Stimulus selection in adaptive psychophysical procedures

In adaptive psychophysical procedures, the stimulus should be presented at a relatively high level rather than near the middle of the psychometric function, which is often defined as the "threshold" value. For some psychometric functions, the optimal stimulus placement level produces 84% to 94% correct responses in a two-alternative forced-choice task. This result is disquieting because the popular two-down one-up rule tracks a relatively low percentage of correct responses, 70.7%. Computer simulations and a variety of psychometric functions were used to confirm the validity of this analysis. These simulations also demonstrate that the precise form of the psychometric function is not critical in achieving the high efficiencies. Finally, data from human listeners indicate that the standard deviation of threshold estimates is indeed larger when the stimulus presented on each trial is at a stimulus level corresponding to 70.7% rather than 94% correct responses.     

A comparison of adaptive procedures for rapid and reliable threshold assessment and training in naive listeners

In psychoacoustic studies there is often a need to assess performance indices quickly and reliably. The aim of this study was to establish a quick and reliable procedure for evaluating thresholds in backward masking and frequency discrimination tasks. Based on simulations, four procedures likely to produce the best results were selected, and data collected from 20 naive adult listeners on each. Each procedure used one of two adaptive methods (staircase or maximum-likelihood estimation, each targeting the 79% correct point on the psychometric function) and two response paradigms (3-interval, 2-alternative forced-choice AXB or 3-interval; 3-alternative forced-choice oddball). All procedures yielded statistically equivalent threshold estimates in both backward masking and frequency discrimination, with a trend to lower thresholds for oddball procedures in frequency discrimination. Oddball procedures were both more efficient and more reliable (test-retest) in backward masking, but all four procedures were equally efficient and reliable in frequency discrimination. Fitted psychometric functions yielded similar thresholds to averaging over reversals in staircase procedures. Learning was observed across threshold-assessment blocks and experimental sessions. In four additional groups, each of ten listeners, trained on the different procedures, no differences in performance improvement or rate of learning were observed, suggesting that learning is independent of procedure.     

A single-interval adjustment-matrix (SIAM) procedure for unbiased adaptive testing

A new unbiased adaptive procedure is described that requires only half as many presentations in achieving the same precision as the well-known two-interval forced-choice (2IFC) 2-step procedure. The procedure is based on a yes-no task which avoids redundant presentation time. Furthermore, certain psychophysical studies can only be realized with yes-no tasks. Every trial contains randomly presented signals or noises and the answer is either yes or no. The outcome (hit, miss, false alarm, correct rejection) is taken into account by adjusting the signal level in a staircase manner. The adjustment matrix is set up to induce a neutral response criterion. Its convergence point can be adjusted at will. The single-interval adjustment-matrix (SIAM) procedure is compared to von Békésy and 2IFC transformed up-down methods using a Monte-Carlo simulation. The SIAM procedure proves to be the fastest of the unbiased procedures. A test on four subjects verified these results. Implications for optimum track length and the number of reversals to discard are discussed.     

Adaptive staircase techniques in psychoacoustics: a comparison of human data and a mathematical model

Data from a simple tone-in-noise simultaneous masking task were used to evaluate each of two common adaptive staircase rules (a "1 up 2 down" rule and a "1 up 3 down" rule) and the parameter estimation by sequential testing (PEST) technique in combination with each of two psychophysical procedures [a two-alternative forced-choice (2AFC) and a three-alternative forced-choice (3AFC) procedure]. These human data were compared to predictions generated by a mathematical model based on Markov theory. The model predicts that threshold estimates obtained with the adaptive techniques should be equal to those derived with equivalent "fixed signal level" techniques. However, the human data indicate that the adaptive techniques tend to yield lower thresholds. The model predicts that the standard error of a threshold estimate obtained from an adaptive technique will decrease and approach zero as the number of trials used to compute the estimate increases. The human data show greater variability than predicted and approach a nonzero value as the number of trials increases. The predictions of the model suggest that the commonly used combination of the 2AFC procedure and the 1 up 2 down rule is the least efficient method of estimating a threshold and that the 3AFC procedure in combination with the 1 up 3 down rule is the most efficient method. The human data are less consistent, but generally show the combination of the 2AFC procedure and the 1 up 2 down rule to be one of the least efficient methods. Possible explanations for the differences between the model's predictions and the human data, as well as suggestions for laboratory practice, are discussed.     

