Subjective time: Cognitive and physical secondary tasks affect timing differently

Humans were trained on a temporal discrimination to make one response when the stimulus duration was short (2 s) and a different response when the stimulus duration was long (8 s). They were then tested with stimulus durations in between to determine the bisection point. In Experiment 1, we examined the effect of a secondary cognitive task (counting backwards by threes) on the bisection point when participants were trained without a cognitive load and were tested with a cognitive load or the reverse (relative to appropriate controls). When the cognitive load increased from training, the psychophysical function plotting long responses against the increase in stimulus duration shifted to the right (as if the internal clock slowed down), and when the cognitive load decreased from training the psychophysical function shifted to the left (as if the internal clock speeded up). In Experiment 2, when the secondary task consisted of exerting continuous force on a transducer (a physically effortful task), it had the opposite effect. When the required force increased from training, the psychophysical function shifted to the left (as if the internal clock speeded up), and when the required force decreased from training, the psychophysical function shifted to the right (as if the internal clock slowed down). The results support an attentional view of the subjective passage of time. A cognitive secondary task appears to decrease attention to temporal cues, resulting in the underestimation of the passage of time, whereas a force requirement appears to increase attention to temporal cues, resulting in the overestimation of the passage of time.     

The psychometric function: I. Fitting, sampling, and goodness of fit.

The psychometric function relates an observer's performance to an independent variable, usually some physical quantity of a stimulus in a psychophysical task. This paper, together with its companion paper (Wichmann & Hill, 2001), describes an integrated approach to (1) fitting psychometric functions, (2) assessing the goodness of fit, and (3) providing confidence intervals for the function's parameters and other estimates derived from them, for the purposes of hypothesis testing. The present paper deals with the first two topics, describing a constrained maximum-likelihood method of parameter estimation and developing several goodness-of-fit tests. Using Monte Carlo simulations, we deal with two specific difficulties that arise when fitting functions to psychophysical data. First, we note that human observers are prone to stimulus-independent errors (or lapses). We show that failure to account for this can lead to serious biases in estimates of the psychometric function's parameters and illustrate how the problem may be overcome. Second, we note that psychophysical data sets are usually rather small by the standards required by most of the commonly applied statistical tests. We demonstrate the potential errors of applying traditional chi2 methods to psychophysical data and advocate use of Monte Carlo resampling techniques that do not rely on asymptotic theory. We have made available the software to implement our methods.     

Subjective time: cognitive and physical secondary tasks affect timing differently

Humans were trained on a temporal discrimination to make one response when the stimulus duration was short (2 s) and a different response when the stimulus duration was long (8 s). They were then tested with stimulus durations in between to determine the bisection point. In Experiment 1, we examined the effect of a secondary cognitive task (counting backwards by threes) on the bisection point when participants were trained without a cognitive load and were tested with a cognitive load or the reverse (relative to appropriate controls). When the cognitive load increased from training, the psychophysical function plotting long responses against the increase in stimulus duration shifted to the right (as if the internal clock slowed down), and when the cognitive load decreased from training the psychophysical function shifted to the left (as if the internal clock speeded up). In Experiment 2, when the secondary task consisted of exerting continuous force on a transducer (a physically effortful task), it had the opposite effect. When the required force increased from training, the psychophysical function shifted to the left (as if the internal clock speeded up), and when the required force decreased from training, the psychophysical function shifted to the right (as if the internal clock slowed down). The results support an attentional view of the subjective passage of time. A cognitive secondary task appears to decrease attention to temporal cues, resulting in the underestimation of the passage of time, whereas a force requirement appears to increase attention to temporal cues, resulting in the overestimation of the passage of time.     

A COGNITIVE THEORY OF PSYCHOPHYSICS. II

The fundamental premise of this paper is that subjects code information in such a way that a variety of psychophysical functions can be obtained with the same stimulus attributes. Four terms must be defined in order to understand psychophysical equations. These terms are: (1) The subject's perceptual channel capacity, (2) the subject's cognitive channel capacity, (3) the experimenter's measure of stimulus information, and (4) the context variables associated with the psychophysical procedure.     

