The Weibull distribution, the power law, and the instance theory of automaticity.

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.

[1]  G D Logan,et al.  The loss of repetition priming and automaticity over time as a function of degree of initial learning , 1993, Memory & cognition.

[2]  B. Gnedenko.  Sur La Distribution Limite Du Terme Maximum D'Une Serie Aleatoire , 1943 .

[3]  Walter Schneider,et al.  Controlled and automatic human information processing: II. Perceptual learning, automatic attending and a general theory. , 1977 .

[4]  John R. Anderson.  Acquisition of cognitive skill. , 1982 .

[5]  R. Ratcliff,et al.  Retrieval Processes in Recognition Memory , 1976 .

[6]  J. S. Huang.  Moment Problem of Order Statistics: A Review , 1989 .

[7]  James L. McClelland,et al.  On the control of automatic processes: a parallel distributed processing account of the Stroop effect. , 1990, Psychological review.

[8]  J T Townsend,et al.  Truth and consequences of ordinal differences in statistical distributions: toward a theory of hierarchical inference. , 1990, Psychological bulletin.

[9]  Allen and Rosenbloom Paul S. Newell,et al.  Mechanisms of Skill Acquisition and the Law of Practice , 1993 .

[10]  J. Anderson,et al.  Automaticity and the ACT* theory. , 1992, The American journal of psychology.

[11]  L. Jacoby.  Memory as cognition. , 1980, Science.

[12]  Roger Ratcliff,et al.  Statistical mimicking of reaction time data: Single-process models, parameter variability, and mixtures , 1995, Psychonomic bulletin & review.

[13]  Alan S. Brown,et al.  Information Processing and Cognition: The Loyola Symposium , 1976 .

[14]  Hans Colonius,et al.  The instance theory of automaticity: Why the Weibull? , 1995 .

[15]  A F Kramer,et al.  An analysis of memory-based theories of automaticity. , 1990, Journal of experimental psychology. Learning, memory, and cognition.

[16]  G. Logan,et al.  Memory-based automaticity in the discrimination of visual numerosity. , 1993, Journal of experimental psychology. Learning, memory, and cognition.

[17]  G. Logan.  Shapes of reaction-time distributions and shapes of learning curves: a test of the instance theory of automaticity. , 1992, Journal of experimental psychology. Learning, memory, and cognition.

[18]  J. Angus.  Extreme Value Theory in Engineering , 1990 .

[19]  M. Posner,et al.  Attention and cognitive control. , 1975 .

[20]  S. Jay Samuels,et al.  Toward a theory of automatic information processing in reading , 1974 .

[21]  G. Logan.  Toward an instance theory of automatization. , 1988 .

[22]  Gordon D. Logan,et al.  Automatizing alphabet arithmetic: I. Is extended practice necessary to produce automaticity? , 1991 .

[23]  Walter Schneider,et al.  Toward a Model of Attention and the Development of Automatic Processing. , 1984 .

[24]  G. Logan.  Repetition priming and automaticity: Common underlying mechanisms? , 1990, Cognitive Psychology.

[25]  Gordon D. Logan,et al.  What Is Learned During Automatization? The Role of Attention in Constructing an Instance , 1994 .

[26]  G D Logan,et al.  The transition from algorithm to retrieval in memory-based theories of automaticity , 1991, Memory & cognition.

[27]  John R. Anderson,et al.  Human memory: An adaptive perspective. , 1989 .