A comparison of threshold estimation methods in children 6-11 years of age

Estimating detection threshold for auditory stimuli in children can be problematic because of lapses in attention and the time limits usually imposed by scheduling restrictions or fatigue. Data reported here were collected to compare the stability of threshold estimation procedures in testing children ages 6 to 11 in a three-alternative, forced-choice paradigm. Stimuli consisted of a 1-kHz tonal signal and a Gaussian noise masker, bandpass filtered between 500-2,000 Hz and presented at 25-dB spectrum level. The signal was either presented for 400 ms in the presence of a continuous masker (simultaneous masking) or for 10 ms just prior to a 400-ms masker (backward masking). For each masking paradigm the 79% correct threshold was assessed via each of three procedures: 3-down, 1-up adaptive staircase (Levitt), maximum likelihood estimation (MLE), and method of constant stimuli. Percent correct was measured at the end of the study for a signal 10 dB above the previously determined threshold in order to estimate the most appropriate psychometric function asymptote for fitting data collected via the method of constant stimuli. Both the MLE and Levitt procedures produced equally stable threshold estimates for both conditions and age groups. This was the case despite considerable variability in backward-masking thresholds.     

A comparison of psychophysical procedures for level-discrimination thresholds

Five different psychophysical procedures were used to measure level-discrimination (also called intensity discrimination) thresholds for 1-kHz tones at two levels (30 and 90 dB SPL) and two durations (10 and 500 ms). The procedures were the classic transformed up-down staircase method with a two-alternative forced-choice (2AFC) paradigm (UPD), 15- and 50-trial implementations of the method of maximum likelihood (MML) with a cued yes-no paradigm, and 18-trial implementations of ZEST using both cued yes-no and 2AFC paradigms. Results obtained from nine normal listeners show that estimates of level-discrimination thresholds for the four conditions are similar across all five procedures when different points of convergence are accounted for. The variance of threshold estimates within listener and condition was smallest for UPD, largest for the MML with 15 trials, and statistically indistinguishable among the others. The sweat factors ranged from 5.5 for MML with 50 trials to about 1.4 for UPD and ZEST. Simulations show that ideal performance of procedures may be far from real-life experience and that these deviations are likely to depend on complex interactions between listener behavior and parameter choices used for implementing the procedures. Therefore, empirical verification is important for judging the effectiveness of psychophysical procedures.     

Cochlear nucleus, inferior colliculus, and medial geniculate responses during the behavioral detection of threshold-level auditory stimuli in the rabbit

Rabbits were conditioned to respond behaviorally to auditory stimuli by pairing a white-noise conditioned stimulus (CS) with a corneal airpuff unconditioned stimulus (US). The conditioned response (CR) was movement of the nictitating membrane (NM). After the subjects were responding at better than the 90% correct level, the intensity of the auditory stimulus was reduced to behavioral threshold using a staircase procedure. Simultaneous measurements of neural unit activity and behavioral NM responses were then made in rabbits performing at behavioral threshold. After the experiment was completed neural unit responses during behavioral detection trials were compared to neural responses made during nondetection trials. Neural unit responses to a constant intensity, white-noise stimulus at behavioral threshold were well defined and essentially identical on behavioral detection and nondetection trials in the ventral cochlear nucleus, the ventrolateral division of the central nucleus of the inferior colliculus, and the ventral division of the medial geniculate body. This suggests that an auditory stimulus can be neuronally "detected" without being behaviorally detected, and that the neural "decision" to respond behaviorally is not made in these nuclei. Responses recorded from the dorsomedial division of the central nucleus of the inferior colliculus, the pericentral nucleus of the inferior colliculus, and less commonly in the medial division of the medial geniculate body were also clearly present and nearly identical during the onset of the auditory stimulus, but were sometimes consistently different for detection and nondetection conditions during the latter part of the auditory stimulus. These brain regions appear to receive both auditory and nonauditory inputs, and show responses which are more highly correlated with detection behavior.     

