Extracting thresholds from noisy psychophysical data

Psychophysical studies with infants or with patients often are unable to use pilot data, training, or large numbers of trials. To evaluate threshold estimates under these conditions, computer simulations of experiments with small numbers of trials were performed by using psychometric functions based on a model of two types of noise:stimulus-related noise (affecting slope) andextraneous noise (affecting upper asymptote). Threshold estimates were biased and imprecise when extraneous noise was high, as were the estimates of extraneous noise. Strategies were developed for rejecting data sets as too noisy for unbiased and precise threshold estimation; these strategies were most successful when extraneous noise was low for most of the data sets. An analysis of 1,026 data sets from visual function tests of infants and toddlers showed that extraneous noise is often considerable, that experimental paradigms can be developed that minimize extraneous noise, and that data analysis that does not consider the effects of extraneous noise may underestimate test-retest reliability and overestimate interocular differences.     

Tracking of nociceptive thresholds using adaptive psychophysical methods

Psychophysical thresholds reflect the state of the underlying nociceptive mechanisms. For example, noxious events can activate endogenous analgesic mechanisms that increase the nociceptive threshold. Therefore, tracking thresholds over time facilitates the investigation of the dynamics of these underlying mechanisms. Threshold tracking techniques should use efficient methods for stimulus selection and threshold estimation. This study compares, in simulation and in human psychophysical experiments, the performance of different combinations of adaptive stimulus selection procedures and threshold estimation methods. Monte Carlo simulations were first performed to compare the bias and precision of threshold estimates produced by three different stimulus selection procedures (simple staircase, random staircase, and minimum entropy procedure) and two estimation methods (logistic regression and Bayesian estimation). Logistic regression and Bayesian estimations resulted in similar precision only when the prior probability distributions (PDs) were chosen appropriately. The minimum entropy and simple staircase procedures achieved the highest precision, while the random staircase procedure was the least sensitive to different procedure-specific settings. Next, the simple staircase and random staircase procedures, in combination with logistic regression, were compared in a human subject study (n = 30). Electrocutaneous stimulation was used to track the nociceptive perception threshold before, during, and after a cold pressor task, which served as the conditioning stimulus. With both procedures, habituation was detected, as well as changes induced by the conditioning stimulus. However, the random staircase procedure achieved a higher precision. We recommend using the random staircase over the simple staircase procedure, in combination with logistic regression, for nonstationary threshold tracking experiments.     

Computation of psychophysical thresholds using the probit technique

Probit analysis is a statistical technique that can be used for the computation of psychophysical thresholds, although it was originally developed for the analysis of pharmacological and toxicological data. Probit analysis may be applied to psychophysical data if the method of constant stimuli has been used for data collection. A computer program written in APPLESOFT BASIC that performs probit analyses on such psychophysical data is presented and explained.     

Microcomputer-based estimation of psychophysical thresholds: The Best PEST

A new, maximally efficient technique for measuring psychophysical thresholds (Pentland, 1980) has been implemented on the microcomputer. This PEST (parameter estimation by sequential testing) technique is the most efficient sequential parameter estimation technique possible, given that the form of the psychometric function is known. The technique is similar to but faster and more accurate than other staircase procedures and may be applied whenever staircase techniques are applicable. The “Best PEST” is easily implemented on the micro-computer; a BASIC program for the Apple II which does so is presented. The Best PEST is compared with other staircase procedures, including one recently implemented on a micro-computer (Corwin, Kintz, & Beaty, 1979).     

Function identification from noisy data with recursive error bounds

New success criteria of inductive inference in computational learning theory are introduced which model learning total (not necessarily recursive) functions with (possibly everywhere) imprecise theories from (possibly always) inaccurate data. It is proved that for any level of error allowable by the new success criteria, there exists a class of recursive functions such that not all f are identifiable via the criterion at that level of error. Also, necessary and sufficient conditions on the error level are given for when more classes of functions may be identified.     

Predicting true patterns of cognitive performance from noisy data

Starting from the premise that the purpose of cognitive modeling is to gain information about the cognitive processes of individuals, we develop a general theoretical framework for assessment of models on the basis of tests of the models’ ability to yield information about the true performance patterns of individual subjects and the processes underlying them. To address the central problem that observed performance is a composite of true performance and error, we present formal derivations concerning inference from noisy data to true performance. Analyses of model fits to simulated data illustrate the usefulness of our approach for coping with difficult issues of model identifiability and testability.     

