Quantitative Properties of Automaticity

The theory is primarily intended to account for the major quantitative properties of automatization, the speed-up in processing and reduction in variability that result from practice. The speed-up is the least controversial of the properties ofautomaticity. It is observed in nearly every task that is subject to practice effects, from cigar rolling to proving geometry theorems (for a review, see Newell & Rosenbloom, 1981). In each case, the speed-up follows a regular function, characterized by substantial gains early in practice that diminish with further experience. More formally, the speed-up follows a power function,

where RT is the time required to do the task, N is the number of practice trials, and a, b, and c are constants. A represents the asymptote, which is the limit of learning determined perhaps by the minimum time required to perceive the stimuli and emit a response; b is the difference between initial performance and asymptotic performance, which is the amount to be learned; and c is the rate of learning. The values of these parameters vary between tasks, but virtually all practice effects follow a power function.

The power-function speed-up has been accepted as a nearly universal description of skill acquisition to such an extent that it is treated as a law, a benchmark prediction that theories of skill acquisition must make to be serious contenders (see, e.g., Anderson, 1982; Crossman, 1959; MacKay, 1982; Newell & Rosenbloom, 1981)J If they cannot account for the power law, they can be rejected immediately. The instance theory predicts a power-function speed-up.

The reduction in variability that accompanies automatization is not well understood, largely because most theories neglect it. The literature shows that variability decreases with practice (e.g., McLeod, McLaughlin, & Nimmo-Smith, 1985; Naveh-Benjamin & Jonides, 1984), but the form of the function has not been specified; there is nothing akin to the power law. The instance theory predicts that the standard deviation will decrease as a power function of practice. Moreover, it predicts a strong constraint between the power function for the mean and the one for the standard deviation: they must have the same exponent, c.

The predictions for the power law follow naturally from the main assumptions of the instance theory--obligatory encoding, obligatory retrieval, and instance representation. The predictions are developed mathematically in Appendix A. The remainder of this section provides an informal account.

The theory assumes that each encounter with a stimulus is encoded, stored, and retrieved separately. Each encounter with a stimulus is assumed to be represented as a processing episode, which consists of the goal the subject was trying to attain, the stimulus encountered in pursuit of the goal, the interpretation given to the stimulus with respect to the goal, and the response made to the stimulus. When the stimulus is encountered again in the context of the same goal, some proportion of the processing episodes it participated in are retrieved. The subject can then choose to respond on the basis of the retrieved information, if it is coherent and consistent with the goals of the current task, or to run off the relevant algorithm and compute an interpretation and a response.

The simplest way to model the choice process is in terms of a race between memory and the algorithm--whichever finishes first controls the response. Over practice, memory comes to dominate the algorithm because more and more instances enter the race, and the more instances there are, the more likely it is that at least one of them will win the race. The power-function speed-up and reduction in variability are consequences of the race.