Effect of variability in level on forward masking and on increment detection

In the first of four experiments, all with the same four subjects, varying the level of a forward masker from interval to interval in a two-interval forced-choice (2IFC) adaptive procedure had little effect on threshold. In the second experiment, the signal level was fixed and performance was measured in units of d'. Varying the level of the forward masker again had little effect. Analyses of trial-by-trial data indicated that subjects did not vote for the interval with the higher-level masker, as would an energy detector. Performance was better on trials where the masker level in the interval with the signal was lower and was relatively independent of masker level in the nonsignal interval. In the third experiment, these results were replicated for a wider range of masker variability and with maskers lower in frequency than the signal. In the fourth experiment, the same range of variability from interval to interval was imposed on the level of the pedestal in an increment-detection task. Results were similar to those observed in forward masking. The results suggest that decision processes involved in both forward masking and increment detection are similar and that neither is based on energy detection. Template matching remains a viable alternative.     

Efficient adaptive procedures for threshold and concurrent slope estimates for psychophysics and speech intelligibility tests

The minimum standard deviations achievable for concurrent estimates of thresholds and psychometric function slopes as well as the optimal target values for adaptive procedures are calculated as functions of stimulus level and track length on the basis of the binomial theory. The optimum pair of targets for a concurrent estimate is found at the correct response probabilities p1 = 0.19 and p2 = 0.81 for the logistic psychometric function. An adaptive procedure that converges at these optimal targets is introduced and tested with Monte Carlo simulations. The efficiency increases rapidly when each subject's response consists of more than one statistically independent Bernoulli trial. Sentence intelligibility tests provide more than one Bernoulli trial per sentence when each word is scored separately. The number of within-sentence trials can be quantified by the j factor [Boothroyd and Nittrouer, J. Acoust. Soc. Am. 84, 101-114 (1988)]. The adaptive procedure was evaluated with 10 normal-hearing and 11 hearing-impaired listeners using two German sentence tests that differ in j factors. The expected advantage of the sentence test with the higher j factor was not observed, possibly due to training effects. Hence, the number of sentences required for a reliable speech reception threshold (approximately 1 dB standard deviation) concurrently with a slope estimate (approximately 20%-30% relative standard deviation) is at least N = 30 if word scoring for short, meaningful sentences (j approximately 2) is performed.     

Child and adult vibrotactile thresholds for sinusoidal and pulsatile stimuli

Three experiments were performed to obtain vibrotactile sensitivity thresholds from hearing children and adults, and from deaf children. An adaptive two-interval forced-choice procedure was used to obtain estimates of the 70.7% point on the psychometric sensitivity curve. When hearing children of 5-6 and 9-10 years of age and adults were tested with sinusoids and haversine pulse stimuli, at 10, 100, 160, and 250 Hz or pps, respectively, only the 10-Hz stimulus resulted in an age effect. For this stimulus, young children were significantly less sensitive than adults. When sinusoids were again tested at 20, 40, 80, and 160 Hz, a small overall effect of age was observed with a significant effect only at 20 Hz. Two prelingually profoundly deaf children were tested with haversine pulse trains at 10, 50, 100, 160, and 250 pps. Both children were at least as sensitive to the tactile stimulation as were the hearing children and adults. Pulsatile stimulation, compared to sinusoidal stimulation, exhibited relatively flat threshold versus frequency functions. The present results, demonstrating no age effect for pulsatile stimulation and similar performance for deaf and hearing children, suggest that pulsatile stimulation would be appropriate in vibrotactile speech communication aids for the deaf.     

