Disentangling the effects of alternation rate and maximum run length on judgments of randomness

Binary sequences are characterized by various features. Two of these characteristics—alternation rate and run length—have repeatedly been shown to influence judgments of randomness. The two characteristics, however, have usually been investigated separately, without controlling for the other feature. Because the two features are correlated but not identical, it seems critical to analyze their unique impact, as well as their interaction, so as to understand more clearly what influences judgments of randomness. To this end, two experiments on the perception of binary sequences orthogonally manipulated alternation rate and maximum run length (i.e., length of the longest run within the sequence). Results show that alternation rate consistently exerts a unique effect on judgments of randomness, but that the effect of alternation rate is contingent on the length of the longest run within the sequence. The effect of maximum run length was found to be small and less consistent. Together, these findings extend prior randomness research by integrating literature from the realms of perception, categorization, and prediction, as well as by showing the unique and joint effects of alternation rate and maximum run length on judgments of randomness.