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.     

Integration of noxious stimulation across separate somatosensory communications systems: a functional theory of pain

Functional measurement analyses and psychophysical techniques were used to assess how separate, cross-modal, aversive events are integrated in judgements of pain. Subjects made magnitude estimations of noxious stimuli produced by a 6 X 6 factorial design of electric shocks and loud tones. Group data and most of the individual results were consistent with a model of linear pain summation: The estimates of pain approximated the linear sum of the pain estimates of the individual electrocutaneous and auditory components. The relation between painful sensation and current intensity could be described by a mildly expansive power function with an exponent of about 1.1. Auditorily produced painful sensation related to sound pressure level by a mildly compressive power function with an exponent of about 0.90 as a representative figure. Results are interpreted in terms of a functional theory of pain. Noxious events are first transformed to psychological scale values via stimulus-specific psychophysical transfer functions. The outputs of these functions are then combined with other pain-related internal representations of either sensory or cognitive origin, according to simple algebraic models.     

Systematic covariation of the parameters in the near-miss to Weber's law, pointing to a new law

The exponent in the power function modeling of the near-miss to Weber's law is known to depend on several experimental factors, such as tone frequency and the presence or absence of noise. This paper presents data that confirm a theoretical argument that the near-miss exponent also depends on the definition of ‘just-noticeably different’ used empirically. Intensity discrimination data were collected for pure, 1000-Hz tones presented in quiet. Referent sound pressure levels ranged from 40 to 80 dB SPL in 10-dB steps. For each referent, the tone judged louder than the referent with probability equal to ν was determined, with ν ranging from 0.16 to 0.84. It was found that the power function exponent decreases monotonically with ν. Moreover, it was found that the two power law parameters co-vary systematically with ν, implying a submodel that has an interesting fixed-point property.     

Pain combines additively across different sensory systems: a further support for the functional theory of pain

Subjects made magnitude estimations of noxious stimuli produced by a 6 X 6 factorial design of electric shocks (pulse trains) and loud tones. Group data and all individual results conformed to a linear additive model of pain. The estimates of pain approximated the linear sum of the pain estimates of the individual electrocutaneous and auditory components. Pain related differently to the two inducing stimuli. It grew as a mildly expansive power function of current intensity (with an exponent of about 1.2) but as a mildly compressive power function of sound-pressure level (with an exponent of about 0.8). These results replicate recent findings by the same authors in 1986 using a more aversive type of electric stimulation. They are interpreted as supportive of a new functional approach to understand pain and pain-related phenomena.     

Loudness and reaction time: I

It is widely assumed, based on Chocholle’s (1940) research, that stimuli that appear equal in loudness will generate the same reaction times. In Experiment 1, we first obtained equal-loudness functions for five stimulus frequencies at four different intensity levels. It was found that equal loudness produced equal RT at 80 phons and 60 phons, but not at 40 phons and 20 phons. It is likely that Chocholle obtained equivalence between loudness and RT at all intensity levels because of relay-click transients in his RT signals. One main conclusion drawn from Experiment 1 is that signal detection (in reaction time) and stimulus discrimination (in loudness estimation) require different perceptual processes. In the second phase of this investigation, the RT-intensity functions from six different experiments were used to generate scales of auditory intensity. Our analyses indicate that when the nonsensory or “residual” component is removed from auditory RT measures, the remaining sensory-detection component is inversely related to sound pressure according to a power function whose exponent is about — 3. The absolute value of this exponent is the same as the .3 exponent for loudness when interval-scaling procedures are used, and is one-half the size of the .6 exponent which is commonly assumed for loudness scaling.     

The measurement of loudness using direct comparisons of sensory intervals

Subjects were required in each trial to directly compare two pairs of tones and indicate which pair of tones had the greater loudness difference. Ten 1200 Hz tones differing only in intensity were employed. Subjects made binary comparisons among the 45 tone pairs which can be formed from the set of ten tones. The subjects' binary comparisons of the tone pairs were found to satisfy the transitivity and monotonicity requirements of a positive difference structure. These comparisons of loudness intervals were used to construct a rank order of loudness difference. A loudness scale was constructed from a nonmetric analysis of the rank order of loudness difference for the 45 tone pairs and indicated that loudness was a power function of sound pressure with an exponent of 0.26.     

Binaural and temporal integration of the loudness of tones and noises

Subjects judged the loudness of tones (Experiment 1) and of bursts of noise (Experiment 2) that varied in intensity and duration as well as in mode of presentation (monaural vs. binaural). Both monaural and binaural loudness, for both types of signals, obeyed the bilinear-interaction prediction of the classic temporal integration model. The loudness of short tones grows as a power function of both intensity and duration with different exponents for the two factors (.2 and .3, respectively). The loudness of wide-band noises grows as a power function of duration (with an exponent of approximately .6) but not of sound pressure. For tones, binaural summation was constant but fell short of full additivity. For noises, summation changed across level and duration. Temporal summation followed the same course for monaural and binaural tonal stimuli but not for noise stimuli. Notwithstanding these differences between tone and noise, we concluded that binaural and temporal summation are independently operating integrative networks within the auditory system. The usefulness of establishing the underlying metric structure for temporal summation is emphasized.     