Stochastic properties of cat auditory nerve responses to electric and acoustic stimuli and application to intensity discrimination

Statistical properties of electrically stimulated (ES) and acoustically stimulated (AS) auditory nerve fiber responses were assessed in undeafened and short-term deafened cats, and a detection theory approach was used to determine fibers' abilities to signal intensity changes. ES responses differed from AS responses in several ways. Rate-level functions were an order of magnitude steeper, and discharge rate normally saturated at the stimulus pulse rate. Dynamic ranges were typically 1-4 dB for 200 pps signals, as compared with 15-30 dB for AS signals at CF, and they increased with pulse rate without improving threshold or changing absolute rate-level function slopes. For both ES and AS responses, variability of spike counts elicited by repeated trials increased with level in accord with Poisson-process predictions until the discharge rate exceeded 20-40 spikes/s. AS variability continued increasing monotonically at higher discharge rates, but more slowly. In contrast, maximum ES variability was usually attained at 100 spikes/s, and at higher discharge rates variability reached a plateau that was either maintained or decreased slightly until discharge rate approached the stimulus pulse rate. Variability then decreased to zero as each pulse elicited a spike. Increasing pulse rate did not substantially affect variability for rates up to 800 pps; rather, higher pulse rates simply extended the plateau region. Spike count variability was unusually high for some ES fibers. This was traced to response nonstationarities that stemmed from two sources, namely level-dependent fluctuations in excitability that occurred at 1-3 s intervals and, for responses to high-rate, high-intensity signals, fatigue that arose when fibers discharged at their maximum possible rates. Intensity discrimination performance was assessed using spike count as the decision variable in a simulated 2IFC task. Neurometric functions (percent correct versus intensity difference) were obtained at several levels of the standard (I), and the intensity difference (delta I) necessary for 70% correct responses was estimated. AS Weber fractions (10 log delta I/I) averaged +0.2 dB (delta IdB = 3.1 dB) for 50 ms tones at CF. ES Weber fractions averaged -12.8 dB (delta IdB = 0.23 dB) for 50 ms, 200 pps signals, and performance was approximately constant between 100 and 1000 pps. Intensity discrimination by single cells in ES conditions paralleled human psychophysical performance for similar signals. High ES sensitivity to intensity changes arose primarily from steeper rate-level functions and secondarily from reduced spike count variability.     

Probe tone thresholds in the auditory nerve measured by two-interval forced-choice procedures

An important goal of auditory physiology is to relate the coding of signals in the auditory nerve to behavioral sensitivity. A useful step towards that goal is to measure physiological thresholds for the detection of tones in the neural spike train that are comparable to psychophysical thresholds. Detectability depends on the variability as well as the mean value of the response. A two-interval forced-choice task provides a criterion-free measure of detectability. On each trial of our experiments a probe tone was taken to be correctly detected if the number of spikes in response to the tone exceeded the number of spikes in an otherwise identical interval that did not contain the probe tone. (Analysis of the pulse-number distributions also allowed construction of ROC curves directly comparable to psychophysical ROC curves.) The proportion of trials that yielded correct detections was measured as a function of stimulus intensity to form a neurometric function, directly comparable to a psychophysical psychometric function. Threshold was defined as the intensity that produced a given proportion correct. The threshold intensity was also measured by an up-down procedure. Agreement between the two measures of threshold was excellent. Using the up-down procedure we could measure threshold in about 1 min, making it practical to measure the thresholds of a single neuron for many conditions. Comparisons of physiological and psychophysical ROC curves and neurometric and psychometric functions show systematic differences indicating that the animal makes its decisions inefficiently, perhaps by basing its decision on the maximum response among many neurons, rather than just the activity of the single most sensitive neuron.     

Comparison of adaptive psychometric procedures motivated by the theory of optimal experiments: simulated and experimental results

The wide use of psychometric assessments and the time necessary to conduct comprehensive psychometric tests has motivated significant research into the development of psychometric testing procedures that will provide accurate and efficient estimates of the parameters of interest. One potential framework for developing adaptive psychometric procedures is the Theory of Optimal Experiments. The Theory of Optimal Experiments provides several metrics for determining informative stimulus values based on a model of the psychometric function to be provided by the investigator. In this study, two methods based on a previous implementation of the Theory of Optimal Experiments are presented for comparison to two fixed step size staircase methods and also an existing adaptive method that utilizes a Bayesian framework. The psychometric procedures were used to measure detection thresholds and discrimination limens on two separate psychoacoustic tasks with normal-hearing subjects. Computer simulations were performed based on the outcomes of the experimental psychoacoustic detection task to analyze performance over a large sample size in the case of known truth. Results suggest that the proposed stimulus selection rules motivated by the Theory of Optimal Experiments perform better than previous techniques and also extend estimation to multiple parameters.     

