The Weibull distribution, the power law, and the instance theory of automaticity.
Gordon D. Logan · Psychological Review · 1995
H. Colonius (1995) agreed with the fundamental tenets of the instance theory of automaticity. His article addressed the mathematical development of the theory, pointing out an error in one of two arguments that G. D. Logan (1988,1992) used to justify the choice of the Weibull as the distribution of retrieval times and suggesting an alternative argument that places different emphasis on the power function speedup and the Weibull distribution. This article attempts to clarify the problematic argument, point out some practical limitations on H. Colonius's (1995) alternative argument, and suggest important future directions for the mathematical development of the theory. For several years, I have been developing the instance theory of automaticity to address a number of phenomena in the literature on skill acquisition and automaticity (Logan, 1988,1990, 1992). The theory accounts for differences between automatic and nonautomatic processing, the conditions required to produce automaticity, the role of attention in the acquisition and expression of automaticity, and the power function speedup that characterizes skill acquisition (see Compton & Logan,