkowski power distance model, the linear model, and Tversky's feature matching model. Maximum likelihood estimation procedures are developed and implemented in the form of a FORTRAN program. An example is given to illustrate the kind of analyses that can be performed by the proposed method.The work reported in this paper is supported by Grant A6394 to the first author from the Natural Sciences and Engineering Research Council of Canada. Portions of this study have been presented at the Psychometric Society meeting in Chapel Hill, N.C., in May, 1981. We thank Tony Marley, Jim Ramsay and anonymous reviewers for their helpful comments. MAXRT, a computer program which performs the computations described in this paper may be obtained by writing to the first author.     

Memory strength and recency judgments

Two experiments were done to examine the effect of memory strength on numerical judgment of recency (JOR). In one experiment, the strong versus weak manipulation was defined by stimulus type (pictures vs. names); and in the other, it was defined by long versus short study durations of pictures. Two hypotheses were contrasted: (1) that strong items seem more recent than weak items (theactivation hypothesis), and (2) that JORs are more accurate for strong items than for weak items (theaccuracy hypothesis). Results of both experiments supported the activation hypothesis. On the basis of these and previous results, it is argued that recency is inferred partly from a memory’s strength or activation and partly from some other time-related clue to the age of the memory.     

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.     

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.     

The effect of the induction of involvement on psychophysical judgments

The present investigation was based on the concept of invariance, which holds that identical principles govern the judgment of stimuli arrayed on both physically and socially defined scales. Two experiments were conducted in which involvement was manipulated through the use of instructions presented in conjunction with category judgments obtained in a training session. This was followed by an anchor session. Experiment 1 employed a series of weights as stimuli, while Experiment 2 used random pattern dot slides. The experiments were similar, except for the inclusion of two additional features in the weight study. These were: (1) positive feedback, introduced as an independent variable between the judgment sessions and tested for its effect as an enhancer of involvement; and (2) two stimuli in the anchor session not part of the original stimulus series. These weights provided a test for the generality of involvement set. Among various hypotheses tested in both studies was the expectancy that the introduction of involvement associated with the formation of a judgment scale would lessen the impact of an anchor on judgment. This expectancy was based on the observed effects of involvement in social judgment contexts. Results of both experiments supported the judgment maintenance hypothesis.     

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.     

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.