Regulatory Focus Effects on Cognitive Flexibility in Rule-Based Classification Learning
W. Todd Maddox 1
Grant C. Baldwin
Arthur B. Markman
University of Texas, Austin
July 25, 2005
In press at Memory & Cognition
Abstract
This paper builds a bridge between research on regulatory focus in motivation and classification learning. It tests the hypothesis that a promotion focus leads to greater cognitive flexibility than a prevention focus and that the fit between the regulatory focus-induced processing characteristics and the nature of the environment influence performance. Experiment
1’s environment is one in which a high level of cognitive flexibility should be advantageous and Experiment 2’s environment is one in which a high level of cognitive flexibility should be disadvantageous. As predicted, promotion focus participants showed better learning in Experiment 1 but worse learning in Experiment 2. Model-based analyses indicated that qualitative shifts in strategy from simple uni-dimensional rules to complex conjunctive rules were associated with the superior performance of promotion focused subjects observed in Experiment 1. The deficit observed for promotion focus participants in Experiment 2 was due to highly variable criterion memory and trial-to-trial placement. Implications for current theories of motivation and classification learning are discussed.
Introduction
The interface between motivation and cognition is crucial for understanding the relationship between learning and behavior (Carver & Scheier, 1998; Higgins, 1997). Research in cognitive psychology has typically focused on the information that people process with little regard for the factors that drive people to act.
However, all behaviors require some impetus to act, and some state of the world that an individual wishes either to bring about or to prevent from occurring.
Much recent work has explored the influence of active goals on behavior (e.g., Aarts, Gollwitzer, &
Hassin, 2004; Ferguson & Bargh, 2004; Fishbach, Friedman, & Kruglanski, 2003; Higgins, 2000).
Furthermore, the motivational system has been the target of theories in cognitive neuroscience (e.g., Ashby,
Isen & Turken, 1999; Gray, 1982; Pickering & Gray, 1999). Despite the clear interest in the influence of motivation on cognition, there has been little research that has targeted the effects of motivation on learning (cf.
Markman, Baldwin, & Maddox, in press). In this paper, we explore motivational influences on classification learning. Classification learning is a particularly apt domain for studying the motivation-cognition interface, because categories are central to the survival of all organisms, and because the long history of the study of categorization in humans has led to the development of sophisticated mathematical models that allow us to provide a precise characterization of people’s performance in learning tasks.
1 This research was supported in part by National Institute of Health Grant R01 MH59196 to WTM, and R21 DA15211 to
ABM. We thank Greg Ashby, Richard Ivry, and Alan Pickering for useful discussions that influenced this work, and three anonymous reviewers for comments on an earlier version of this manuscript. We also thank Scott Lauritzen for help with data collection. Correspondence concerning this article should be addressed to W. Todd Maddox or Arthur Markman both at: University of Texas, 1 University Station A8000, Department of Psychology, Austin, Texas, 78712 (e-mail: maddox@psy.utexas.edu
or markman@psy.utexas.edu
.)

In this paper, we focus on the influence of regulatory focus on classification learning. In the next section, we provide a brief overview of Regulatory Focus theory (Higgins, 2000) and review some of the relatively simple experimental manipulations that have been used to influence participant’s regulatory focus.
Then, we discuss the implications of this model for classification. Next, we present two studies that explore the influence of regulatory focus on people’s flexibility in classification. Finally, we discuss the implications of these findings for behavioral research.
Regulatory Focus Theory and Classification Learning
The motivation literature makes a distinction between approach and avoidance goals (e.g., Carver &
Scheier, 1998; Lewin, 1935; Markman & Brendl, 2000, Miller, 1959). Approach goals have desirable states that someone wishes to bring about. Avoidance goals have undesirable end states that someone wishes to prevent from occurring. Higgins and colleagues (Higgins, 1987, 1997) extended this idea of approach and avoidance to suggest that, orthogonal to approach and avoidance goals, there may be psychological states of readiness or sensitivity for potential gain/non-gain or non-loss/loss goals that tune the sensitivity of the motivational system. On this view, a promotion focus activates an approach mode of processing that focuses the motivational system on the presence or absence of gains in the environment. In contrast, a prevention focus activates an avoidance mode of processing that focuses the motivational system on the presence or absence of losses in the environment. Higgins and colleagues demonstrated that the type of regulatory focus people have in a given task affects cognitive processing and decision making (Crowe & Higgins, 1997; Shah & Higgins, 1997).
An advantage of using regulatory focus theory to study the effects of motivation on cognition is the fact that situational manipulations of regulatory focus are quite easy to instantiate, but can lead to powerful effects.
