Mean response times, variability, and skew in the responding of ADHD children: a response time distributional approach

Response time (RT) distributions from three fixed foreperiod conditions (2, 4, and 8 s) in a warned four-choice RT task were obtained for a group of boys with attention-deficit/hyperactivity disorder, combined type (ADHD; n = 17) and for two groups of normal control boys (age-matched, n = 18, and younger-aged, n = 10). Quantitative measures of distributional shape were derived by fitting the ex-Gaussian distributional model to the individual RT data. Statistical results indicate that the ADHD distributions differ from the age-matched control distributions with respect to the size of the tail (larger for the ADHD boys), but differ from the younger control distributions with respect to the location of the leading edge (slower for the younger control boys). Receiver operating characteristic (ROC) results reveal that the ex-Gaussian exponential component is highly diagnostic of the ADHD boys.     

Attention, spatial integration, and the tail of response time distributions in Stroop task performance

A few studies have examined selective attention in Stroop task performance through ex-Gaussian analyses of response time (RT) distributions. It has remained unclear whether the tail of the RT distribution in vocal responding reflects spatial integration of relevant and irrelevant attributes, as suggested by Spieler, Balota, and Faust (2000). Here, two colour-word Stroop experiments with vocal responding are reported in which the spatial relation between colour and word was manipulated. Participants named colours (e.g., green; say "green") while trying to ignore distractors that were incongruent or congruent words (e.g., red or green), or neutral series of Xs. The vocal RT was measured. Colour words in colour, white words superimposed onto colour rectangles (Experiment 1), and colour rectangles combined with auditory words (Experiment 2) yielded Stroop effects in both the leading edge and the tail of the RT distributions. These results indicate that spatial integration is not necessary for effects in the tail to occur in vocal responding. It is argued that the findings are compatible with an association of the tail effects with task conflict.     

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.     

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.     

A hierarchical model for estimating response time distributions

We present a statistical model for inference with response time (RT) distributions. The model has the following features. First, it provides a means of estimating the shape, scale, and location (shift) of RT distributions. Second, it is hierarchical and models between-subjects and within-subjects variability simultaneously. Third, inference with the model is Bayesian and provides a principled and efficient means of pooling information across disparate data from different individuals. Because the model efficiently pools information across individuals, it is particularly well suited for those common cases in which the researcher collects a limited number of observations from several participants. Monte Carlo simulations reveal that the hierarchical Bayesian model provides more accurate estimates than several popular competitors do. We illustrate the model by providing an analysis of the symbolic distance effect in which participants can more quickly ascertain the relationship between nonadjacent digits than that between adjacent digits.     

Evidence from auditory simple reaction times for both change and level detectors

We examine the form of distributions of simple reaction time. The stimuli we use are the offset of weak pure tones masked by wide-band noise. The hazard functions of the RT distributions (i.e, the probability of a response given that one has not already occurred) are monotone increasing for very weak tones but become peaked for stronger tones. Of the models available in the literature, none is very satisfactory, although two can account for the general qualitative shape of the peaked hazard functions. We propose a model wherein both a change and a level detector function in parallel. If one assumes that the change detector and level detector have slightly different thresholds, this model can account for both the monotone increasing and the peaked hazard functions.     

Word frequency, repetition, and lexicality effects in word recognition tasks: beyond measures of central tendency

Response time (RT) distributions obtained from 3 word recognition experiments were analyzed by fitting an ex-Gaussian function to the empirical data to determine the main effects and interactive influences of word frequency, repetition, and lexicality on the nature of the underlying distributions. The ex-Gaussian analysis allows one to determine if a manipulation simply shifts the response time (RT) distribution, produces a skewing of the RT distribution, or both. In contrast to naming performance, the lexical decision results indicated that the main effects and interactions of word frequency, repetition, and lexicality primarily reflect increased skewing of the RT distributions, as opposed to simple shifts of the RT distributions. The implications of the results were interpreted within a hybrid 2-stage model of lexical decision performance.     

Evaluating the unequal-variance and dual-process explanations of zROC slopes with response time data and the diffusion model

We tested two explanations for why the slope of the z-transformed receiver operating characteristic (zROC) is less than 1 in recognition memory: the unequal-variance account (target evidence is more variable than lure evidence) and the dual-process account (responding reflects both a continuous familiarity process and a threshold recollection process). These accounts are typically implemented in signal detection models that do not make predictions for response time (RT) data. We tested them using RT data and the diffusion model. Participants completed multiple study/test blocks of an "old"/"new" recognition task with the proportion of targets and the test varying from block to block (.21, .32, .50, .68, or .79 targets). The same participants completed sessions with both speed-emphasis and accuracy-emphasis instructions. zROC slopes were below one for both speed and accuracy sessions, and they were slightly lower for speed. The extremely fast pace of the speed sessions (mean RT=526) should have severely limited the role of the slower recollection process relative to the fast familiarity process. Thus, the slope results are not consistent with the idea that recollection is responsible for slopes below 1. The diffusion model was able to match the empirical zROC slopes and RT distributions when between-trial variability in memory evidence was greater for targets than for lures, but missed the zROC slopes when target and lure variability were constrained to be equal. Therefore, unequal variability in continuous evidence is supported by RT modeling in addition to signal detection modeling. Finally, we found that a two-choice version of the RTCON model could not accommodate the RT distributions as successfully as the diffusion model.     

