Magnitude Estimation Functions Research Articles

Pure-Tone-Spondee Threshold Relationships in Functional Hearing Loss: A Test of Loudness Contribution.

The purpose of this article is to examine explanations for pure-tone average-spondee threshold differences in functional hearing loss. Loudness magnitude estimation functions were obtained from 24 participants for pure tones (0.5 and 1.0 kHz), vowels, spondees, and speech-shaped noise as a function of level (20-90 dB SPL). Participants listened monaurally through earphones. Loudness predictions were obtained for the same stimuli by using a computational, dynamic loudness model. When evaluated at the same SPL, speech-shaped noise was judged louder than vowels/spondees, which were judged louder than tones. Equal-loudness levels were inferred from fitted loudness functions for the group. For the clinical application, the 2.1-dB difference between spondees and tones at equal loudness became a 12.1-dB difference when the stimuli were converted from SPL to HL. Nearly all of the pure-tone average-spondee threshold differences in functional hearing loss are attributable to references for calibration for 0 dB HL for tones and speech, which are based on detection and recognition, respectively. The recognition threshold for spondees is roughly 9 dB higher than the speech detection threshold; persons feigning a loss, who base loss magnitude on loudness, do not consider this difference. Furthermore, the dynamic loudness model was more accurate than the static model.

Some factors affecting loudness measurement and prediction

The current ANSI standard (ANSI S3.4, 2007) estimates the loudness of sustained sound, but many naturally occurring sounds have time-varying levels. Glasberg and Moore (2002) published a model for the prediction of time-varying sounds and this aspect should be considered as part of a revision to the ANSI standard. To assess the predictions of the dynamic model, loudness magnitude estimation functions were obtained for 24 listeners using pure tones (0.5 and 1.0 kHz), vowels, spondees, and speech-shaped noise (SSN) presented at levels from 40 to 90 dB SPL. Inferred equal-loudness levels from the fitted loudness functions were compared to the model predictions. The loudness model was qualitatively consistent with the behavioral data. The model predicted SSN to be louder than vowels and spondees which would be louder than tones; however, the model over-predicted the loudness differences. Possible explanations for the over-prediction include biases in loudness judgments, cognitive factors regarding learned expectations for loudness, assumptions regarding the free-field-to-headphone transfer function, and the model’s over-prediction of spectral, loudness summation, a result found recently (Schlittenlacher et al., 2014) for the ANSI standard and DIN 45631.

Effect of Tactile Location, Pulse Duration, and Interpulse Interval on Perceived Urgency

Tactile displays hold promise as an effective and efficient means of presenting a wide range of information to the driver. This study examined the subjective perceptions of urgency and annoyance for tactile signals of different pulse duration, interpulse interval (IPI), and pulse pattern from devices called tactors located on the wrist, on the waist belt, or in the seat pan. Results revealed significant utility (steep increases in urgency without similarly steep increases in annoyance) for signals presented in pulse durations from 10 to 150 ms with decreasing utility beyond this range (200 ms or greater). Perceived urgency showed a decreasing trend as the IPI increased. Strikingly similar magnitude estimation functions were obtained across the three tactor locations. Results are discussed in terms of their implications for tactile display design in vehicles.

Tactile roughness perception with a rigid link interposed between skin and surface.

Subjects made roughness judgments of textured surfaces made of raised elements, while holding stick-like probes or through a rigid sheath mounted on the fingertip. These rigid links, which impose vibratory coding of roughness, were compared with the finger (bare or covered with a compliant glove), using magnitude-estimation and roughness differentiation tasks. All end effectors led to an increasing function relating subjective roughness magnitude to surface interelement spacing, and all produced above-chance roughness discrimination. Although discrimination was best with the finger, rigid links produced greater perceived roughness for the smoothest stimuli. A peak in the magnitude-estimation functions for the small probe and a transition from calling more sparsely spaced surfaces rougher to calling them smoother were predictable from the size of the contact area. The results indicate the potential viability of vibratory coding of roughness through a rigid link and have implications for teleoperation and virtual-reality systems.

On the nature and meaning of sinuosity in magnitude-estimation functions.

Magnitude-estimation functions for single observers, derived from multiple judgments of closely spaced stimuli, exhibit a sinuous form in logarithmic coordinates, an observation frequently confirmed since first reported by Luce and Mo (1965). We propose that this can result from reliance on a restricted pool of responses, called "preferred numbers" by Baird and Noma (1975). We describe a model featuring a response band centered on an assumed power function, from which the observer selects from among preferred numbers with equal probability. In simulations, the expected values of these selections oscillate around the underlying power function with an appearance similar to that of Luce-Mo functions. The appearance of these functions depends on values assumed for the scale factor of the power function, the range of intensities considered, and the width of the band from which responses are drawn. We conclude that sinuosity in magnitude-estimation functions does not disconfirm the psychophysical power law.