The basic logic of these manipulations is to focus people on gain/non-gains for a promotion focus or losses/nonlosses for a prevention focus. The manipulation need not even be directly connected to the task of central interest in the study. For example, Crowe and Higgins (1997; see also Markman, Kim, & Brendl, 2005) told all participants that they would complete a recognition memory task followed by a second task. The promotion participants were told that if they did well on the recognition task, the second task would be one that they
“liked”, whereas prevention participants were told that if they did not do well on the recognition task the second task would be one that they “disliked” (liked and disliked tasks were determined separately for each participant based on pretesting). A different manipulation was used by Lee and Aaker (2004). They exposed participants to advertisements and varied the tag line in the ad so that it either focused on potential positive states (e.g., “Get energized”) for a promotion focus or potential negative states (e.g., “Prevent clogged arteries.”) for a prevention focus. As a third example, Shah, Higgins, and Friedman (1998) had participants solve anagrams. The promotion participants were paid a base salary of $4 but were told that they could earn an extra $1 if the found
90% of the anagram solutions, whereas prevention participants were paid a base salary of $5 but were told that they would lose $1 if they did not find 90% of the anagram solutions. In all cases, this simple, easy to instantiate regulatory focus manipulation had a large effect on performance. To anticipate, we use a regulatory focus manipulation modeled after that of Shah et al. (1998) in the studies reported below.
How might regulatory focus affect classification learning? This article tests the hypothesis that a promotion focus affects information processing by increasing cognitive flexibility, whereas a prevention focus reduces cognitive flexibility. We provide a definition of cognitive flexibility specific to our task shortly, but generally, we suggest that cognitive flexibility implies an increase in one’s ability or willingness to try different strategies across trials to achieve some stated goal, as opposed to utilizing more gradual incremental changes in strategy. As will become clear shortly, we are not arguing that increased cognitive flexibility always leads to the use of very different strategies. If the task is one for which a simple, highly salient strategy will achieve the participant’s goal or one in which the necessary rule is obvious from the start, then the increase in willingness to try more complex rules associated with cognitive flexibility may not be acted upon. In contrast, if the task is one for which a complex, low salience strategy is necessary to achieve the participant’s goal and this rule is not obvious initially then increased cognitive flexibility should be advantageous.
There are a number of reasons to think this hypothesis is plausible. First, at a theoretical level, regulatory focus theory suggests that a promotion focus should lead people to try to maximize the number of correct responses they make, even at the expense of potential errors of commission. Thus, people may be more likely to attempt complex strategies at the risk of failure when the strategy has a chance to lead to increased accuracy (Crowe & Higgins, 1997; Higgins, 1997). Second, empirically, Crowe and Higgins (1997) showed that participants given a promotion focus generated more alternatives in an anagram task than did participants

given a prevention focus, and generated a greater number of classification rules for sets of objects than did prevention focused participants. Third, Isen (1993, 1999) has found that a mild positive affect manipulation leads participants to generate more “associates” in the Remote Associates Task (RAT; M.T. Mednick, Mednick
& Mednick, 1964). Although a promotion focus and positive affect are not equivalent, the manipulations in many studies of positive affect focus in part on positive outcomes or gains. For example, in many of Isen’s studies, positive affect is induced by giving participants a small gift. Taken together, this work suggests that people with a promotion focus will be more flexible in their cognitive processing than will people with a prevention focus.
To test the hypothesis that regulatory focus affects classification learning through its effects on cognitive flexibility we need a classification learning task for which variations in cognitive flexibility will lead to observable performance differences. Rule-based classification learning tasks support this goal because they require the participant to generate, test, and either accept or reject specific classification strategies or hypotheses. In addition, rules vary in their complexity and salience. Uni-dimensional rules of the sort “respond
A if the object is small and respond B if the object is large” are simple and highly salient. Conjunctive rules of the sort “respond A if the object is small and black or large and white; otherwise respond B” are complex and less salient (Feldman, 2000; Shepard, Hovland, & Jenkins, 1961). A participant high in cognitive flexibility should be more willing to abandon a highly salient uni-dimensional rule in favor of a less salient conjunctive rule if it becomes clear that the simple rule will not achieve the stated goal. In contrast, a participant low in cognitive flexibility should be less willing to abandon the highly salient rule. Thus, when the optimal rule (i.e., the rule that maximizes accuracy) is a conjunctive rule, and several highly salient uni-dimensional rules are available that yield reasonable (albeit sub-optimal) performance, the person high in cognitive flexibility should learn more quickly then the person low in cognitive flexibility.
Of importance to this account, cognitive flexibility is only advantageous for classification learning, when the task requires a participant to abandon a simple and highly salient rule that yields good but not optimal performance for a more complex and less obvious rule that yields better performance. It is only under these conditions that promotion focus should lead to better classification performance than should prevention focus.
In contrast, when the nature of the optimal categorization rule is obvious from the outset, and the participant need only fine-tune the decision criteria, heightened cognitive flexibility might lead to too much variability in strategy use and thus poorer performance (assuming that the rule is difficult enough that participants do not achieve optimal performance quite quickly regardless of their willingness to be flexible). In this case, we should observe better performance by those with a prevention focus than by those with a promotion focus.