The locus of the benefits of repetition-lag memory training

The current study examined the effects of responses on error-adjacent trials (i.e., those immediately preceding or following errors) on age differences in measures of intraindividual variability and the shape of response time (RT) distributions on a two-back task. Removing error-adjacent responses reduced variability as measured by the coefficient of variation, but did so similarly for younger and older adults. However, older adults’ standard deviations (SDs) were less than those of younger adults with comparable RTs, raising questions regarding the validity of the coefficient of variation. An ex-Gaussian analysis revealed that removing the RTs on error-adjacent trials reduced the length of the tails of distributions and the skewness of the distributions. These properties were reduced more for older adults than for younger adults. These results indicate that the influence of error-adjacent trials should be considered when analyzing intraindividual variability and the shape of RT distributions to test theories of cognitive aging.     

An ARC-REM model for accuracy and response time in recognition and recall

This article presents a model for accuracy and response time (RT) in recognition and cued recall, fitted to free-response and signal-to-respond data from Experiment 1 of P. A. Nobel and R. M. Shiffrin (2001). The model posits that recognition operates through parallel activation in a single retrieval step and cued recall operates as a sequential search. Because the data for recognition showed that variations in list length and study time per list had a large effect on accuracy but a small or negligible effect on (a) free-response RT distributions and (b) retrieval dynamics in signal-to-respond, the timing of the recognition decision is based on an assessment of retrieval completion (ARC), rather than on a sufficiency of evidence in favor of 1 of the response options. By assuming within-trial forgetting, the model predicts both the dissociation of accuracy and RT and the finding that errors are slower than correct responses. For cued recall, this model was incorporated as the 1st step in a search consisting of cycles of sampling and recovery.     

The boundaries of self face perception: Response time distributions,perceptual categories,and decision weighting

The current study uses an RT distribution analysis approach to examine the self-bias in face categorization. In two experiments we systematically manipulated the decision boundaries between the self, familiar, and unfamiliar others in face categorization tasks. For the first time in studies of self-categorization we estimated parameters from ex-Gaussian fits of reaction time distributions in order to capture the influence of different boundaries on the latency distribution of the categorization responses. The results showed that the distribution of responses to self faces was stable regardless of the face context and the task demands, and changes in context only shifted the response distribution in time. In contrast, varying the decisions with familiar and unfamiliar faces changed the shape of the RT distributions in addition to shifting RTs in time. The results indicate that, in contrast to our perception of familiar and unfamiliar faces of other people, self face perception forms a unique perceptual category unaffected by shifts in context and task demands.     

The resurrection of Tweedledum and Tweedledee: Bimodality cannot distinguish serial and parallel processes

Simultaneously presented signals may be processed in serial or in parallel. One potentially valuable indicator of a system’s characteristics may be the appearance of multimodality in the response time (RT) distributions. It is known that standard serial models can predict multimodal RT distributions, but it is unknown whether multimodality is diagnostic of serial systems, or whether alternative architectures, such as parallel ones, can also make such predictions. We demonstrate via simulations that a multimodal RT distribution is not sufficient by itself to rule out parallel self-terminating processing, even with limited trial numbers. These predictions are discussed within the context of recent data indicating the existence of multimodal distributions in visual search.     

Manual and verbal responses to completely masked (unreportable) stimuli: exploring some conditions for the metacontrast dissociation.

As reported by Neumann and Klotz [1994, in Attention and Performance XV: Conscious and Nonconscious Information Processing Eds C Umiltà, M Moscovitch (Cambridge, MA: MIT Press) pp 123-150], a geometric shape masked by metacontrast can affect response latency (RT) even if it is not visible, i.e. if it yields a d' value of zero in a signal-detection (SD) task (metacontrast dissociation). In the initial study as well as in most subsequent experiments, the RT task was manual and the SD task was verbal. Hence tasks and output modes were confounded. In the present study, two experiments were conducted to find out which of these factors is responsible for the metacontrast dissociation. In experiment 1, participants performed an RT task in either a manual or a verbal output mode. In experiment 2, these output modes were compared in an SD task. Independently of output modes, the masked primes affected RT but could not be detected in the SD task. It is concluded that tasks, but not output modes, are crucial for the metacontrast dissociation. Implications for the mechanisms underlying the metacontrast dissociation and for the functional difference between judgments and responses are discussed.     