The shape of the vibrotactile loudness function: the effect of stimulus repetition and skin-contactor coupling.

In the psychophysical literature describing the relationships between physical and psychological magnitudes, as physical intensity increases, perceived intensity often grows much faster near threshold than at higher levels. In this laboratory, however, the loudness curve for sinusoidal vibrotactile stimuli was best fit by a single-limbed function rather than by the expected two-limbed function. In the present study, we measured the growth of vibrotactile loudness of 250-Hz sinusoidal stimuli by the method of absolute magnitude estimation to explore the source of the one- versus two-limbed discrepancy. The number of times that the stimulus was presented was varied, as well as whether the stimulator contacted the skin with constant force or constant penetration. Neither of these manipulations affected the shape of the loudness function consistently. Number of repetitions influenced the shapes of the magnitude estimation functions, but only for a few individuals. Skin-contactor coupling did not affect the shapes of the functions, although the absolute level (vibrotactile loudness) was consistently greater for constant indentation.

Individual magnitude estimation functions and their relation to the Pacinian (P) and non-Pacinian (NP) channels

Four distinct channels of information can combine to signal the sensation magnitude of tactile stimuli. For example, a 250-Hz vibratory stimulus of large size (2.9 cm2) and of low/moderate intensities activates the P channel, but at higher intensities the NP channels also are activated. Because of saturation and the potentially different functional properties of the various channels, crossing from one channel (e.g., P) to another (e.g. NP II) along the intensity domain may result in breaks in the overall sensation magnitude functions. Absolute magnitude estimation (AME) experiments were performed on six observers [250 Hz and narrow-band noise (175–350 Hz), 700-ms duration, 500-ms rise/fall time, thenar eminence, 2.9-cm2 contactor size; 15, 30, 40 °C skin surface temperature]. Results of individual observers were of particular interest since averaging across observers can obscure breaks due to idiosyncratic differences in their location. As previously shown, the averaged AME functions approximated power law relationships. The individual functions, however, were scalloped in shape with breaks that coincided with the individual P/NP II crossovers. Other breaks occurring at SL levels below the NP II threshold may be explained by the manner in which P corpuscle fibers entrain to vibratory stimuli and how this entrainment is disrupted by noise. [Work supported by NIH Grant Nos. DC00380 and DC00098.]

Magnitude estimation and cross-modal matching of lingual vibrotactile and auditory sensation.

The present experiment was a preliminary attempt to use the psychophysical scaling methods of magnitude estimation and cross-modal matching to investigate suprathreshold judgments of lingual vibrotactile and auditory sensation magnitudes for 20 normal young adult subjects. A 250-Hz lingual vibrotactile stimulus and a 1000-Hz binaural auditory stimulus were employed. To obtain judgments for nonoral vibrotactile sensory magnitudes, the thenar eminence of the hand was also employed as a test site for 5 additional subjects. Eight stimulus intensities were presented during all experimental tasks. The results showed that the slopes of the log-log vibrotactile magnitude estimation functions decreased at higher stimulus intensity levels for both test sites. Auditory magnitude estimation functions were relatively constant throughout the stimulus range. Cross-modal matching functions for the two stimuli generally agreed with functions predicted from the magnitude estimation data, except when subjects adjusted vibration on the tongue to match auditory stimulus intensities. The results suggested that the methods of magnitude estimation and cross-modal matching may be useful for studying sensory processing in the speech production system. However, systematic investigation of response biases associated with vibrotactile-auditory psychophysical scaling tasks appears to be a prerequisite.

Response characteristics of peripheral mechanoreceptive units in man: Relation to the sensation magnitude and to the subject's task

The characteristics of responses of 23 peripheral mechanoreceptive units to tactile pulses of varying amplitude (50–950 μm) were studied by means of human microneurography during two different tasks. The simultaneously recorded unit responses were related to estimates of sensation magnitude in order to study the coding properties of units. The possible effects of the tasks were studied by comparing the responses to identical stimulus pulses during the two tasks. The S-R functions of single units had smaller exponents than the magnitude estimation functions, but the relation between the number of impulses/frequency of impulses and the simultaneously given magnitude estimate was well described by linear function for 74% of units. Thus both of these parameters may serve as codes for stimulus amplitude. For 18 units differences were obtained between the two task situations when thresholds, latency of the first impulse, mean frequency of impulses, or number of impulses in responses were compared. The differences were partly due to a continous decrease of sensitivity of units with time. However, the results indicate also that the sensitivity of the units was higher during the magnitude estimation than during the counting task. The effect of the task of the subject on the sensitivity of the peripheral mechanoreceptive units may be mediated through direct neural connections. The results indicate that the reorganization of the neural processes according to the task of the subject is not limited to the central nervous system, but involves also the periphery.

