A limited-capacity response process in absolute identification

In two absolute identification experiments, the dependency of the current response, Rn, on the immediately preceding stimulus, Sn-1, and response, Rn-1, was measured by means of multivariate information transmission (see McGill, 1954). In these experiments, the amount of stimulus information available to subjects, measured as the amount of information transmission from a current stimulus, Sn, to Rn, was manipulated. The magnitude of the dependency of Rn on Sn-1 and Rn-1 was inversely proportional to that of information transmission from Sn to Rn, supporting the argument of Ward and Lockhead (1971) that the less stimulus information the subjects get, the more their responses will be likely to depend on previous stimuli and responses. Interestingly, the sum of information transmission from Sn, Sn-1, and Rn-1 to Rn was always about 2.5 bits, without respect to the variance of each term. This result could have arisen from the operation of a limited-capacity response process.     

Range and regression effects in magnitude scaling

The relation between power law exponents obtained by magnitude estimation and magnitude production was studied for both loudness and perceived distance. While the results confirm the usual finding of higher values for production for relatively large stimulus ranges, just the opposite occurs when the stimulus range is short, necessitating a revision of the Stevens-Greenbaum regression principle. The relation between range and exponent was explored, both for the case in which several intensities are presented for judgment and for the simpler case of only two intensities. In both cases, a power relation was described relating stimulus ratios to judgmental ratios, with exponents containing both range-dependent and range-independent components.     

Binaural summation after learning psychophysical functions for loudness

Do response-related processes affect perceptual processes? Sometimes they may: Algom and Marks (1990) produced different loudness exponents by manipulating stimulus range, and thereby also modified the rules of loudness summation determined by magnitude scaling. The present study manipulated exponents by having a dozen subjects learn prescribed power functions with exponents of 0.3, 0.6, or 1.2 (re sound pressure). Subjects gave magnitude estimates of the loudness of binaural signals during training, and of monaural and binaural signals after training. During training, subjects’ responses followed the nominal functions reasonably well. Immediately following training, subjects applied the numeric response scales uniformly to binaural and monaural signals alike; the implicit monaural-binaural loudness matches, and thus the basic rules underlying binaural summation, were unaffected by the exponent learned. Comparison of these results with those of Algom and Marks leads us to conclude that changing stimulus range likely influences underlying perceptual events, whereas “calibrating” a loudness scale through pretraining leaves the perceptual processes unaffected.     

Power functions of loudness magnitude estimations and auditory brainstem evoked responses

The correspondence between subjective and neural response to change in acoustic intensity was considered by deriving power functions from subjective loudness estimations and from the amplitude and latency of auditory brainstem evoked response components (BER). Thirty-six subjects provided loudness magnitude estimations of 2-sec trains of positive polarity click stimuli, 20/sec, at intensity levels ranging from 55 to 90 dB in 5-dB steps. The loudness power function yielded an exponent of .48. With longer trains of the same click stimuli, the exponents of BER latency measures ranged from -.14 for wave I to -.03 for later waves. The exponents of BER amplitude-intensity functions ranged from .40 to .19. Although these exponents tended to be larger than exponents previously reported, they were all lower than the exponent derived from the subjective loudness estimates, and a clear correspondence between the exponents of the loudness and BER component intensity functions was not found.     

Identification variability as a measure of loudness: an application to gender differences.

It is well known that discrimination response variability increases with stimulus intensity, closely related to Weber's Law. It is also an axiom that sensation magnitude increases with stimulus intensity. Following earlier researchers such as Thurstone, Garner, and Durlach and Braida, we explored a new method of exploiting these relationships to estimate the power function exponent relating sound pressure level to loudness, using the accuracy with which listeners could identify the intensity of pure tones. The log standard deviation of the normally distributed identification errors increases linearly with stimulus range in decibels, and the slope, a, of the regression is proportional to the loudness exponent, n. Interestingly, in a demonstration experiment, the loudness exponent estimated in this way is greater for females than for males.     