As a thorough test of our cognitive flexibility hypothesis we examined both situations. Experiment 1 examined the effects of regulatory focus on classification learning when the optimal rule required the participant to abandon a reasonably accurate simple rule in favor of a more complex optimal rule. In this case, we expect participants with a promotion focus to perform better than those with a prevention focus. Experiment
2 examined the effects of regulatory focus on classification learning when the structure of the optimal rule was fairly transparent and the participant need only fine-tune their strategy. In this case, we expect participants with a prevention focus to perform better than those with a promotion focus. In both experiments we examined the effects of regulatory focus on learning using global measures of accuracy. In addition, and to better understand the nature of participants’ strategy development, we also applied a series of computational models to the data.
Experiment 1
Experiment 1 examined the effects of regulatory focus (promotion vs. prevention) on participants’ ability to learn a two-category conjunctive rule-based task. The task was designed so that a simple, highly salient rule yielded reasonable performance, but a more complex less salient rule yielded higher performance that allowed the participant to exceed a performance criterion.
The category structure used in Experiment 1 was motivated by the one used in Medin, Altom, Edelson, and Freko (1982; Experiment 4). They had people learn categories with binary-valued dimensions in which a one-dimensional rule supported moderately accurate performance, but perfect performance could be achieved by using a complex (XOR) rule on two other dimensions. Our structure was similar in the sense that onedimensional rules yielded reasonable performance, whereas a two-dimensional rule yielded perfect performance. However, in order to use mathematical models that allow us to assess people’s decision criteria, we used stimuli with continuous-valued dimensions.

The stimulus on each trial was a line whose length, orientation, and horizontal position on the computer screen varied across trials. A scatter-plot of the stimuli in three-dimensions along with the optimal decision criteria on length and orientation is displayed in Figure 1. The optimal decision rule was conjunctive and required the participant to set a criterion on length and a criterion on orientation and to use the rule: Respond A if the length is long and the orientation is steep; otherwise respond B. A participant using the optimal length and orientation decision criteria could attain 100% accuracy, whereas the most accurate uni-dimensional rules on length, and orientation yielded 83% accuracy. The position dimension was irrelevant but a uni-dimensional rule on position also yielded 83% correct. The position dimension was included because pilot studies conducted in our lab suggest that it is highly salient and thus we expected participants to focus initially on this dimension.
Each participant completed 12 48-trial blocks in the experiment.
Participants in the promotion focus condition were told that they could earn an entry into a drawing for
$50 if they exceeded a performance criterion during the final block of trials (equivalent to meeting or exceeding
90% accuracy). Participants in the prevention focus condition were given an entry into the drawing for $50 upon entry into the laboratory, but were told that they had to exceed the same performance criterion in order to keep the entry. Notice that any participant using a uni-dimensional rule will not exceed the performance criterion. Instead, the participant must abandon the simple uni-dimensional rule (either on length, orientation or position) in favor of the more complex conjunctive rule to exceed the performance criterion. Because discovery of the optimal conjunctive rule requires greater cognitive flexibility (i.e., a willingness to abandon the reasonably accurate, simple uni-dimensional rule in favor of the more complex conjunctive rule required to exceed the performance criterion), we predicted that participants given a promotion focus will discover the rule sooner, and thus will learn more quickly than participants given a prevention focus.
Methods
Participants
Sixty participants were solicited from the University community and either received course credit or $6 payment for participation. In addition, participants were given the opportunity to obtain a 1 in 10 chance of receiving $50 in a random drawing (details provided below). Thirty participated in the promotion focus condition, and 30 in the prevention focus condition.
Stimuli and Stimulus Generation.
The stimulus on each trial was a white line with some length and orientation presented against a black background vertically centered in the middle of a 650 pixel x 650 pixel box with some horizontal displacement from the left side of the box. A total of 576 unique stimuli were samples with 288 from Category A and 288 from Category B. Category A consisted of stimuli sampled from 12 bivariate normal distributions on length and orientation with 24 stimuli sampled from each. Category B consisted of stimuli sampled from 4 bivariate normal distributions on length and orientation with 72 sampled from each. The value along the position dimension was generated independently with the position values for Category A items being sampled from a univariate normal distribution with mean = 253 pixels from the left side of the box and standard deviation = 75 and the Category B items having a mean = 397 pixels and standard deviation = 75. This yielded a wide range of positions and helped make the position dimension especially salient. The category distribution parameters are outlined in Table 1. The stimuli were randomized separately for each participant.
-------------------Figure 1 and Table 1 -----------------------------
Procedure.