Response time distributions in multidimensional perceptual categorization

Three speeded categorization experiments were conducted using separable dimension stimuli. The form of the category boundary was manipulated across experiments, and the distance from category exemplars to the category boundary was manipulated within each experiment. Observers completed several sessions in each experiment, yielding 300–400 repetitions of each stimulus. The large sample sizes permitted accurate estimates of the response time (RT) distributions and RT hazard functions. Analyses of these data indicated: (1) RT was faster for stimuli farther from the category boundary, and this stochastic dominance held at the level of the RT distributions; (2) RT was invariant for all stimuli the same distance from the category boundary; (3) when task difficulty was high, errors were slower than correct responses, whereas this difference disappeared when difficulty was low; (4) small, consistent response biases appeared to have a large effect on the relation between correct and error RT; (5) the shape of the RT hazard function was qualitatively affected by distance to the category boundary. These data establish a rich set of empirical constraints for testing developing models of categorization RT.     

A diffusion model decomposition of the practice effect

When people repeatedly perform the same cognitive task, their mean response times (RTs) invariably decrease. The mathematical function that best describes this decrease has been the subject of intense debate. Here, we seek a deeper understanding of the practice effect by simultaneously taking into account the changes in accuracy and in RT distributions with practice, both for correct and error responses. To this end, we used the Ratcliff diffusion model, a successful model of two-choice RTs that decomposes the effect of practice into its constituent psychological processes. Analyses of data from a 10,000-trial lexical decision task demonstrate that practice not only affects the speed of information processing, but also response caution, response bias, and peripheral processing time. We conclude that the practice effect consists of multiple subcomponents, and that it may be hazardous to abstract the interactive combination of these subcomponents in terms of a single output measure such as mean RT for correct responses. Supplemental materials may be downloaded from http://pbr .psychonomic-journals.org/content/supplemental.     

A random-walk model of accuracy and reaction time applied to three experiments on pigeon visual discrimination

A random-walk model of visual discrimination is described and applied to reaction time (RT) distributions from three discrete-trial experiments with pigeons. Experiment 1 was a two-choice hue discrimination task with multiple hues. Choice percentages changed with hue discriminability; RTs were shortest for the least and most discriminable stimuli. Experiments 2 and 3 used go/no-go hue discriminations. Blocks of sessions differed in reward probability associated with a variable red stimulus in Experiment 2 and with a constant green stimulus in Experiment 3. Changes in hue had a large effect on response percentage and a small effect on RT; changes in reward shifted RT distributions on the time axis. The "random-walk, pigeon" model applied to these data is closely related to Ratcliff's diffusion model (Ratcliff, 1978; Ratcliff & Rouder, 1998). Simulations showed that stimulus discriminability affected the speed with which evidence accumulated toward a response threshold, in line with comparable effects in human subjects. Reward probability affected bias, modeled as the amount of evidence needed to reach one threshold rather than the other. The effects of reward probability are novel, and their isolation from stimulus effects within the decision process can guide development of a broader model of discrimination.     

Gradual growth versus shape invariance in perceptual decision making

A dominant theme in modeling human perceptual judgments is that sensory neural activity is summed or integrated until a critical bound is reached. Such models predict that, in general, the shape of response time distributions change across conditions, although in practice, this shape change may be subtle. An alternative view is that response time distributions are shape invariant across conditions or groups. Shape invariance is predicted by some race models in which the first of several parallel fibers to communicate the signal determines the response. We competitively assess a specific gradual growth model, the one-bound diffusion model, against a natural shape-invariant competitor: shape invariance in an inverse Gaussian distribution. Assessment of subtle shape change versus shape invariance of response time distributions is aided by a Bayesian approach that allows the pooling of information across multiple participants. We find, conditional on reasonable distributional assumptions, subtle shape changes in response time that are highly concordant with a simple diffusion gradual growth model and discordant with shape invariance.     

Combining shape and position expectancies: hierarchical processing and selective inhibition.

Two experiments report the effects of generating a concurrent position expectancy and form expectancy. Ss were precued to a stimulus position where 1 target shape was most probable, and they made a speeded 2-choice response to the orientation of the displayed shape. Response time (RT) was faster for an expected position than an unexpected position and faster for a likely shape than for an unlikely shape. This replicates the work of Lambert and Hockey (1986). It was also observed, however, that when a stimulus appeared at an unexpected position where 2 shapes were equally improbable, RT was slower for the shape that had been likely rather than unlikely at the cued position. This finding is incompatible with the probability-matching hypothesis of Lambert and Hockey. The data support a hierarchical-expectancy model of attentional selectivity.