An application of a dynamic model of judgment to magnitude production

A dynamic model of judgment, together with a model of stimulus context effects, is applied to magnitude production (MP) and magnitude estimation (ME) experiments. Participants' responses in MP were correlated across trials, as is typically found for ME. The magnitudeof the autocorrelation, however, was small, which suggests that participants in MP tend to rely more heavily on a long-term frame of reference. Second, a stimulus context effect found for ME did not appear for MP, most likely because of the different nature of the task (i.e., intermediate values of the stimulus were heard while the participant produced a response). A fit of an earlier regression model, on the other hand, suggests that the number presented on the previous trial in MP has a large contrastive effect on the current response.The present model offers a different view of this result, in that it shows that a negative coefficient for the earlier model is consistent with a positive judgmental effect. The regression effect noted by Stevens and Greenbaum (1966), which is a value of the estimated ME exponent that is smaller than the inverse of the estimated MP exponent, was also found; it i s shown that the effect did not arise from bias in estimation.     

Bias effects on magnitude and ratio estimation power function exponents

A bias model of relative judgment was used to derive a ratio estimation (RE) power function, and its effectiveness in providing estimates of exponents free of the effects of standards was evaluated. The RE bias model was compared with the simple RE power function that ignores bias. Results showed that when bias was not taken into account, estimates of exponents exhibited the usual effects of standards observed in previous research. However, the introduction of bias parameters into the RE power function virtually eliminated these effects. Exponents calculated from "equal-range segments" (e.g., low stimulus range vs. high stimulus range) judged by magnitude estimation (ME) were examined: the effects of equal-range segments on exponents were much stronger for ME than standards were for RE, using the bias model.     

Range and regression, loudness scales, and loudness processing: toward a context-bound psychophysics

How does context affect basic processes of sensory integration and the implicit psychophysical scales that underlie those processes? Five experiments examined how stimulus range and response regression determine characteristics of (a) psychophysical scales for loudness and (b) 3 kinds of intensity summation: binaural loudness summation, summation of loudness between tones widely spaced in frequency, and temporal loudness summation. Context affected the overt loudness scales in that smaller power-function exponents characterized larger versus smaller range of stimulation and characterized magnitude estimation versus magnitude production. More important, however, context simultaneously affected the degree of loudness integration as measured in terms of matching stimulus levels. Thus, stimulus range and scaling procedure influence not only overt response scales, but measures of underlying intensity processing.     

A linear relation between loudness and decibels

A total of 37 uninitiated observers made repeated numerical magnitude judgments of the loudness of a sequence of octave band noises spaced at 1-dB intervals, from 0 to 5 dB above a standard of about 80 dB(A), which was called 10. The observers were not instructed to use numbers as ratios. When the median responses are plotted linearly against decibels, they are fitted by straight lines. Each extra decibel adds an average of 1 unit of loudness, range for individual observers 10 through .25 units. This is consistent with the view that the subjectively equal stimulus spacing for the loudness of noise is linear in decibels, and that the observers use numbers linearly in judging the loudness.     

Stability of individual loudness functions obtained by magnitude estimation and production

A correlational analysis of individual magnitude estimation and production exponents at the same frequency was perfor.med, as well as an analysis of individual exponents produced in different sessions by the same procedure across frequency(250, 1, 000, and 3, 000 Hz). Taken together, results show, first, that individual exponent differences do not decrease by counterbalancing magnitude estimation with magnitude production, and, second, that individual exponent differences remain stable over time despite changes in stimulus frequency. Further results disclose that although individual magnitude estimation and production exponents do not necessarily obey the .6 power law, it is possible to predict the slope (exponent) of an equal-sensation function averaged for a group of listeners from individual magnitude estimation and production data. Assuming that individual listeners with sensorineural hearing loss also produce stable and reliable magnitude functions, it is also shown that the slope of the loudness-recruitment function measured by magnitude estimation and production can be predicted for individuals with bilateral losses of long duration. Thus, results obtained in normal and in pathological ears suggest that individual listeners can produce loudness judgments that reveal, albeit indirectly, the input-output characteristic of the auditory system.     