Participants were tested individually in a dimly lit room. They were informed that there were two categories and that they should emphasize accuracy over speed of responding. A correct response resulted in a gain of two points, and an incorrect response resulted in a gain of zero points. Participants in the promotion focus condition were told that they would be given the opportunity to obtain an entry into a drawing for $50 if they gained 86 or more points over the final 48 trials (the last block) of the experiment (86 points = 43 of 48 trials correct = 90% correct). Participants in the prevention focus condition were given an entry into a drawing for $50 upon arrival in the laboratory but were informed that they would lose the entry if they did not gain 86 or more points over the final 48 trials of the experiment. Both groups were told that 10 participants were involved in the study and thus that they had at least a 1-in-10 chance of winning the drawing if they gained (or kept) their entry.
Each experimental session consisted of the presentation of 12, 48-trial blocks. At the beginning of each block a vertically oriented “point meter” was set to zero. The point meter was displayed on the right side of the

computer screen and consisted of a 750 pixel tall x 50 pixel wide unfilled rectangle. The criterion was shown as a line across the meter, and was labeled “Bonus.” The region above the bonus line was labeled “Yes” and the region below “No,” to indicate that the bonus was earned when the point meter was above the line and not earned below the line. On each trial a stimulus was displayed until the participant pressed either the A or B key.
Following their response visual feedback was provided below the stimulus presentation box for 300ms. If the response was correct the word “Correct” was displayed. If the response was incorrect, the word “Incorrect” was displayed. While this visual feedback remained on the screen, the point meter was updated. If the response was correct, the point meter filled in from the bottom up at the rate of 7 pixels per point. The region of change in the meter flashed three times (200ms for each flash) to emphasize that the meter was increasing. Additionally, the subject heard a cash register sound associated with each flash. There was a 100ms pause and then the current point total was shown both graphically on the meter and in text next to the point meter for 300ms. If the response was incorrect the point meter did not change, but the participant heard a buzzer for 600ms followed by a 100ms pause. For correct and incorrect responses, the stimulus display disappeared but the point meter remained visible, there was a 250ms inter-trial-interval and the initiation of the next trial.
At the end of each block of trials the participants were given feedback on their performance in that block. If they exceeded the bonus criterion in the promotion condition they were told “If that had been the last block of trials you would have earned an entry into the drawing for $50.” If they exceeded the bonus criterion in the prevention condition they were told “If that had been the last block of trials you would have kept you entry into the drawing for $50.” If it was the final block they were told whether they gained or kept their entry into the drawing.
Results and Theoretical Analyses
We took a two-pronged approach to the data analysis. We began with an examination of the accuracy rates to determine how regulatory focus affected the accuracy of the participants’ responding. Next we applied a series of quantitative models to the data in an attempt to identify the types of strategies that participants used to solve the task and to determine what cognitive processes were affected by the regulatory focus manipulation.
Accuracy Analyses
We conducted a number of separate analyses on the accuracy data to provide converging evidence in support of our hypothesis that a promotion focus will lead to greater cognitive flexibility and thus to faster learning. First, for each participant we identified the first block of trials for which their accuracy met or exceeded the 90% performance criterion. This denotes the first block of trials for which the participant would have received feedback that, had that been the final block of trials, they would have earned an entry into the drawing (promotion focus) or they would have kept their entry into the drawing (prevention focus). Any participant who failed to meet or exceed the criterion at any time during the experiment was coded with a 13 because that would be the minimum number of blocks that a participant would need to achieve the criterion if they had not done it by the final (12 th ) block of trials. The results of a t-test confirmed that participants given a promotion focus exceed the performance criterion sooner (after 4.30 blocks on average) than do participants given a prevention focus (after 5.97 blocks on average) [t(58) = 1.701, p = .06].
Second, for each block of trials we compared the proportion of promotion and prevention focus participants who met or exceeded the 90% performance criterion (see Figure 2a). We used a binomial test to determine whether the proportion of promotion participants who exceeded the criterion was significantly larger than the proportion of prevention participants who exceeded the criterion. The binomial test for the final block was significant (p < .01) with 63.3% of promotion participants but only 36.7% of prevention participants meeting or exceeding criterion. Binomial tests conducted on a block by block basis suggested that the promotion advantage was significant in blocks 3, 5, 10, and 11 (p < .05). The differences were non-significant in every other block except block 2 which showed an advantage for the prevention regulatory focus 2 . Collapsing across all blocks, 40% of the time the promotion focus participants exceeded criterion, whereas only 27% of the time the prevention focus participants exceeded criterion.
-------------------Figure 2 -----------------------------
2 An alternative approach is to compare frequencies using a

2 test. The final block frequency difference was significant based on a

2 test [

2 (1) = 4.267, p < .05]. However, due to the lower power associated with

2 the only other frequency differences that emerged were in blocks 3, 5, and 10.