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.

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.

Peripheral neural basis of tactile sensations in man: I. Effect of frequency and probe area on sensations elicited by single mechanical pulses on hairy and glabrous skin of the hand

Tactile thresholds and sensation magnitudes for single mechanical pulses of varying frequency and probe area were studied in order to provide psychophysical data for correlations of tactile sensations with functional properties of different types of human peripheral nerve fibers. Single mechanical pulses were delivered to the hairy or glabrous skin of the hand by means of a perspex probe (area 0.07, 0.7, 3.1, or 12.5 sq.-mm) fixed to the moving coil of an electromechanical vibrator. The frequency of the single pulse was 20, 60 or 150 Hz. Absolute and touch thresholds were measured with a method of production. Suprathreshold sensations were measured with the method of magnitude estimation (6 predetermined displacement amplitudes ranging from 50 to 950 μm). Both absolute and touch thresholds were significantly higher on the hairy than on the glabrous skin. The absolute thresholds varied between 44 and 140 μm on the hairy and between 9 and 45 μm on the glabrous skin; the touch threshold varied between 75 and 300 μm and 24 and 153 μm, respectively. Lower threshold values were obtained on both skin areas with increasing frequency of the pulse and probe area, the latter effect being significant only for the hairy skin. Standardized magnitude estimation functions could be described with power functions on both skin areas, the exponents of the functions varying between 0.70 and 1.41 on the hairy and between 0.55 and 0.86 on the glabrous skin. The equi-sensation contours showed the difference of sensitivity between the skin areas. Larger sensation magnitudes were obtained with increasing frequency of the pulse and probe area on both skin areas. These psychophysical findings indicate that there is a functional difference at absolute sensation thresholds between hairy and glabrous skin. This difference, however, disappears at higher sensation levels.

Electrocutaneous psychophysical input-output functions and temporal integration.

Electrocutaneous magnitude estimation functions were generated by stimuli ranging from 1.0 to 5.0 mA and from 100 to 6,400 msec in duration. The results indicate that when these functions are fitted by a two-parameter power function (ME = aIb), the values of the constant, a, and the exponent, b, are altered by increases in stimulus duration, with a increasing and b decreasing. The exponent decreases from around 1.4 to 0.93 as duration increases from 100 to 6,400 sec. Equal magnitude estimation contours drawn for estimates ranging from “2“ to “50“ can be fitted by an equation representing partial integration, I × ta = K. The exponent a decreases as a function of the level of the magnitude estimation, indicating less partial integration at higher than at lower levels of estimated magnitude. The electrocutaneous data are compared to data in other sensory modalities.

Categorization of tonal intervals by musicians: Perceptual effect or response bias?

Siegel and Sopo [J. Acoust. Soc. Am. 57, 511 (1975)] presented data from a magnitude estimation study in which musicians judged the size of 20 tonal intervals spread over five semitones. It was found that some musicians showed five discrete steps in their magnitude estimation functions, that they used only five different numerical responses, and that they reported hearing the stimuli as “in tune.” We interpreted these findings as evidence for categorical perception of intervals. One could, however, infer that the step functions resulted from a simple response bias, a tendency to round off the numerical ratings to a value corresponding to the nearest semitone. Here we present data of other musicians in the same task who attempted to make finer discriminations, and used more than five response categories. The data showed that, even though these subjects detected out-of-tune intervals, their magnitude estimates had definite scallops corresponding to the chromatic scale in some musicians, and to the diatonic scale in others. Moreover, the variability of responding was cyclical, with the largest standard deviations occurring at the category boundaries. Our results converge with those of Burns and Ward [J. Acoust. Soc. Am. 55, 456 (1974)] which demonstrate categorical perception of intervals in a forced-choice discrimination task.

Tonal intervals are perceived categorically by musicians with relative pitch

Musicians with relative pitch were tested in interval-naming and magnitude-estimation experiments. They judged 20 intervals ranging over five musical categories, from unison to a major third. The results indicated that, for some musicians, the naming distributions showed sharp category boundaries, as with speech continua, and the magnitude-estimation functions showed discrete steps corresponding to the standard musical categories. Some subjects used only five different numbers in the magnitude estimation task, even though there were 20 physically different intervals. Post-experimental interviews revealed (a) that subjects who categorized believed that most of the stimuli were “in tune” even though three-fourths were inaccurate musically; and (b) that tonal intervals possess unique sound qualities. We conclude that categorical perception is not unique to speech, but may occur for other physical continua which subjects learn to identify over a protracted period of time.