The psychometric function: I. Fitting, sampling, and goodness of fit

The psychometric function relates an observer’s performance to an independent variable, usually some physical quantity of a stimulus in a psychophysical task. This paper, together with its companion paper (Wichmann & Hill, 2001), describes an integrated approach to (1) fitting psychometric functions, (2) assessing the goodness of fit, and (3) providing confidence intervals for the function’s parameters and other estimates derived from them, for the purposes of hypothesis testing. The present paper deals with the first two topics, describing a constrained maximum-likelihood method of parameter estimation and developing several goodness-of-fit tests. Using Monte Carlo simulations, we deal with two specific difficulties that arise when fitting functions to psychophysical data. First, we note that human observers are prone to stimulus-independent errors (orlapses). We show that failure to account for this can lead to serious biases in estimates of the psychometric function’s parameters and illustrate how the problem may be overcome. Second, we note that psychophysical data sets are usually rather small by the standards required by most of the commonly applied statistical tests. We demonstrate the potential errors of applying traditionalX ² methods to psychophysical data and advocate use of Monte Carlo resampling techniques that do not rely on asymptotic theory. We have made available the software to implement our methods.     

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.     

The duality principle: irreducibility of sub-threshold psychophysical computation to neuronal brain activation

A key working hypothesis in neuroscience is ‘materialistic reductionism’, i.e., the assumption whereby all physiological, behavioral or cognitive phenomena is produced by localized neurochemical brain activation (but not vice versa). However, analysis of sub-threshold Weber’s psychophysical stimulation indicates its computational irreducibility to the direct interaction between psychophysical stimulation and any neuron/s. This is because the materialistic-reductionistic working hypothesis assumes that the determination of the existence or non-existence of any psychophysical stimulation [s] may only be determined through its direct interaction [di1] with a given neuron/s [N] that together forms the ‘neural registry’ computational level [NR/di1]. But, this implies that in cases of (initial) sub-threshold (sensory-specific) psychophysical stimulation which is increased above the sensory-specific threshold but below Weber’s psychophysical ‘dv’—the psychophysical computational processing [PCP] produces an apparently ‘computationally indeterminate’ output. This is because materialistic reductionism asserts the contingency of PCP upon the existence of a direct interaction between ‘s’ and ‘N’ within the NR/di1 level, but in the special case of Weber’s sub-threshold psychophysical stimulation the same PCP/di1 also asserts the non-existence of ‘s’ (as demanded by Weber’s psychophysical law). However, given robust empirical evidence indicating the capability of PCP to determine whether (or not) ‘s’ exists, we must conclude that PCP may not be carried out from within NR’s direct interaction between a particular psychophysical stimulation and any set of neuron/s in the brain. Hence, the Duality Principle asserts the conceptual irreducibility of sub-threshold psychophysical stimulation to any direct NR/di1: s-N interaction, thereby challenging the current materialistic-reductionistic assumption.     

The effects of age on sensory thresholds and temporal gap detection in hearing, vision, and touch

Differences in sensory function between young (n 5 42, 18—31 years old) and older (n 5 137, 60—88 years old) adults were examined for auditory, visual, and tactile measures of threshold sensitivity and temporal acuity (gap-detection threshold). For all but one of the psychophysical measures (visual gap detection), multiple measures were obtained at different stimulus frequencies for each modality and task. This resulted in a total of 14 dependent measures, each based on four to six adaptive psychophysical estimates of 75% correct performance. In addition, all participants completed the Wechsler Adult Intelligence Scale (Wechsler, 1997). Mean data confirmed previously observed differences in performance between young and older adults for 13 of the 14 dependent measures (all but visual threshold at a flicker frequency of 4 Hz). Correlational and principalcomponents factor analyses performed on the data from the 137 older adults were generally consistent with task and modality independence of the psychophysical measures.     

Perception of the form of stimulus increment as a method in assessment of the psychophysical relationship

Among numerous procedures for determination of the psychophysical relation, one approach has seldom been applied. Essential in this method is to present a set of stimuli whose intensity increases in fixed time following different forms. The objective stimulus increment, which the subjects perceive as linear growth directly, represents the inverse psychophysical relation. In this paper the method was tested in the fields of click frequency and sound pressure. This procedure was named "Perception of the Form of Stimulus Increment in Time". In comparison to other psychophysical approaches, this one has several advantages. The principal ones are the following: (1) In assessing the psychophysical relation it is not necessary to try to measure the perceptual magnitude; and (2) the psychophysical relation is directly determined by its dynamic pattern. In this paper modifications to the method are reported which facilitate the subject's task and avoid some differences in subjects' individual approaches to the task. The modified procedure leads to results satisfactory independent of the influence of the factors irrelevant to the psychophysical relationship.     

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.     