Finally, as shown in Figure 2b, we computed the average accuracy in each block for the promotion and prevention participants. As expected, promotion participants were significantly more accurate (91.3%) than prevention participants (86.5%) during the final block of trials [t(58) = 2.017, p < .05]. A performance advantage for the promotion focus condition held in all blocks (except block 4) and was significant based on a ttest in blocks 5, 10, and marginally significant in block 11.
Taken together the accuracy-based analyses converge in suggesting that participants given a promotion focus (a) exceed the performance criterion earlier in training, (b) are more likely in general to exceed the performance criterion necessary to earn (or keep) an entry into the drawing, and (c) obtain higher overall accuracy rates.
Model-Based Analyses
The accuracy-based analyses support the prediction that a promotion focus increases cognitive flexibility leading participants to learn more quickly and attain a higher accuracy rate. Implicit in this hypothesis is the assumption that participants in the promotion focus group learn to abandon simple unidimensional rules in favor of the more complex, optimal conjunctive rule. We cannot test this assumption rigorously based only on the accuracy data, but we have available quantitative models that allow us to determine with greater certainty how the promotion focus manipulation is affecting each participant’s response strategy. As a step toward a deeper understanding of strategy use we fit a number of decision bound models
(Ashby & Maddox, 1993; Maddox & Ashby, 1993) separately to the data from each participant on a block-byblock basis. All analyses were performed at the individual-participant level because of concerns with modeling aggregate data (e.g., Ashby, Maddox, & Lee, 1994; Estes, 1956; Maddox, 1999; Maddox & Estes, 2004; Smith
& Minda, 1998).
Decision bound models are derived from general recognition theory (GRT; Ashby & Townsend, 1986), which is a multivariate generalization of signal detection theory (e.g., Green & Swets, 1966). GRT assumes that there is trial-by-trial variability in the perceptual information obtained from every stimulus, no matter what the viewing conditions (Ashby & Lee, 1993). On each trial, the percept is represented as a point in a multidimensional psychological space. Decision bound theory assumes that each participant partitions the perceptual space into response regions. On each trial, the participant determines which region the percept is in, and then emits the associated response.
Five decision bound models were fit to the data. The optimal conjunctive rule model assumes that the participant sets a criterion on the length dimension and on the orientation dimension that is optimal (i.e., the criteria that maximize performance). This model has one free parameter: the variance of internal (perceptual and criterial) noise (i.e., σ 2 ). The sub-optimal conjunctive rule model allows the length and orientation decision criteria to be estimated from the data. This model has three free parameters: two decision criteria and the variance of internal noise (i.e., σ 2 ). The uni-dimensional length model assumes that the participant sets a criterion on length and gives one response for short lines and the other response for long lines and completely ignores orientation and position. The uni-dimensional orientation model assumes that the participant sets a criterion on orientation and gives one response for shallow lines and the other response for steep lines and completely ignores length and position. The uni-dimensional position model assumes that the participant sets a criterion on position and gives one response for lines to the left and the other response for lines to the right and completely ignores length and orientation. The three uni-dimensional models each contain two free parameters
(i.e., one decision criterion and the noise variance).
The model parameters were estimated using maximum likelihood (Ashby, 1992; Wickens, 1982) and the goodness-of-fit statistic was
AIC = 2r - 2lnL, where r is the number of free parameters and L is the likelihood of the model given the data (Akaike, 1974;
Takane & Shibayama, 1992). The smaller the AIC, the closer a model is to the “true model,” regardless of the number of free parameters. Thus, the best model is the one with the smallest AIC value (for a discussion of the complexities of model comparisons see Myung, 2000; Pitt, Myung, & Zhang, 2002).
Table 2 displays the percentage of promotion and prevention participants’ data best fit by a conjunctive rule model, the uni-dimensional position model, and the uni-dimensional length or uni-dimensional orientation models separately by block 3 . For ease of comparison with the accuracy data, we also plot the proportion of
3 We collapsed across optimal and sub-optimal conjunctive models because the proportion of participants who were optimal was low, although accuracy for optimal participants was higher. Similarly, we collapsed across the uni-

promotion and prevention participants’ data best fit by a conjunctive rule in Figure 2c. In addition, we present the average accuracy rate for participants in each model class. Before summarizing the model results, it is important to determine whether the models provided a good account of the data. Poor fitting models should not be interpreted. The models fit the data well with the most general, sub-optimal conjunctive rule model accounting for 92% and 86% of the final block responses for the promotion and prevention condition participants, respectively.
