Journal of Experimental Psychology: Learning, Memory, and Cognition 2001, Vol. 27, No. 2, 483-498 Copyright 2001 by the American Psychological Association, Inc. 0278-7393/01/$5.00 DOI: 10.1037//0278-7393.27.2.483 Implicit Learning of First-, Second-, and Third-Order Transition Probabilities Gilbert Remillard and James M. Clark University of Winnipeg Most sequence-learning studies have confounded different types of information, making it difficult to know precisely what is learned. Addressing many of the confounds, the current study shows that people can learn 1st-, 2nd-, and 3rd-order transition probabilities. Measures directly assessing awareness of the probabilities show that the knowledge is implicit early in training and becomes explicit with extended training. Implicit sequence learning has been studied using the serial reaction time (SRT) task in which people respond to the loca- tion of a target that follows a structured sequence of locations. People often learn the structure of the sequence, as evidenced by changes in reaction time (RT) and yet show no explicit knowledge of the structure as assessed by free-recall, cued- recall, or recognition tasks (e.g., Cleeremans & McClelland, 1991; Curran & Keele, 1993; Lewicki, Hill, & Bizot, 1988; McDowall, Lustig, & Parkin, 1995; Reed & Johnson, 1994; Stadler, 1989, 1993; 1995; Willingham, Nissen, & Bullemer, 1989). Unfortunately, SRT task studies often fail to identify which of a number of possible sequential constraints have been learned. Determining precisely what is learned is important for accurately assessing explicit knowledge of the information learned (Perruchet, Gallego, & Savy, 1990; Shanks, Green, & Kolodny, 1994; Shanks & St. John, 1994) and for understanding the mechanisms of implicit sequence learning (Cleeremans & Jimenez, 1998; Hoffman & Koch, 1998). An nth-order transition probability, P(E\A n -... -A 2 -Ai), is the probability of an event E occurring on trial t given the occurrence of events A u A 2 ,... A n on trials t — I, t — 2,... t — n, respec- tively, and is defined as the number of times that E follows the run A n -... -A-fA^ divided by the total number of times that A n -... -A 2 -A l occurs. When exposed to a sequence of events, people apparently can learn first-, second-, or third-order proba- bilities (e.g., Cleeremans, 1993; Cleeremans & Jimenez, 1998; Heuer & Schmidtke, 1996; Howard & Howard, 1997; Jackson, Jackson, Harrison, Henderson, & Kennard, 1995; Jimenez & Men- dez, 1999; Reed & Johnson, 1994; Schvaneveldt & Gomez, 1998; Gilbert Remillard and James M. Clark, Department of Psychology, University of Winnipeg, Winnipeg, Manitoba, Canada. This research was supported by a Natural Sciences and Engineering Research Council (NSERC) of Canada postgraduate scholarship to Gilbert Remillard and by an NSERC operating grant. We thank Michael Stadler and Axel Cleeremans for their comments on an earlier version of this article. Correspondence concerning this article should be addressed to Gilbert Remillard, Department of Psychology, University of Winnipeg, 515 Por- tage Avenue, Winnipeg, Manitoba R3B 2E9, Canada. Electronic mail may be sent to gremilla@uwinnipeg.ca. Stadler, 1992; 1993). For example, Cleeremans and McClelland (1991) have found that RTs tend to be shorter on transitions with higher than lower first- and second-order probabilities. The evidence for learning of first-, second-, or third-order prob- abilities is not conclusive for a number of reasons, however. First, Lag 2 and second-order probabilities are often confounded. A Lag 2 probability, P(E\A-x) y is the probability of an event E occurring on trial t given the occurrence of event A on trial t — 2. Often the situation is such that, for example, if P(l)3-4) > P(2|l-3) thenP(l|3-x) > P(2\l-x). Second, Lag 3 and third-order probabilities are, in some cases, confounded. A Lag 3 probability, P(E\A-x-x), is the probability of an event E occurring on trial t given the occur- rence of event A on trial t — 3. Cleeremans and McClelland (1991) found evidence for learning of third-order probabilities, whereas Jimenez, Mendez, and Cleeremans (1996) did not. Interestingly, Lag 3 probability was a confound in the former but not the latter study. Third, first-, second-, and third-order probabilities are often confounded. For example, if i°(l|4) > />(2|3), then />(l|3-4) > P(2|l-3), or vice versa. Fourth, transitions are rarely counterbalanced across probabili- ties. For example, if 1-3 and 1-2 had low and high first-order probabilities, respectively, the assignments would seldom be re- versed, possibly confounding transition probability with finger combination and ease of execution (e.g., see footnote 1). Fifth, number of response alternatives has been confounded with transition probability in some studies. As an example, for se- quences of the form 1-2-3-2-4-3, RT on 2 following 1 and on 3 following 4, which have first-order probabilities of 1.0, is shorter than that on other transitions, which have first-order probabilities of .5 (Curran & Keele, 1993, Experiment 2; Frensch, Buchner, & Lin, 1994). However, 1 and 4 are each followed by only one location (i.e., one response alternative), whereas 2 and 3 are each followed by two possible locations (i.e., two response alterna- tives). Increasing the number of response alternatives tends to increase RT (Hyman, 1953; Kornblum, 1975; Miller & Ulrich, 1998). Finally, there is the problem of differential run involvement. Responses to events (e.g., 3) and sequential pairings of events 483