Stimulus sequence and the exponent of the power function for loudness

In two experiments, 15 and 13 subjects estimated the loudness of 12 sound-pressure levels (38-104 dB; 6-dB intervals) of a 1000-Hz tone by the method of magnitude estimation with a modulus assigned to the first stimulus presented. The tone duration was 1 sec. and the interstimulus interval was 6 sec. The presentation order was systematically ascending-descending in one experiment and balanced-irregular in the other. The results indicate that (1) loudness is a power function of sound pressure with an exponent of 0.60 for the systematic order and 0.29 for the irregular order. (2) For both the irregular and systematic orders, a large step-size (12 or 18 dB) between the stimulus on Trial n and on Trial n-1 (or n-3) results in a slight assimilation effect. This also occurs for the small step-size (6 dB) in the irregular order. (3) The size of momentary exponents (based on two points, Trials n and n-1 or n-3) depends on the sound pressures of successive stimuli, whether the steps are positive or negative, and whether the stimuli have been presented in systematic or irregular order. For positive steps, the momentary exponent is lower for a soft tone (Trial n) than for a loud tone, whereas for negative steps the momentary exponent is lower for a loud tone than for a soft tone. These effects ar more pronounced when these stimuli are presented in an irregular order. A relative judgment model is offered for magnitude estimation. It assumes that subjects judge the loudness of a stimulus in terms of three reference markers: the minimum and maximum sound pressures as well as the sound pressure of the previous stimulus.     

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.     

On predicting exponents for cross-modality matches

Mashhour and Hosman used magnitude estimations to scale seven continua: line length, time duration, finger span, loudness of noise, weight, gray reflectance, and surface area. The first four continua also served as the adjusted stimuli in 17 cross-modality matches among the various continua. Contrary to the view expressed by Mashhour and Hosman, the results appear to support the psychophysical power law. A reanalysis of the data shows that the exponents of the power functions obtained in cross-modality matches agree with the exponents of the power functions produced by magnitude estimations, provided correction is made for the regression effect. The measured discrepancies between the exponents predicted and those actually obtained show scatter that is consistent with that of other experiments. In particular, the scatter accords well with the distribution of 68 exponents predicted by Moskowitz from experiments in which Os matched both number and loudness to various taste concentrations.     

Prepulse effects on magnitude estimation of startle-eliciting stimuli and startle responses

The present studies investigated the relationship between prepulse effects on the modification of the brainstem startle reflex and magnitude estimates of startle-eliciting stimuli. In Experiment 1, startle eyeblink responses were elicited in 24 students, half of whom were instructed to estimate the loudness of the startle stimulus (actual intensities of 80, 90, and 100 dB) and half of whom were instructed to estimate the magnitude of their eyeblink. When weak acoustic prepulses preceded the startle-eliciting stimulus, eyeblink amplitude was inhibited, and estimates of response magnitude decreased, but estimates of startle stimulus magnitude decreased only when 100-dB startle stimuli were presented. In Experiment 2, the same startle stimuli were preceded on some trials by a vibrotactile prepulse to the hand. In conditions in which startle amplitude was inhibited, startle stimulus magnitude estimates were not affected. This suggests that the effect of acoustic prepulses on 100-dB startle stimuli in Experiment 1 may have been due to loudness assimilation, an effect independent of the prepulse inhibition of startle responding.     

Individual differences in loudness processing and loudness scales

Parameters of the psychophysical function for loudness (a 1000-Hz tone) were assessed for individual subjects in three experiments: (a) binaural loudness summation, (b) temporal loudness summation, and (c) judgments of loudness intervals. The loudness scales that underlay the additive binaural summation closely approximated S. S. Stevens's (1956) sone scale but were nonlinearly related to the scales that underlay the subtractive interval judgments, the latter approximating Garner's (1954) lambda scale. Interindividual differences in temporal summation were unrelated to differences in scaling performance or in binaural summation. Although the exponents of magnitude-estimation functions and the exponents underlying interval judgments varied considerably from subject to subject, exponents computed on the basis of underlying binaural summation varied less. The results suggest that interindividual variation in the exponent of magnitude-estimation functions largely reflects differences in the ways that subjects use numbers to describe loudnesses and that the sensory representations of loudness are fairly uniform, though probably not wholly uniform, among people with normal hearing. The magnitude of individual variation in at least one measure of auditory intensity processing, namely, temporal summation, seems at least as great as the magnitude of the variation in the underlying loudness scale.     