Following the approach taken with the accuracy data, we conducted a number of separate analyses on the modeling results in an attempt to provide converging evidence in support of the hypothesis that a promotion focus leads to greater cognitive flexibility and thus to faster learning. First, as expected, the uni-dimensional length and uni-dimensional orientation models rarely fit the data best; providing the best fit for over 25% of the data in only the first block of trials for promotion and prevention participants and rarely fitting best for more than 10% of the data in any other block. In contrast, the proportion of data sets best fit by the uni-dimensional position model was high and in all but blocks 1 and 3, and was higher for prevention participants than promotion participants. This pattern suggests that prevention focus participants were less likely to abandon this simple rule in favor of the more complex conjunctive rule. Second, we identified the first block of trials for which a conjunctive rule model provided the best account of the data separately for each participant. Any participant whose data was never best fit by a conjunctive model was coded with a 13. The results of a t-test confirmed that promotion participants’ data was best fit by a conjunctive model earlier (after 3.87 blocks on average) than prevention participants (after 6.07 blocks on average) [t(58) = 1.830, p < .05]. Finally, we determined whether the proportion of participants whose data was best fit by a conjunctive rule model was higher for promotion participants than prevention participants using binomial tests. Although the proportion of promotion participants whose data was best fit by a conjunctive rule was larger than that for prevention participants in all but the first block of trials, the promotion focus advantage was only statistically significant in blocks 5, 6, 7, 8 and 10 (p < .05) 4 .
Taken together these results suggest that promotion focus participants are more cognitively flexible than prevention participants because they abandon the simple uni-dimensional rule in favor of the more complex conjunctive rule more quickly. However, once a participant (promotion or prevention) abandons the uni-dimensional rule for a conjunctive rule, learning should proceed at approximately the same rate. To test this hypothesis we examined the change in the noise parameter across blocks for promotion and prevention participants best fit by a conjunctive rule model. Specifically, we identified the first block of trials for which a conjunctive rule model fit each participant’s data and then tracked the noise value from that “first” block out four additional blocks. We analyzed only five blocks from the first use of a conjunctive rule, because many subjects completed the experiment within five blocks of using the conjunctive rule for the first time. The average noise standard deviations were: 44, 36, 26, 34, and 28 for the promotion condition and were 41, 35, 31,
34, and 29 for the prevention condition. T-tests comparing the promotion and prevention noise values on a block by block basis were all non-significant (all t’s < 1.0) supporting our claim that promotion and prevention participants performance profile should be the same once they shift to a conjunctive model. An examination of the best fitting decision criteria revealed an identical pattern.
-------------------Table 2 -----------------------------
Discussion
Experiment 1 tested the hypothesis that a promotion focus leads to greater cognitive flexibility than a prevention focus. Greater cognitive flexibility was advantageous because to meet the performance goal the participant must abandon the simple, salient rule in favor of a more complex conjunctive rule. As predicted, participants given a promotion focus exceeded the performance criterion sooner, and achieved a higher overall level of performance during the final blocks of trials than people given a prevention focus. The model-based analyses suggested that participants given a promotion focus shifted away from a uni-dimensional rule strategy toward a conjunctive rule strategy sooner than prevention participants resulting in quicker, better learning. dimensional length and orientation models because the proportion of participants was low for both models and performance was similar.
4 An alternative approach is to compare frequency counts of conjunctive vs. non-conjunctive rule models using a

2 test.
This test is less powerful and yielded significant difference in only blocks 5 and 8.

Interestingly though, once a promotion or prevention participant abandoned the uni-dimensional rule in favor of the conjunctive rule, then their learning profile was the same. This latter finding suggests that the regulatory focus manipulation affected the speed of the shift from uni-dimensional to conjunctive rule use, but not the adjustments to the conjunctive rule decision criteria once that shift was achieved.
Experiment 2
Based only on the results of Experiment 1, one might draw the conclusion that a promotion focus leads to better performance in classification tasks than does a prevention focus. This conclusion is premature, however, because the category structure used in Experiment 1 was one that required flexibility in order to be learned. Quite different results might be obtained in a task in which flexibility is not warranted. In that case, people with a prevention focus might ultimately exhibit better performance.
To explore this issue, we designed a classification task in which conservative changes in a person’s criterion would lead to better performance in the task than would large changes that might be associated with high flexibility. As in Experiment 1 we used a conjunctive rule-based classification learning task, but instead of a two-category problem where uni-dimensional rules existed that yielded good performance, we used a fourcategory problem where it was clear early in learning that a two-dimensional rule was required. The stimulus on each trial was a line whose length and orientation varied across trials. The optimal rule can be described as follows: “Respond A if the length is short and the orientation is shallow; Respond B if the length is short and the orientation is steep; Respond C if the length is long and the orientation is shallow; Respond D if the length is long and the orientation is steep”. Because the two-dimensional nature of the optimal rule is clear early in learning, the type of cognitive flexibility associated with qualitative shifts in the nature of the decision rule will not be useful. Instead, good performance will be achieved through slower, more incremental changes in the decision criterion values. These slower, more incremental changes should be associated with lower levels of cognitive flexibility and thus a prevention focus.