Simultaneously measured behavioral and electrophysiological hearing thresholds in a bottlenose dolphin (Tursiops truncatus)

Dolphin auditory thresholds obtained via evoked potential audiometry may deviate from behavioral estimates by 20 dB or more. Differences in the sound source, stimulus presentation method, wave form, and duration may partially explain these discrepancies. To determine the agreement between behavioral and auditory evoked potential (AEP) threshold estimates when these parameters are held constant, behavioral and AEP hearing tests were simultaneously conducted in a bottlenose dolphin. Measurements were made in-air, using sinusoidal amplitude-modulated tones continuously projected via a transducer coupled to the pan region of the dolphin's lower jaw. Tone trials were presented using the method of constant stimuli. Behavioral thresholds were estimated using a 50% correct detection. AEP thresholds were based on the envelope following response and 50% correct detection. Differences between AEP and behavioral thresholds were within +/-5 dB, except at 10 kHz (12 dB), 20 kHz (8 dB), 30 kHz (7 dB), and 150 kHz (24 dB). In general, behavioral thresholds were slightly lower, though this trend was not significant. The results demonstrate that when the test environment, sound source, stimulus wave form, duration, presentation method, and analysis are consistent, the magnitude of the differences between AEP and behavioral thresholds is substantially reduced.     

Evidence for an analytic perception of multiharmonic sounds in the bat, Megaderma lyra, and its possible role for echo spectral analysis

For echolocation, the gleaning bat Megaderma lyra relies on short and broadband calls consisting of multiple harmonic components, each of which is downward frequency modulated. The harmonic components in M. lyra's calls have a relatively small frequency excursion and do not overlap spectrally. Broadband calls of other bat species, on the other hand, often consist of only a few harmonics which are modulated over broad and sometimes overlapping frequency ranges. A call consisting of narrow and nonoverlapping harmonic components may provide a less complete representation of target structure than a call which consists of broadly modulated components. However, a multiharmonic call may help the bats to perceive local spectral changes in the echo from shifts in the peak frequencies of single harmonics, and thereby to extract additional information about the target. To assess this hypothesis, the accuracy with which M. lyra can analyze frequency shifts of single partials in multiharmonic complex tones was investigated. A two-alternative, forced-choice behavioral task was used to measure M. lyra's frequency discrimination threshold for the third partial in complex tones whose spectral composition resembled that of the bat's sonar calls. The discrimination threshold for the third partial in a 21.5-kHz harmonic tone amounted to about 2% and was similar to the bat's pure-tone discrimination threshold at 64.5 kHz. Discrimination performance was essentially unaffected by random frequency changes of the other partials and by reducing stimulus duration from 50.5 to 1.5 ms. Both findings are in accordance with predictions made on the basis of the shape of M. Ivra's cochlear filters. The comparison between the observed frequency discrimination performance and a computational estimate of the expected frequency shift in the third harmonic of an echo reflected by a simple, two-front target showed that M. lyra's frequency resolution is sufficient for analyzing the target-specific information conveyed by shifts in the peak frequency of single echo components.     

A maximum-likelihood procedure for estimating psychometric functions: Thresholds, slopes, and lapses of attention

Green [J. Acoust. Soc. Am. 87, 2662-2674 (1990)] suggested an efficient, maximum-likelihood-based approach for adaptively estimating thresholds. Such procedures determine the signal strength on each trial by first identifying the most likely psychometric functions among the pre-proposed alternatives based on responses from previous trials, and then finding the signal strength at the "sweet point" on that most likely function. The sweet point is the point on the psychometric function that is associated with the minimum expected variance. Here, that procedure is extended to reduce poor estimates that result from lapses in attention. The sweet points for the threshold, slope, and lapse parameters of a transformed logistic psychometric function are derived. In addition, alternative stimulus placement algorithms are considered. The result is a relatively fast and robust estimation of a three-parameter psychometric function.     

