Re-evaluating age-of-acquisition effects: are they simply cumulative-frequency effects?

The time it takes to read or produce a word is influenced by the word's age of acquisition (AoA) and its frequency (e.g. Quarterly Journal of Experimental Psychology 12 (1973) 85). Lewis (Cognition 71 (1999) B23) suggested that a parsimonious explanation would be that it is the total number of times a word has been encountered that predicts reaction times. Such a cumulative-frequency hypothesis, however, has always been rejected because the statistical effects of AoA and frequency are additive. Here, it is demonstrated mathematically that the cumulative-frequency hypothesis actually predicts such results when applied to curvilinear learning. Further, the data from four influential studies (two of which claim support for independent effects of AoA and frequency) are re-analyzed to reveal that, in fact, they are consistent with a cumulative-frequency hypothesis. The conclusion drawn is that there is no evidence with which to refute the most parsimonious of explanations, i.e. cumulative frequency can account for both frequency and AoA effects.