Fast and accurate measurement of taste and smell thresholds using a maximum-likelihood adaptive staircase procedure

This paper evaluates the use of a maximum-likelihood adaptive staircase psychophysical procedure (ML-PEST), originally developed in vision and audition, for measuring detection thresholds in gustation and olfaction. The basis for the psychophysical measurement of thresholds with the ML-PEST procedure is developed. Then, two experiments and four simulations are reported. In the first experiment, ML-PEST was compared with the Wetherill and Levitt up-down staircase method and with the Cain ascending method of limits in the measurement of butyl alcohol thresholds. The four Monte Carlo simulations compared the three psychophysical procedures. In the second experiment, the test-retest reliability of ML-PEST for measuring NaCl and butyl alcohol thresholds was assessed. The results indicate that the ML-PEST method gives reliable and precise threshold measurements. Its ability to detect malingerers shows considerable promise. It is recommended for use in clinical testing.     

Fast and accurate measurement of taste and smell thresholds using a maximum-likelihood adaptive staircase procedure.

This paper evaluates the use of a maximum-likelihood adaptive staircase psychophysical procedure (ML-PEST), originally developed in vision and audition, for measuring detection thresholds in gustation and olfaction. The basis for the psychophysical measurement of thresholds with the ML-PEST procedure is developed. Then, two experiments and four simulations are reported. In the first experiment, ML-PEST was compared with the Wetherill and Levitt up-down staircase method and with the Cain ascending method of limits in the measurement of butyl alcohol thresholds. The four Monte Carlo simulations compared the three psychophysical procedures. In the second experiment, the test-retest reliability of MLPEST for measuring NaCl and butyl alcohol thresholds was assessed. The results indicate that the ML-PEST method gives reliable and precise threshold measurements. Its ability to detect malingerers shows considerable promise. It is recommended for use in clinical testing.     

Ipsilateral loudness adaptation over multiple intensity levels

Could monaural loudness adaptation be a simple artifact of psychophysical contrast? From adaptation data based on the Ipsilateral Comparison Paradigm (ICP), A. J. Dange, J. S. Warm, E. M. Weiler, and W. N. Dember (1993) concluded that loudness adaptation was not an artifact of psychophysical contrast, but their conclusion was dependent on results from one intensity. This study, involving multiple intensities, re-examined the issue of contrast versus adaptation and generally supported the conclusions of Dange et al. The results also showed an unexpected asymmetry of adaptation based on the direction of the referent modulation used with the ICP technique. Some implications are discussed.     

The use of chromatic information for motion segmentation: differences between psychophysical and eye-movement measures

Previous psychophysical studies have shown that chromatic (red/green) information can be used as a segmentation cue for motion integration. We investigated the mechanisms mediating this phenomenon by comparing chromatic effects (and, for comparison, luminance effects) on motion integration between two measures: (i) directional eye movements with the notion that these responses are mediated mainly by low-level motion mechanisms, and (ii) psychophysical reports, with the notion that subjects' reports should employ higher-level (attention-based) mechanisms if available. To quantify chromatic (and luminance) effects on motion integration, coherent motion thresholds were obtained for two conditions, one in which the signal and noise dots were the same 'red' or 'green' chromaticity (or the same 'bright' or 'dark' luminance), referred to as homogeneous, and the other in which the signal and noise dots were of different chromaticities (or luminances), referred to as heterogeneous. 'Benefit ratios' (theta(HOM)/theta(HET)) were then computed, with values significantly greater than 1.0 indicating that chromatic (or luminance) information serves as a segmentation cue for motion integration. The results revealed a high and significant chromatic benefit ratio when the measure was based on psychophysical report, but not when it was based on an eye-movement measure. By contrast, luminance benefit ratios were roughly the same (and significant) for both measures. For comparison to adults, eye-movement data were also obtained from 3-month-old infants. Infants showed marginally significant benefit ratios in the luminance, but not in the chromatic, condition. In total, these results suggest that the use of chromatic information as a segmentation cue for motion integration relies on higher-level mechanisms, whereas luminance information works mainly through low-level motion mechanisms.     

Understanding the structural determinants of object confusion in memory: an assessment of psychophysical approaches to estimating visual similarity

Computer-generated shapes varying on visual dimensions such as curvature, tapering, and thickness have been used to investigate identification deficits in the category-specific visual agnosia (CSVA) Patient E.L.M.. However, whether the implemented variations on each of these dimensions were perceived by novice observers as "similar amounts of change" is unknown. To estimate distance in psychophysical shape space, sets of shapes were developed using two different scaling methods--an objective method based on visual search, and a subjective method based on judgments of similarity--and a third approach that did not involve scaling. How well each method estimated psychophysical shape space was assessed by measuring the confusions within memory among the shapes. The results suggested that, although neither of the approaches perfectly reflected psychophysical shape space, subjective scaling was a better estimator of distance in psychophysical shape space than were other approaches. The number of confusions produced on each set of shapes was used to develop a new set of shapes that accurately estimated distance in psychophysical shape space. These results suggest that a combination of approaches is preferable in order to accurately estimate distance in psychophysical shape space.     

