The Wickelgren Power Law and the Ebbinghaus Savings Function

battle with Lou Gehrig’s disease, studied the time course of forgetting more assiduously and more effectively than anyone since Hermann Ebbinghaus. In a classic article, Wickelgren (1974) derived an equation that is remarkable in several respects, including in its ability to characterize the famous Ebbinghaus (1885/1913) savings function. Under typical conditions, Wickelgren’s power law reduces to m lð1 þ btÞ c; ð1Þ where m is memory strength, and t is time (i.e., the retention interval). The equation has three parameters: l is the state of longterm memory at t 5 0 (i.e., the degree of learning), c is the rate of forgetting, and b is a scaling parameter. Wixted (2004) showed that Equation 1 provides an accurate description of forgetting data that have been averaged over many subjects. It not only fits the data well in terms of the percentage of variance accounted for—an admittedly weak test—but also accurately predicts where future points will fall as the retention interval increases, which is a stronger test. Because of possible averaging artifacts in group data, an even stronger test would be to accurately predict the course of forgetting using data from individual subjects. A practical problem with that approach is that such data are usually quite noisy. However, the eight data points of the Ebbinghaus (1885/1913) savings function constitute a rare and notable exception. Previous work has shown that the Ebbinghaus data are reasonably well characterized by a twoparameter power function of the form m yt c; ð2Þ which can be considered an approximation of Equation 1 (Anderson & Schooler, 1991; Wixted & Ebbesen, 1991). Although Equation 2 offers a much better fit of the savings function than other two-parameter candidates, it is undefined at t 5 0, which is theoretically unsatisfying and limits the equation’s practical utility (e.g., it cannot be used to estimate the degree of learning).