Two additional characteristics of the task were added to bias the task in favor of low cognitive flexibility. First, the category distributions overlap and thus the participants must learn the “noisy” criterion between “short” and “long” lines and between “shallow” and “steep” orientations. Second, a base-rate manipulation was introduced. Specifically, categories C and D were presented three times as often as categories
A and B. Base-rate manipulations affect the location of the optimal decision criterion and in the present study shifted the location of the optimal length criterion away from the equal likelihood criterion. When the base-rates are unequal, the optimal classifier sacrifices accuracy on the low base-rate categories to increase accuracy on the more prevalent high base-rate categories effectively increasing overall accuracy and long-run reward. In the present study, optimal accuracy for categories A and B was 77%, and for categories C and D was 89%. Thus, the fact that a) the two-dimensional nature of the optimal rule is clear early, b) the location of the optimal criteria are noisy due to category overlap, and c) the base-rate difference shifts the criteria away from the equal likelihood criteria should provide an environment that fits well with the low cognitive flexibility, prevention focus manipulation.
The regulatory focus manipulation is one that is fairly subtle and thus should not be expected to lead to differential patterns of performance under all conditions. For example, if one constructs a situation in which the
“bonus” is easily attainable even with a sub-optimal rule, there should be little effect of regulatory focus because both promotion and prevention focus participants should achieve the goal easily. In contrast, if we create a situation in which the bonus is rarely or never attainable we should observe larger effects of the regulatory focus manipulation. To investigate this possibility, we examined the effects of regulatory focus
(promotion vs. prevention) on four-category conjunctive rule-based classification learning under two “goal states”; one for which the bonus was easily attainable (the attainable goal condition) and one for which the bonus was unattainable (the unattainable goal condition). This resulted in a 2 regulatory focus x 2 goal state factorial design.
Participants in the promotion focus condition were told that they could earn an entry into a drawing for
$50 if they exceeded a performance criterion during the final block of trials. Participants in the prevention focus condition were given an entry into the drawing for $50 upon entry into the laboratory, but were told that they had to exceed a performance criterion (identical to that in the promotion focus condition) during the final block of trials to keep the entry. Participants in the attainable goal condition received two points for each correct response and no points for incorrect responses. Participants in the attainable goal condition could obtain or keep the drawing entry if they achieved 75% of the performance level obtained by the optimal classifier (Maddox &

Bohil, 1998). Participants in the unattainable goal condition received one point for each correct response and no points for incorrect responses. Participants in this condition could not obtain or keep the drawing entry even if they responded correctly on every trial in the experiment.
We predicted that regulatory focus and goal state should interact in their effect on performance.
Specifically, we predicted no effect of regulatory focus when the goal state was highly attainable because both promotion and prevention participants could easily achieve the stated goal. In contrast, we predicted a strong effect of regulatory focus on performance when the goal state was unattainable. Under these conditions, promotion and prevention participants were unable to achieve the goal state but were attempting to do so throughout the session. If, a promotion focus leads to high levels of cognitive flexibility, then promotion focus participants should be biased toward large changes in their decision criteria across trials. In contrast, if a prevention focus leads to lower levels of cognitive flexibility, then prevention focus participants should be biased toward smaller changes in their decision criteria across trials. Learning of noisy decision criteria under unequal base-rate conditions should be better when small decision criterion changes are made. Thus, this task is better suited for a prevention regulatory focus.
Methods
Participants
One-hundred-three participants were solicited from the University community and received course credit or $6 payment for participation. In addition, participants were given the opportunity to obtain a 1 in 10 chance of receiving $50 in a random drawing. Twenty-five participated in the Promotion-Attainable condition, with 26 participating in the Promotion-Unattainable, Prevention-Attainable, and Prevention-Unattainable conditions. No one participated in more than one condition.
Stimuli and Stimulus Generation.
The stimulus on each trial was a white line with some length and orientation presented against a black background centered on in the middle of a 650 pixel x 650 pixel box in the upper left corner of the computer screen. Because the categories overlap, optimal accuracy is 77% for the low base-rate categories and 89% for the high base-rate categories. Seventy-two unique stimuli were generated from the two low base-rate categories
(A and B), and 216 unique stimuli were generated from the two high base-rate categories (C and D) for a total of 576 unique stimuli. Each category consisted of stimuli from four bivariate normal distributions. Eighteen items were sampled from each of the A and B sub-categories whereas 54 were sampled from each of the C and
D sub-categories. The category-distribution parameters are outlined in Table 3, and a scatter-plot of the stimuli along with the optimal bounds is displayed in Figure 3. The stimuli were randomized separately for each participant.
-------------------Table 3 and Figure 3-----------------------------
Procedure.