Loudness “ratios” and “differences” involve the same psychophysical operation

Subjects judged both “atios” of loudness and “differences” in loudness between pairs of tones that varied in intensity. The pairs were constructed from factorial designs, permitting separation of stimulus and response scaling for each subject. Ratings of “differences” and estimations of “ratios” were monotonically related, inconsistent with the hypothesis that subjects perform both subtractive and ratio operations on a common scale. Instead, the data suggest that both tasks involve the same psychophysical comparison operation with different response transformations. If the operation can be represented by the subtractive model, then category ratings involve a nearly linear transformation and magnitude estimations involve a nearly exponential transformation.     

Sequential effects in absolute judgments of loudness

The effects of preceding stimuli on the judgments of current stimuli were examined in a study using absolute judgments of loudness with feedback. It was found that the response on a given trial was dependent on the stimuli in the preceding sequence of at least five trials. Both assimilation and contrast effects were observed. The form of the dependency of a response on a prior stimulus was a function of the ordinal position of the stimulus in the preceding sequence of trials. The stimulus on the immediately preceding trial had an assimilative effect on the response and preceding stimuli two to five trials removed all showed a contrast effect on a given response. The extent to which these preceding stimuli contributed to the contrast effect was an increasing function of their recency. The reversal of the dependency of the response, from assimilation to the stimulus one trial back, to contrast with the stimuli two and more trials back, indicates a unique function of the immediately preceding stimulus in this task. Since there was a reduction in the variance of responses to those stimuli similar in value to the immediately preceding stimulus, it is proposed that the stimulus and feedback on the last trial were remembered and used asa standardin judging the presented stimulus. A model is presented in which it is assumed that the memory of the magnitude of the immediately preceding stimulus is contaminated in specified ways by prior stimuli in the series. The empirical findings of assimilation and contrastare expected consequences of the proposed memorial processes.     

The range effect as a function of stimulus set,presence of a standard,and modulus

The intramodal range effect (an inverse relationship between stimulus range and exponent in Stevens’s power law) has been well documented, but its conditions have not been tested. Both the estimates of stimulus magnitudes and their exponents are affected by context, stimulus location, and different standards and moduli, but how these variables might interact with the variable of stimulus range has not been studied. In the present research, exponents were derived from magnitude estimates of line length for each of three different stimulus: ranges at two different locations on the scale of length, with or without a modulus. Moduli of 50 and 500 permitted an analysis of the effect of response magnitude on the range effect. Because different ranges had stimulus values in common, the effect of range and location on exponents from those common values could be determined. Exponents decreased as stimulus range increased, but only in the free-modulus condition. For that condition, exponents derived from magnitude estimates of only the common stimuli also showed the range effect and response magnitude did not influence the range effect. Exponents were higher for stimulus ranges at the lower location, but location does not appear to contribute to the range effect. Although the range effect is not explained, the conditions under which it holds and some factors that may influence it are considered.     

Magnitude estimation of apparent sums and differences

Os first scaled two continua by magnitude estimation: apparent area of circles and loudness of 1,000-Hz tones. They then gave magnitude estimations of apparent sums and apparent differences for IS pairs of stimuli on each of the two continua. The scales for sums and differences were in some cases nearly linearly related to the power function obtained when the same as scaled the underlying continuum. However, systematic departure from linearity was the usual result. The power law exponents obtained were generally smaller than those usually reported for the two sensory continua.     

Intraindividual consistencies in cross-modal matching across several continua

To determine the relationship between individual exponents for cross-modal stimulus matches for both directions of matching, and to assess the transitivity of individual exponents, subjects were asked to adjust both the judgment and criterion stimuli. Experiment 1 involved four continua paired in 12 ordered combinations; Experiment 2 involved five continua and 20 ordered combinations. Two subjects served in each experiment. The individual exponent of the power function for matches of A to B was close to the inverse of the exponent for matches of B to A, but there was systematic deviation, indicating the presence of a small regression effect. Transitivity of individual exponents was determined by forming ratios of exponents from matches involving other continuum pairs to predict obtained exponents; the means of the distribution of deviations of obtained from predicted values was ?.02 log units, and the standard deviation was .15 log units, indicating that, on the average, predicted values were close to obtained exponents—that is, transitivity of exponents holds for individuals.