Loudness and loudness discrimination

A model is developed which holds that pure-tone intensity discrimination and suprathreshold loudness judgments are based on the same sensory representation. In this model, loudness is a power function of sound intensity. When two tones are presented sequentially, each gives rise to a loudness value along the sensory continuum. In intensity-discrimination experiments, threshold is reached when the loudness difference between the tones exceeds a criterial value. For suprathreshold presentations of tone pairs, judgments of loudness differences are based on the loudness difference between the two tones. The model is shown to accord well with data from both classes of experiments.     

Slippery context effect and critical bands.

This article explored the slippery context effect: When Ss judge the loudness of tones that differ in sound frequency as well as intensity, stimulus context (relative intensity levels at the 2 frequencies) can strongly influence the levels that are judged equally loud. It is shown that the size of the slippery context effect depends on the frequency difference between the tones: Small frequency differences (less than a critical bandwidth) produced essentially no slippery effect; much larger differences produced substantial effects. These results are consistent with a model postulating the existence of a central attentional or preattentive "filter-like" process whose weighting coefficients represent the size of the absolute as opposed to the relative (contextual) component of loudness perception and judgment.     

BRIGHTNESS SCALES FOR MONOCHROMATIC LIGHT

By means of amethod of ratio estimation, scale values were obtained for the subjective brightness of various physical intensities of monochromatic light of various wave lengths. In a second experiment the scale was constructed by a method of magnitude estimation. The brightness functions were studied by plotting the scale values against stimulus intensity for each wave length. The two experiments gave essentially the same results. It was shown: (1) Brightness of monochromatic light is a power function of stimulus intensity. The exponent of the function is approximately one-third for all wave lengths. (2) Properties of the brightness functions can explain certain empirical relations between brightness, hue and saturation.     

SCALES FOR SUBJECTIVE DISTANCE

By means of the method of ratio estimation, scale values were obtained for subjective distance. In three experiments different stimulus ranges of the objective distances were used. It was found: ( 1 ) Subjective distance is a power function of the objective distance. ( 2 ) The exponent of the function varies with the stimulus range. With increasing stimulus range the exponent has a tendency to decrease. It is conceivable that the change of the exponent may be explained by an adaptation of the subjective range to the stimulus range.     

Time perception: Effects of sex and sound intensity on scales of subjective duration

Six women and six men reproduced ten time intervals varying in logarithmic steps between 1.3 and 20 s. The durations were indicated by white noise of 10, 25, 40 and 55 dB SL, different sound intensities in different sessions. It was found that (i) greater sound intensity entails shorter reproductions, and (ii) reproductions by male observers are shorter than those by female, although for both (i) and (ii) there is an interaction with the standard durations. The data were treated in accordance with the "parallel-clock model" (Eisler, 1975), whereby the parameters of the psychophysical power function are determined from duration reproduction data. As in previous experiments (Eisler, 1975), the data showed a break in the function entailing two segments. The effect of sound intensity could be attributed to the exponent, which was lower for stronger noise, and the effect of sex to the weight coefficient of the upper relative to the lower segment of the psychophysical function, the coefficient being lower for men.     

A test of a two-stage model of magnitude judgment

It has been suggested that the power law J = aⁿ, describing the relationship between numerical magnitude judgments and physical magnitudes, confounds a sensory or input function with an output function flawing to do with O’s use of numbers. Judged magnitudes of differences between stimuli offer some opportunity for separating these functions. We obtained magnitude judgments of differences between paired weights, as well as magnitude judgments of the weights making up the pairs. From the former we calculated simultaneously an input exponent and an output exponent, working upon Attneave’s assumption that both transformations are describable as power functions. The inferred input and output functions, in combination, closely predict the judgments of individual weights by the same Os. Although pooled data (geometric means of judgments) conform fairly well to a linear output function, individual data do not; i.e., individual Os deviate quite significantly fromlinearity and from one another in their use of numbers. Individual values of the inferred sensory exponent, k, show significantly better uniformity over Os than do values of the phenotypica! magnitude exponent previously found to describe interval judgments of weight.     

