Marbe's Law, Stimulus Expectancy, and Response Competition

Abstract

The hypothesis was that word-association response latency is an increasing linear function of overt response competition (measured by conditional response uncertainty) and of stimulus unexpectedness (measured by negative log stimulus probability). Both relationships were monotonic-increasing, as predicted, but neither was linear. Rather, response speed (reciprocal latency) decreased linearly with overt response competition and with stimulus unexpectedness. A more general, more precise form of Marbe's law is proposed, and a neurophysiologically oriented model of word-association behavior is sketched. It has been amply demonstrated that word-association response latency depends on response-word frequency. Thumb and Marbe (1901) were the first to report a decrease in latency with increasing response frequency, a result verified since by Wreschner (1907), Menzerath (1908), Cason and Cason (1925), and Schlosberg and Heineman (1950). This relationship is sometimes referred to as the Thumb-Marbe law, or simply as Marbe's law. Baker and Eliott (1948) found shorter latencies for the same stimulus-response pairs when subjects were instructed to restrict their responses to opposite meanings than when no such restriction was imposed. This suggests that latency increases with response competition. Moreover, it seems intuitively plausible that a high-probability response occurs with less competition from other 'response tendencies' than does a low-probability one-which may account for Marbe's law. More generally, a stimulus word that evokes a large number of equiprobable responses provides evidence of more response competition than one with a single response that occurs with probability 1. This in turn suggests that conditional response uncertainty may reflect wordassociation response competition. If P(Ri[Sj) is the probability that response i will be given when stimulus j is presented, and rj is the number of distinct responses with nonzero probability, then the con