Cognitive psychologists have now studied the response performance of children with attention-deficit/hyperactivity disorder (ADHD) on a wide variety of information processing tasks (for a comprehensive review see Douglas, 1999). In conjunction with the fact that ADHD children often make more errors than control children, the most consistent finding in the ADHD cognitive literature is that the overall response times of ADHD children are typically both slower and more variable than those of control children. However, as noted by Douglas (1999), because much of the theoretical and empirical research involving ADHD children has focussed on more specific task manipulations, these two pervasive phenomena of slow and highly variable ADHD response times have still not been adequately addressed.

This study will directly address these phenomena through a detailed statistical examination of the actual distributions of response times obtained from ADHD and control children within a four-choice warned reaction time (4C-WRT) task conducted at McGill University. In this task, groups of ADHD and age-matched control boys provided spatially compatible responses indicating which one of four, highly discriminable, stimuli had been presented in a stimulus display. On each choice trial, the relevant stimulus appeared at the conclusion of either a 2-, 4-, or 8-s fixed foreperiod (also known as a preparatory interval [PI]) that was marked by the presentation of an initial warning signal. In addition, parallel data were collected from a group of control boys several years younger than the ADHD and age-matched control boys to also determine whether the response time distributional profiles of the ADHD boys simply reflect an immature pattern of responding typical of younger children.

We were motivated to undertake an investigation of ADHD response time distributional data for several reasons. First, it is our view that dysfunctional regulatory or control processes are responsible for the performance problems associated with ADHD. In her recent review of the empirical ADHD findings, Douglas (1999) points out that the high degree of variability in ADHD performance on many cognitive tasks seems to signify a pervasive manifestation of regulatory problems involving the inconsistent allocation of effort. Hence, the acquisition of a better understanding of the nature of this variability represents an essential scientific step towards a determination of the precise role of this aspect of regulatory or control processing in ADHD.

Second, upon a closer examination of these types of data, we are continually struck by the fact that the response time distributions of ADHD children can typically be distinguished from those of control children more by the presence of a substantially larger number of abnormally slow responses than by an overall pattern of slow responses, who reported experimental work in which suboptimal processing conditions mainly affected the right end of the response time distributions of hyperactive children). In other words, the standard positive skewing, or asymmetry, that is typically present in the response time distributions obtained within almost all psychological research paradigms is highly exaggerated in the response time distributional profiles of ADHD children. Statistically, positive skew leads to a number of extreme values that have a disproportionate influence on the calculation of the response time mean and, similarly, on the size of the variance measure. We believe that this skew is an important empirical marker that reflects the presence of periodic attentional ‘lapses’ in the responding of ADHD children, in contrast to a general inability to respond quickly. Given the obvious nature of the potential theoretical implications of such a phenomenon, it is important to consider ways in which it might be measured in a quantitative fashion that then allows it to be subjected to a rigorous statistical analysis.

Third, there is a growing recognition that a quantitative study of the shapes of empirical response time distributions can provide much more information from a set of response time data than that which is given by the more standard statistical summary measures of the mean and the variance. That is, response time distributional analyses can be used to describe psychological performance at a more fine-grained level than those standard measures and, thus, can also provide a fuller set of empirical constraints against which to evaluate any existing psychological theories for the underlying process(es) in question. Finally, the recent availability of a statistical package now allows cognitive researchers to easily obtain quantitative summary measures of the shapes of response time distributions (in terms of the three parameters of the ex-Gaussian distributional model).

Our foray into response time distributional analyses has proven fruitful. In this article, it will be demonstrated that these analyses lead to the identification of one specific aspect of the ADHD distributional data that we believe uniquely characterizes the responding of ADHD populations in these types of cognitive psychological tasks; so much so, that this aspect will be shown to be highly diagnostic of ADHD in this sample of boys. Moreover, it will also be established that the two phenomena of slow and highly variable ADHD response times are intimately coupled, in that both can be explained mainly in terms of this same aspect of the ADHD response time distributions. Finally, the additional information obtained from these analyses will also show that, unlike either the response time means or standard deviations, the overall distributional pattern of ADHD responding can be dissociated from that of the younger control responding.

The ex-Gaussian distributional model can be used to provide useful quantitative measures of the distributional properties of a set of response times. This model assumes that each response time can be represented as the sum of a normally distributed random variable and an independent exponentially distributed random variable, and therefore, that the full distribution of response times can be characterized as a convolution of the normal and exponential distribution functions. Parametrically, the ex-Gaussian distribution has three constituents: mu (?) and sigma (?), that, respectively, describe the mean and standard deviation of the normal component, and tau (?), that describes the mean of the exponential component. Fig. 1 shows the probability densities of two ex-Gaussian distributions, along with their normal and exponential distributional components. Each of the two ex-Gaussian distributions in Fig. 1 have identical normal components but differ with respect to their exponential components.

Fig. 1. Probability density (p.d.) functions for two normal distributions with ?=500 ms and ?=75 ms ((a), (b)), two exponential distributions with ?=150 ms (a) and ?=350 ms (b), and the two resultant ex-Gaussian response time (RT) distributions.