In a number of studies, Kail (1986, 1988a, 1992) has shown that estimates of young children's information processing speeds using a variety of tasks and task conditions (that invoke many different processes) are perfectly correlated with older children's processing speeds. Kail has argued that this supports the view that changes in speeded task performance are due to a single global factor that influences all processes. In this paper, I challenge this claim by simulating the consequences of using specific developmental functions (for different processes) for estimated processing times for children of different ages. The simulations demonstrate that Kail's correlational technique is insensitive to differences in underlying developmental functions. Further, the correlational technique is sensitive, unfortunately, to arbitrary differences in the experimental designs used to gather the data.