Optimal Sequences of Trials for Balancing Practice and Repetition Effects

This paper describes procedures for generating trial sequences to balance out practice effects and intertrial repetition effects in experiments consisting of repeated trials. In the sequences presented, each stimulus appears an equal number of times, is preceded equally often by itself and by each other stimulus and is distributed in a "balanced" manner throughout the block of trials. Two criteria for balance are employed. One criterion aims to equalize the average position of each stimulus in the sequence. The second criterion maintains, as much as possible, a uniform interval between appearances of each stimulus in the sequence. For each criterion, optimal or near-optimal sequences are presented for experiments involving from three to nine different stimulus conditions. Suggestions are included for extending (e.g., doubling or tripling) the length of the sequences. A typical reaction time (RT) experiment consists of a series of trials. On each trial, the subject selects and executes a response depending on the identity of the stimulus presented. Typically, each stimulus is presented a number of times in some predetermined or randomly generated sequence. The experimenter computes the mean or median RTs and error rates for each of the different stimulus conditions to examine the effects of the experimental treatment. When subjects perform repeated trials on a speeded choice task, their RT on a particular trial may be affected by several factors other than the specific stimulus presented. For example, performance may be affected by practice effects that emerge within a block or over several blocks of trials (Pashler & Baylis, 1991a; Woodworth, 1938). There may also be an intertrial repetition effect where performance on a given trial is affected by the nature of the preceding trial (e.g., Bertelson, 1961; Pashler & Baylis, 1991b; Smith,1968; Williams,1966). In addition, RT may be affected by the probability of stimulus occurrence (e.g., Hinrichs & Craft, 1971). In an attempt to control these possible sources of confounding within a block of trials, experimenters generally present each stimulus equally often in a random sequence. Emerson and Tobias recently presented a computer program for randomly generating sequences of trials, such that each stimulus condition: 1) appears an equal number of times, and 2) is preceded equally often by itself and by each of the other stimuli (Emerson & Tobias, 1995). The number of possible sequences exhibiting these properties is, in general, quite large; the algorithm of Emerson and Tobias produces sequences with equalprobability sampling. An alternative control strategy would be to employ sequences of trials which are optimal in the sense that each stimulus condition, in addition to satisfying properties (1) and (2) above, is as evenly distributed as possible throughout the block of trials. This paper describes criteria for optimality of these sequences and presents optimal sequences for