Using contextual effects to derive psychophysical scales

This paper presents a functional measurement analysis of Parducci’s range-frequency theory. The theory provides a basis for (1)finding context-invariant psychophysical scales, (2)establishing the validity of rating scales, and (3) explaining contextual effects in judgment. In an experimental illustration, Ss judged the magnitude of numerals in nine different distributions. All data were used to obtain the psychophysical function for numerals and also to test the model. The large contextual effects were consistent with the model. Quantitative tests of fit supported the equal-interval assumption of the category scale. The psychophysical function appeared nearly linear but with a significant negative acceleration. The data were shown to be qualitatively inconsistent with generalizations of Helson’s theory of adaptation level and Johnson’s correlation-regression theory. They supported Parducci’s range-frequency theory and illustrated how it could be used to factor out contextual effects from effects of stimulus magnitude. Extensions of the range-frequency approach are also discussed.     

The perceptual buildup of three-dimensional structure from motion

We present a set of psychophysical experiments that measure the accuracy of perceived three-dimensional (3-D) structure derived from relative motion in the changing two-dimensional image. The experiments are motivated in part by a computational model proposed by Ullman (1984), called the incremental rigidity scheme, in which an accurate 3-D structure is built up incrementally, by considering images of moving objects over an extended time period. Our main conclusions are: First, the human visual system can derive an accurate model of the relative depths of moving points, even in the presence of noise in their image positions; second, the accuracy of the 3-D model improves with time, eventually reaching a plateau; and third, the 3-D structure currently perceived appears to depend on previous 3-D models. Through computer simulations, we relate the results of our psychophysical experiments with the predictions of Ullman's model.     

“Adaptation and repulsion in the figural after-effect” and the psychophysical theory

Data recently presented by Wilson (1965) seem to demonstrate the separate effects of adaptation and of after-effect repulsion during and following continued observation of a curved line. Inasmuch as the experiment was performed without apparent reference to the psychophysical theory of figural after-effects (Taylor, 1962), it is interesting to note that the results on adaptation agree qualitatively with one of the major presuppositions of the theory, and the results on repulsion agree quantitatively with its predictions.     

Psychophysics with children: Investigating the effects of attentional lapses on threshold estimates

When assessing the perceptual abilities of children, researchers tend to use psychophysical techniques designed for use with adults. However, children’s poorer attentiveness might bias the threshold estimates obtained by these methods. Here, we obtained speed discrimination threshold estimates in 6- to 7-year-old children in UK Key Stage 1 (KS1), 7- to 9-year-old children in Key Stage 2 (KS2), and adults using three psychophysical procedures: QUEST, a 1-up 2-down Levitt staircase, and Method of Constant Stimuli (MCS). We estimated inattentiveness using responses to “easy” catch trials. As expected, children had higher threshold estimates and made more errors on catch trials than adults. Lower threshold estimates were obtained from psychometric functions fit to the data in the QUEST condition than the MCS and Levitt staircases, and the threshold estimates obtained when fitting a psychometric function to the QUEST data were also lower than when using the QUEST mode. This suggests that threshold estimates cannot be compared directly across methods. Differences between the procedures did not vary significantly with age group. Simulations indicated that inattentiveness biased threshold estimates particularly when threshold estimates were computed as the QUEST mode or the average of staircase reversals. In contrast, thresholds estimated by post-hoc psychometric function fitting were less biased by attentional lapses. Our results suggest that some psychophysical methods are more robust to attentiveness, which has important implications for assessing the perception of children and clinical groups.

     

The effect of judges' attitudes on ratings of attitude statements. A theoretical analysis

Judgments of attitude statements with the method of equal-appearing intervals have been found to vary as a function of the judges' attitudes. In this paper explanations of the relationship between judges' attitudes and judgments of attitude statements in terms of models of psychophysical judgment are discussed. It is argued that psychophysical models such as adaptation-level theory, the range-frequency model, and the ‘rubber-band’ model and its derivations, cannot account satisfactorily for judges' performance of the attitude rating task in a great number of studies. The reason for this failure, it is argued, is that the stimulus series employed in the psychophysical judgment research on which these models are based typically varied only on the dimension being judged. The sets of statements judged in attitude rating studies, however, vary not only on the dimension of interest (favourability—Unfavourability) but also on a number of other dimensions. It is suggested that this incidental stimulus variation of attitude statements may account for the failure of psychophysical models to predict accurately the performance of judges in the attitude rating task. It is argued that if principles which could account for the effects of this incidental stimulus variation on attitude ratings could be incorporated into psychophysical models, the predictive qualities of these models could be improved considerably. One such model is discussed.