Effects of frequency modulation on absolute, masked, and reflex thresholds

Behavioral and acoustic reflex thresholds were determined for five normal-hearing subjects in response to carrier signals of 500 and 2000 Hz which were unmodulated or modulated sinusoidally at rates of 2, 20, and 200 times per second with frequency deviations (delta f) of 30, 100, and 300 Hz. Behavioral (absolute and masked) thresholds were determined using an adaptive two-alternative forced-choice procedure. Acoustic reflex thresholds were determined by visual inspection of stored reflex waveforms. Frequency modulation was not found to exert a systematic effect at absolute threshold. Frequency modulation did affect threshold estimates systematically, but differentially, at masked threshold and acoustic reflex threshold. Increasing the frequency deviation of the modulation was associated with an increase in masked threshold and with a decrease in acoustic reflex threshold at both test frequencies. The findings are discussed in terms of critical band phenomena.     

Effects of interaural decorrelation and acoustic spectrum on detecting the motion of an auditory target

The ability to detect the motion of an auditory target based on dynamic changes in interaural time differences was measured as a function of interaural correlation and acoustic spectrum in a single-interval forced-choice design. Three subjects listened to headphone-presented noise containing a dynamic linear change in interaural delay (500 μs/s). The stimulus spectrum was broadband (0.1 to 10 kHz), highpass above 1.5 kHz, or lowpass below 1.2 kHz, and interaural correlation ranged from 0.1 to 1.0. Subject performance was nearly identical for the broadband and lowpass conditions, with near perfect detection for interaural correlations of 0.5 or greater, and above threshold (d′ > 1) detection for a correlation of 0.3. Performance was near random when the correlation was 0.1. In the highpass condition, performance rapidly deteriorated from substantially above threshold (d′ > 2) to random level as interaural correlation was reduced from 1.0 to 0.7. This rapid decline in performance at high frequencies may be explained in terms of interaural envelope decorrelation. The text was submitted by the authors in English.     

Sensory threshold estimation from a continuously graded response produced by reflex modification audiometry

This article describes the use of reflex modification to determine sensory detection thresholds. The method is based upon the finding that low-intensity sensory stimuli presented shortly before a reflex eliciting stimulus are able to modify the amplitude of the reflex. The extent of such modification is related to the intensity of the initial low-intensity stimulus. In contrast to earlier reported procedures for threshold estimation, the method described in this article consists of fitting a smooth function to the relationship between startle response amplitude and the intensity of the inhibiting stimulus. The method entails fitting a cubic spline function to the medians of the square-root reflex amplitude at each prestimulus intensity. The resulting audiometric curves closely approximate audiometric data obtained from traditional operant methods both in sensitivity and shape. Parametric data are also presented that allow for optimizing stimulus presentation so as to obtain reliable thresholds using a minimal number of test trials. The procedures developed in this article may prove useful in other situations involving the estimation of a threshold effect from a continuously graded response.     

Dolphin and sea lion auditory evoked potentials in response to single and multiple swept amplitude tones

Measurement of the auditory steady-state response (ASSR) is increasingly used to assess marine mammal hearing. These tests normally entail measuring the ASSR to a sequence of sinusoidally amplitude modulated tones, so that the ASSR amplitude function can be defined and the auditory threshold estimated. In this study, an alternative method was employed, where the ASSR was elicited by an amplitude modulated stimulus whose sound pressure level was slowly varied, or "swept," over a range of levels believed to bracket the threshold. The ASSR amplitude function was obtained by analyzing the resulting grand average evoked potential using a short-time Fourier transform. The suitability of this technique for hearing assessment of bottlenose dolphins and California sea lions was evaluated by comparing ASSR amplitude functions and thresholds obtained with swept amplitude and discrete, constant amplitude stimuli. When factors such as the number of simultaneous tones, the number of averages, and the frequency analysis window length were taken into account, the performance and time required for the swept-amplitude and discrete stimulus techniques were similar. The decision to use one technique over another depends on the relative importance of obtaining suprathreshold information versus the lowest possible thresholds.