Ewart A. C. Thomas

Cognitive processing and time perception

When a visual field is presented for 40 or 80 msec and a subject is asked to judge the duration of the stimulus, judged duration is found to be less when the field is blank than when the field contains three letters, but is the same whether the three letters form a word or not. The perceived difference between “filled” and “blank” fields increases when the subject is required to memorize the presented letters. These data are consistent with a theory which assumes,inter alia, that a stimulus is analyzed by a visual information processor and a timer, that attention is shared between these processors, and that temporal judgments are based on the output of both processors.

Behavior-dependent contexts for repeated plays of the Prisoner's Dilemma II: Dynamical aspects of the evolution of cooperation

Iterated Prisoners Dilemma models are proposed in which, at any trial, the probability of staying in the game depends on the outcome of the previous trial. If a players choice depends on its own play (cooperate or defect) at the previous trial, it becomes possible for cooperative strategies to increase when rare in a population of egoists. A dynamic analysis is used to demonstrate that stable polymorphisms may result, and may involve more strategies than just Tit-for-Tat and all-Defect. The tendency for clustering among like strategists to enhance their initial increase when rare is also explored dynamically.

Effect of level of confusability on reporting letters from briefly presented visual displays

In a report paradigm, two letters are presented on a trial which are either confusable(e.g., P and R) or nonconfusable (e.g., P and M) in terms of visual features. Across trials, interletter distance, retinal location, duration, and visual field are varied. Identification accuracy on confusable trials was generally lower than on nonconfusable trials, and this effect of level of confusability increased with distance from the fixation point, decreased with duration, and was smaller on the central letter than on the more peripheral letter. A quantitative model, incorporating aspects of the interactive channels model (Estes, 1972) and feature perturbation model (Wolford, 1975), is developed and tested. One parameter of the model measures the effective similarity between two letters after lateral inhibition has occurred, and other parameters measure the probability of feature perturbation in foveal and peripheral directions.

On the duality of simultaneous time and size perception

When subjects are asked to judge the duration and size of visually presented circles that vary in duration and size, perceived duration is directly related to stimulus size and perceived size is, in most cases, directly related to stimulus duration. When subjects are asked to process time and size information simultaneously, their time judgments are the same as when only time processing is required, but their size judgments are less than when only size processing is required. These data are discussed within the context of an explicit model for the processing of size information, added to which is the assumption that time judgments are influenced by the time spent processing size information.

On appropriate procedures for combining probability distributions within the same family

Abstract This article considers procedures for combining individual probability distributions that belong to some “family” into a “group” probability distribution that belongs to the same family. The procedures considered are Vincentizing, in which quantiles are averaged across distributions; generalized Vincentizing, in which the quantiles are transformed before averaging; and pooling based on the distribution function or the probability density function. Some of these results are applied to models of reaction time in psychological experiments.

On the dynamics of two-person interactions

A class of discrete-state probabilistic models is discussed that allow for the separate assessment of the effects of both self-regulatory processes, including predispositions, and interactive processes on the complementary, reciprocal, and reinforcing tendencies of observable responses. In most of these models, the two responses made at Time t + 1 by members of an interacting dyad are statistically independent, given the pair of responses made at Time t. For each model, estimable parameters are denned in terms of state transition probabilities and are labeled, for the most part, as measures of bias or of sensitivity to previous own and other behavior. The models are applied to data collected by other researchers on the self-fulfilling nature of social stereotypes, on aggression in a natural setting, and on parent-infant interactions, and the resulting parameter estimates are discussed. Possible applications of the models for as sessing the effects of small group interaction are also mentioned.

On a class of additive learning models: Error-correcting and probability matching

Abstract A general model for learning signal detection in a Yes-No task is considered in which (a) the decision criterion shifts upward and downward by equal steps, and (b) the probability that the criterion shifts on a trial depends on the stimulus-response pair on that trial. Conditions are given for this process to have a unique stationary distribution, and the behavior of the process, as the step-size decreases to zero, is studied. The special model where criterion shifts may occur only on error trials can account for the probability matching behavior and for the interaction between signal strength and signal probability typically observed when the payoff matrix is symmetrical. Further, when the shift probability is assumed to be an increasing function of the distance of the sensory input from the criterion, the stationary mean criterion values are less extreme than the values that yield probability matching. It is shown that the model provides a way of incorporating payoff matrix asymmetry. Finally, the standard error in the maximum likelihood parameter estimates is calculated and a statistic is proposed for discriminating the error-correcting model from the more general model.

Simultaneous time and size perception

Judgments of the apparent duration and size of visually presented circles vary directly with the duration and size of the presented stimuli. When the frequencies of stimulus duration (short vs. long) and stimulus area (small vs. large) are varied, perceived size and duration are directly related to the frequency of the lower attribute value (short or small). These data are compared to the predictions of different information-processing models. The model which accounts for the data best is one in which it is assumed that perceived size and perceived duration grow together over the course of time spent sampling size information, and that attribute frequency affects the rate of sampling and/or the point at which sampling stops.

Control of attention in the processing of temporal and spatial information in complex visual patterns.

Eighteen stimuli were created by orthogonally varying the area (A), perimeter (P), and exposure duration of checkerboard patterns. Subjects judged either the area and duration of the presented shapes (area-time group) or the perimeter and duration (perimeter-time group) of the same figures. Perceived duration, area, and perimeter varied with changes in the uninstructed an the instructed stimulus dimensions. The discussion focuses on the ability of subjects to control the allocation of attention to instructed stimulus dimensions, as well as on the evidence in the data in favor of detailed sequential or fast holistic processing. It is suggested that the concept of stimulus complexity, defined as P2/A, is useful in describing the temporal and spatial illusions obtained in this study.

Sufficient conditions for monotone hazard rate an application to latency-probability curves

Abstract It is assumed that when a subject makes a response after comparing a random variable with a fixed criterion, his response latency is inversely related to the distance between the value of the variable and the criterion. This paper then examines the relationship to response probability of (a) response latency, (b) difference between two latencies and (c) dispersion of latency, and also some properties of the latency distribution. It is shown that the latency-probability curve is decreasing if and only if the hazard function of the underlying distribution is increasing and, by using a fundamental lemma, sufficient conditions are obtained for monotone hazard rate. An inequality is established which is satisfied by the slope of the Receiver Operating Characteristic under these sufficient conditions. Finally, a Latency Operating Characteristic is defined and it is suggested that such a plot can be useful in assessing the consistency between latency data and theory.