On optimal smoothing and derivative estimation from noisy displacement data in biomechanics

Estimating derivatives from noisy displacement data is a notoriously ill-posed problem in signal processing and biomechanics. Following the work of Wood and Jennings (1978) and Hatze (1979, 1981), the present paper describes the use of optimally regularized, natural quintic splines for estimating smoothed positions, velocities, and accelerations from equidistantly sampled, noisy position measurements. It appears that the nature of the boundary conditions of the data is of some importance, since various algorithms used hitherto result in artefacts throughout the data if the true derivatives at the record ends differ significantly from zero. Natural quintic splines do not suffer from this disadvantage below the third derivative.The ill-posed character of movement analysis has some interesting implications for movement synthesis and optimization, similar to the indeterminacy of muscular co-contraction from merely external, biomechanical measurements.     

Comparison of cupulometric and psychophysical thresholds for perception of rotation and the oculogyral illusion

The purpose of this study was to compare thresholds for angular acceleration derived by subjective cupulometry and by a staircase method. Thresholds for the perception of rotation and the oculogyral illusion were determined for 10 Os who were rotated about their vertical axis. The cupulometric thresholds were significantly higher, more variable, and not predictable from the staircase thresholds. Furthermore, cupulometry failed to distinguish between the thresholds for the perception of rotation and the oculogyral illusion, although both indicators functioned according to the prediction of the underlying linear model. Individual differences supported the general conclusion that cupulometric thresholds bear no relationship to the sensory threshold derived in a classical psychophysical manner.     

Extracting a maximum of useful information from statistical research data

The practice of statistical inference in psychological research is critically reviewed. Particular emphasis is put on the fast pace of change from the sole reliance on null hypothesis significance testing (NHST) to the inclusion of effect size estimates, confidence intervals, and an interest in the Bayesian approach. We conclude that these developments are helpful for psychologists seeking to extract a maximum of useful information from statistical research data, and that seven decades of criticism against NHST is finally having an effect.     

Adaptive procedures in psychophysical research.

As research on sensation and perception has grown more sophisticated during the last century, new adaptive methodologies have been developed to increase efficiency and reliability of measurement. An experimental procedure is said to be adaptive if the physical characteristics of the stimuli on each trial are determined by the stimuli and responses that occurred in the previous trial or sequence of trials. In this paper, the general development of adaptive procedures is described, and three commonly used methods are reviewed. Typically, a threshold value is measured using these methods, and, in some cases, other characteristics of the psychometric function underlying perceptual performance, such as slope, may be developed. Results of simulations and experiments with human subjects are reviewed to evaluate the utility of these adaptive procedures and the special circumstances under which one might be superior to another.     

Comparison of sensitivity of psychophysical and electrophysiological measures of scotopic thresholds in the vicinity of the blind spot

A section of the blind spot was mapped by obtaining detection and averaged EEG threshold measurements using three stimulus light intensities. It was found that averaged EEG and detection measures of the blind spot were equally sensitive when the two highest stimulus intensities were used, although more observations of the stimulus were required with averaged EEG. Detection thresholds were superior to averaged EEG measures with the dimmest stimulus.

     

Temporal discrimination and a free-operant psychophysical procedure.

Pigeons were presented a series of keylight time periods (separated by blackouts) during which two response keys were lit, one by blue light and the other either by orange or green. Blue-key responses changed the color on the other key. Orange-key responses sometimes produced food during the first half of a time period; green-key responses sometimes produced food during the second half. In three experiments, the probability of a green-key response increased as a function of elapsed time. Experiment 1 compared performance when the duration of the keylight periods was varied across a wide range. Discrimination of performance was similar across the range of durations. Experiment 2 varied both relative reinforcement rate and the local reinforcement rate for orange-key and green-key responses. These manipulations produced changes in response bias but not discrimination sensitivity. Experiment 3 varied the local temporal placement of reinforcers within time periods and demonstrated that choice behavior was affected by differential reinforcement at different points during the time periods. The results were consistent with previous research on duration discrimination that used psychophysical trials procedures.     

Some characteristics of psychophysical data obtained with a group version of the up-and-down method

Effects of backgroun reflectance on the shapes of scales of lightness were investigated in two experiments. In Experiment I, 25 Ss compared similaritiesofpairs ofgray chips that were viewed against black, gray. or white backgrounds. In Experiment 2, 33 Ss positioned a series of gray chips, viewed against a white, gray. or black background, so that the distances between successive chips represented the perceived differences in lightness between them. The results of both studies indicated that scale shape was influenced by background. The nature of the effect was that interstimulus differences in the region of a background were enhanced relative to interstimulus differences far from a background.