On the relation between the mean and the variance of a diffusion model response time distribution

Almost every empirical psychological study finds that the variance of a response time (RT) distribution increases with the mean. Here we present a theoretical analysis of the nature of the relationship between RT mean and RT variance, based on the assumption that a diffusion model (e.g., Ratcliff (1978) Psychological Review, 85, 59-108; Ratcliff (2002). Psychonomic Bulletin & Review, 9, 278-291), adequately captures the shape of empirical RT distributions. We first derive closed-form analytic solutions for the mean and variance of a diffusion model RT distribution. Next, we study how systematic differences in two important diffusion model parameters simultaneously affect the mean and the variance of the diffusion model RT distribution. Within the range of plausible values for the drift rate parameter, the relation between RT mean and RT standard deviation is approximately linear. Manipulation of the boundary separation parameter also leads to an approximately linear relation between RT mean and RT standard deviation, but only for low values of the drift rate parameter.     

The mean and standard deviation of the distribution of group assembly sums

An interesting problem in linear programming is the group assembly problem which is mathematically equivalent to the general transportation problem of economics. Computer programs designed for the determination of exact and approximate optimal group assemblies have been available for some time. This paper presents formulas for the mean and squared standard deviation of the distribution of all possible group assembly sums. Computational techniques are presented and the results are related to those of the analysis of variance of ak-factor problem withn levels of each factor.This research was supported in part by the United States Air Force under Project No. 7713, Task No. 77232, and Contract No. AF 18(600)-1050, monitored by the Crew Research Laboratory of the Air Force Personnel and Training Research Center. Permission is granted for reproduction, translation, publication, use, and disposal in whole and in part by or for the United States Government.     

Estimating the quantitative relation between incongruent information and response time

In Eriksen's flanker paradigm, participants' responses are slower and more error-prone when task-relevant and simultaneously available task-irrelevant cues are incongruent. The influence of task-irrelevant information decreases as its distance from the task-relevant information increases. Here, we manipulated the quantity of task-irrelevant information while keeping the distance constant. We asked whether when the impact on response selection processes was stronger the more incongruent information was available, or whether the impact on response selection depended only on its presence or absence. We conducted an experiment, in which subjects had to discriminate the direction of motion of a central point-light-walker that was flanked by two, four, or eight point-light-walkers at an equal distance from the center. The experiment showed that reaction times increased with the number of incongruent walkers. This effect was modulated by the total number of walkers, showing that the effect of incongruent information saturates when the display is cluttered.     

Neuroticism as mental noise: a relation between neuroticism and reaction time standard deviations

Those higher in neuroticism are often more variable in their behavior and experience. On the basis of this observation, the authors hypothesized that the trait of neuroticism might be correlated with the variability of performance pertaining to relatively basic cognitive operations. Three studies involving 242 college undergraduates supported this prediction in that neuroticism correlated positively with the variability of performance across trials of reaction time tasks. These results link neuroticism to cognitive noise that intervenes between stimulus and response. Such noise has been associated with executive dysfunctions (e.g., frontal lobe injury) in previous research. The present findings are potentially useful for understanding why neuroticism often correlates with variations in the functionality of cognition and behavior.     

On the form of the relation between response rates in a multiple schedule

Three pigeons received training on multiple variable-interval schedules with brief alternating components, concurrently with a fixed-interval schedule of food reinforcement on a second key. Fixed-interval performance exhibited typical increases in rate within the interval, and was independent of multiple-schedule responding. Responding on the multiple-schedule key decreased as a function of proximity to reinforcement on the fixed-interval key. The overall relative rate of responding in one component of the multiple schedule roughly matched the overall relative rate of reinforcement. Within the fixed interval, response rate during one multiple-schedule component was a monotonic, negatively accelerated function of response rate during the other component. To a first approximation, the data were described by a power function, where the exponent depended on the relative rate of reinforcement obtained in the two components. The relative rate of responding in one component of the multiple schedule increased as a function of proximity to fixed-interval reinforcement, and often exceeded the overall obtained relative rate of reinforcement. The form of the function relating response rates is discussed in relation to findings on rate-dependent effects of drugs, chaining, and the relation between response rate and reinforcement rate in single-schedule conditions.     

An abac for determining the mean deviation of a class from the general mean

The abac is presented with instructions for use.     