Two classes of models for magnitude estimation

One class of models assumes that presentation of a signal results in an internal representation as a random variable. Depending on whether the signal is close to or far from the preceding signal, the variance of the representation is smaller or larger. Responses are determined largely by this random variable; however, when the signal is close to the preceding one, the response is generated by modifying the representation multiplicatively by some function of the ratio of the previous response to its representation. Power and linear functions are explored. The form of the random variable is assumed to be that arising from either the timing or the counting model operating on a Poisson process. Detailed analyses are carried out successfully only for the timing model with neural sample sizes independent of intensity; however, the data require the sample to increase with intensity. The linear response function coupled with the constant sample size counting model appears somewhat viable, but detailed calculations are very difficult to carry out. The second class of models postulates a power function relation between magnitude estimates and signals intensity for which the exponent is a Gaussian distributed random variable and the unit is the product of two log normal random variables. Again we assume an attention band such that succesive stimuli that are widely separated in intensity lead to independent samples of the random variables while a variety of assumptions is explored for successive stimuli that are near each other in intensity. Although they each give rise to the qualitative features of the data, estimates of parameters are sufficiently inconsistent that we are led to reject all of the submodels studied.     

Top-down gain control in the auditory system: evidence from identification and discrimination experiments

The influence of intensity range in auditory identification and intensity discrimination experiments is well documented and is usually attributed to nonsensory factors. Recent studies, however, have suggested that the stimulus range effect might be sensory in origin. To test this notion, in one set of experiments, we had listeners identify the individual tones in a set. One baseline condition consisted of identifying four 1-kHz, low-intensity tones; the other consisted of identifying four 1-kHz, high-intensity tones. In the experimental conditions, these baseline tone sets were augmented by adding a fifth tone at either 1 or 5 kHz. Added 5-kHz tones had little effect on identification accuracy for the four baseline tones. When an added 1-kHz tone differed substantially in intensity from the four baseline tones, it adversely affected performance, with the addition of a high-intensity tone to a set of low-intensity tones having a more deleterious effect than the addition of a low-intensity tone to a set of high-intensity tones. These and further results, obtained in an exploration of this asymmetrical range effect in a third identification experiment and in two intensity-discrimination experiments, were consistent with the notion of a nonlinear amplifier under top-down control whose functions include protection against sensory overload from loud sounds. The identification data were well described by a signal-detection model using equal-variance Laplace distributions instead of the usual Gaussian distributions.     

Changes in absolute detection threshold and in subjective intensity of suprathreshold stimuli during olfactory adaptation and recovery

Olfactory adaptation and recovery to methyl isobutyl ketone at a concentration 10 times the absolute detection threshold (I_{t o}) was intensively studied in two human Ss. A combined psychophysical procedure was used that allowed comparisons of changes in threshold (I_t) with changes in the subjective intensity of suprathreshold stimuli. Information was also obtained on the effect of the adapting stimulus on the psychophysical power function for this odorant. A threshold detection procedure was used to estimate changes in I_t; an unstructured magnitude-estimation procedure was used to monitor changes in the subjective intensity of suprathreshold stimuli and the psychophysical power function. The data provided additional information on the behavioral course of olfactory adaptation and recovery and suggested that this combined method can be used profitably for further investigations of this kind. Complementary to the work of Cain and Engen (1969), the results suggested an increase in the exponent of the power function with increasing adaptation.     

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.     

Attention bands in absolute identification

If both the number of one-dimensional signals and their range are sufficiently large (about 7 and 20 dB for loudness), the information transmitted in absolute identification is not much increased by increasing either variable (Miller, 1956; Braida & Durlach, 1972). The data can be represented in terms of Thurstonian discriminal dispersions in which the variance is proportional to the square of the signal range in decibels (Durlach & Braida, 1969; Gravetter & Lockhead, 1973), but it is by no means obvious what sorts of mechanisms would lead to this model. An alternative is proposed, namely, that there is a roving attention band, about 10 to 15 dB wide, such that signals falling within the band are represented by a sensory sample size about an order ot magnitude larger than when the same signal falls outside the band. With reasonable choices for parameters, including the subjective continuum growing as a power function of intensity with an exponent about 3, this nicely accounts for the data. In an attempt to examine the change of performance with range, we replicated the BraidaoDurlach experiment with many additional points. These data are not, however, adequate to decide between the two models.     

Detection and identification thresholds for consonant-vowel syllables

Detection and identification thresholds were obtained for 6- and 10-year-old normal children and normal adults using five-formant synthesized consonant-vowel ([baHdflrfea]) stimuli. Sixyear-old children were found to have poorer detection than adults, just as they do for pure tones. For the identification task, the slopes of the performance-intensity functions were more shallow for 6-year-old children than for 10-year-olds and adults. Consequently, compared with 10-yearolds and adults, 6-year-old listeners require a greater increase in stimulus intensity above detection threshold to identify these stimuli at a high performance level. The influence of acoustic characteristics of the stimuli on all listeners is also discussed.