On kristof's test for a linear relation between true scores of two measures

The hypothesis that two variables have a perfect disattenuated correlation and hence measure the same trait, except for errors of measurement, is discussed. Equivalently, the underlying variables, the true scores, are related linearly. We show that several previously proposed ad hoc tests are in fact likelihood ratio tests. The cases when the linear relation is specified and when it is unspecified are both discussed.This work was done while the author was at Purdue University Under Air Force Grant AFOSR-72-2350B.     

How to fit a response time distribution

Among the most valuable tools in behavioral science is statistically fitting mathematical models of cognition to data—response time distributions, in particular. However, techniques for fitting distributions vary widely, and little is known about the efficacy of different techniques. In this article, we assess several fitting techniques by simulating six widely cited models of response time and using the fitting procedures to recover model parameters. The techniques include the maximization of likelihood and least squares fits of the theoretical distributions to different empirical estimates of the simulated distributions. A running example is used to illustrate the different estimation and fitting procedures. The simulation studies reveal that empirical density estimates are biased even for very large sample sizes. Some fitting techniques yield more accurate and less variable parameter estimates than do others. Methods that involve least squares fits to density estimates generally yield very poor parameter estimates.     

On the relation between time and space in the visual discrimination of velocity.

Is the perception of velocity determined by the prior discrimination of spatial and temporal distances? Two experiments sought to answer this question by comparing the discriminabilities of moving stimuli varied in spatial extent, temporal duration, or in redundant combinations of both variables. The subject's task was to identify which of two alternative stimuli was presented on each trial. A set of four stimuli was constructed from two values of spatial extent and two values of temporal duration. Separate conditions required discrimination of each of the six possible pairs of these stimuli. Experiment 1 examined continuous motion and Experiment 2 examined apparent motion for stimuli with short (50 versus 65 msec) and with long (500 versus 650 msec) interstimulus intervals. With continuous motion and with good apparent motion (short intervals), the discrimination between the different-velocity bivariate pairs was too accurate to be attributed only to discriminations of the spatial and temporal extents of the motion. This did not occur with poor apparent motion. Evidently, time and space are perceptually related.     

A linear relation between loudness and decibels

A total of 37 uninitiated observers made repeated numerical magnitude judgments of the loudness of a sequence of octave band noises spaced at 1-dB intervals, from 0 to 5 dB above a standard of about 80 dB(A), which was called 10. The observers were not instructed to use numbers as ratios. When the median responses are plotted linearly against decibels, they are fitted by straight lines. Each extra decibel adds an average of 1 unit of loudness, range for individual observers 10 through .25 units. This is consistent with the view that the subjectively equal stimulus spacing for the loudness of noise is linear in decibels, and that the observers use numbers linearly in judging the loudness.     

Testing a linear relation between true scores of two measures

We concern ourselves with the hypothesis that two variables have a perfect disattenuated correlation, hence measure the same trait except for errors of measurement. This hypothesis is equivalent to saying, within the adopted model, that true scores of two psychological tests satisfy a perfect linear relation. Statistical tests of this hypothesis are derived when the relation is specified with the exception of the additive constant. Two approaches are presented and various assumptions concerning the error parameters are used. Then the results are reinterpreted in terms of the possible existence of an unspecified perfect linear relation between true scores of two psychological tests. A numerical example is appended by way of illustration. Research reported in this paper has been supported by grant GB-18230 from National Science Foundation.     

Attention control and the antisaccade task: a response time distribution analysis

In three experiments response time (RT) differences between correct prosaccade and antisaccade trials were examined via distribution analyses by fitting an ex-Gaussian function to individual RT distributions. Experiment 1 demonstrated that antisaccades are slower than prosaccades and this difference is due to both a shift in the overall distribution as well as a lengthening of the tail of the distribution. Experiment 2 demonstrated that manipulating foreperiod duration led to changes in both accuracy and RT for antisaccades but not prosaccades. Furthermore, the change in RT for antisaccades resulted in a lengthening in the tail of the distribution but not a shift in the distribution. Finally, Experiment 3 demonstrated that with sufficient practice performance on antisaccades was equated with performance on prosaccades in terms of both accuracy and RT. An examination of the RT distributions suggested that practice led to parallel changes in both the mean of the distribution and the tail of the antisaccade distribution. These results are interpreted within a two-factor theory of attention control that suggests that performance on antisaccades is driven by both competition resolution and goal-maintenance abilities.