Participants were tested individually in a dimly lit room. They were informed that there were four categories and that they should emphasize accuracy over speed of responding. There was no mention of the base-rate manipulation. Participants in the promotion focus condition were told that they would be given the opportunity to obtain an entry into a drawing for $50 if they gained 67 or more points over the final 48 trials
(the last block) of the experiment. Participants in the prevention focus condition we given an entry into a drawing for $50 upon arrival in the laboratory but were informed that they would lose the entry if they did not gain 67 or more points over the final 48 trials if the experiment. In the attainable goal condition, a correct response resulted in a gain of two points, whereas in the unattainable goal condition, a correct response resulted in a gain of only one point. In both conditions, no points were gained or lost for an incorrect response. In the attainable goal condition, the ideal observer obtains 90 points in a block of trials. Based on pilot research we found that nearly all participants can reach 75% of optimal or 67 points within a few blocks (usually 3 or 4). All other aspects of the experimental procedure were identical to those from Experiment 1.
Results and Theoretical Analyses
As in Experiment 1, we begin with an examination of the accuracy rates to determine how regulatory focus and goal state affected the accuracy of the participants’ responses. Then we turn to the models in an attempt to identify what cognitive processes were affected by the regulatory focus and goal state manipulations.
Accuracy Analyses

Because the goal was highly attainable in the attainable goal state conditions we expected that promotion and prevention participants would meet or exceed the performance criterion early in learning and at the same rate. As a test of this prediction, we determined the first block of trials for which each promotion and prevention participant met or exceeded the goal. As expected, both groups achieved the goal early (average for promotion = 2.76; prevention = 3.35) and there was no difference across regulatory focus groups [t(49) = 1.16, p > .05]. The same analyses could not be conducted on the unattainable goal participants since the goal was not attainable even if the participant was correct on every trial. Thus, to determine how regulatory focus and goal state affected performance we conducted a 2 regulatory focus (Promotion vs. Prevention) x 2 goal state
(Attainable vs. Unattainable) x 12 block ANOVA on the proportion correct data. Figure 4a displays the proportion correct (averaged across participants) for the 12, 48-trial blocks for the Promotion-Attainable,
Promotion-Unattainable, Prevention-Attainable and Prevention-Unattainable conditions. The main effects of regulatory focus [F(1, 99) = 5.41, p < .05, MSE = .08], goal state [F(1, 99) = 9.30, p < .01, MSE = .08], and block [F(11, 1089) = 60.46, p < .001, MSE = .01] were all significant. Block did not interact with regulatory focus, goal state, or the combination (all F’s < 1.0), but the regulatory focus x goal state interaction was significant [F(1, 99) = 4.38, p < .05, MSE = .08]. The interaction is depicted in Figure 4b. Three comments are in order. First, regulatory focus had no effect on performance when the goal was attainable (t<1.0). Second, performance in the prevention-unattainable goal condition was equivalent to performance for the promotion- and prevention-attainable goal conditions (t’s < 1.0). Finally, performance in the promotion-unattainable goal condition was significantly worse than in each of the other three conditions (p’s < .01). Taken together, these data suggest that a prevention focus leads to better conjunctive rule-based classification learning when the goal is unattainable. When the goal is attainable, regulatory focus has no effect on performance.
-------------------Figure 4-----------------------------
Model-Based Analyses
Four decision bound models were fit separately to each participant’s block-by-block data 5 . Each assumes that the participant used a conjunctive, rule-based strategy, but the models differ in their assumptions about the optimality of the decision criterion placement along the length and orientation dimensions. The optimal model assumes that the participant used the length and orientation criteria that maximized performance.
This model has only the internal noise variance as a free parameter. The sub-optimal-length model allows the length criterion to be estimated from the data, whereas the sub-optimal-orientation model allows the orientation criterion to be estimated from the data. These two models contain two free parameters (i.e., one criterion and the noise variance). The sub-optimal-length-orientation model allows the length and orientation criteria to be estimated from the data (along with the noise variance).
AIC was used to determine the best fitting model for each participant separately by block. As one might expect performance became more nearly optimal over blocks. Interestingly there was a shift from the suboptimal-length-orientation model dominating early toward better fits of the sub-optimal-length model. Recall that this latter model assumes the optimal decision criterion along the orientation dimension and a sub-optimal decision criterion along the length dimension. This pattern was expected as the base-rate manipulation was along the length dimension, and it is well established that participants’ under-estimate the criterion shift associated with optimal responding when base-rates are unequal (see Maddox, 2002 for a review). Despite this one interesting aspect of the model-based learning profile, the most important model based results can be obtained by examining model performance averaged across blocks.
Table 4 displays the percentage of participants whose data was best fit by each of the models (averaged across the 12 blocks) along with the average accuracy rate for each class of participants separately for the four regulatory focus by goal state conditions. Two main comments are in order. First, the proportion of participants best fit by each model was relatively unaffected by the regulatory focus and goal state manipulations, although a slightly higher proportion of participants used the optimal decision strategy in the Prevention-Unattainable condition. Second, of the four models, the sub-optimal-length model provided the best fit for approximately
40% of the participants across conditions. This finding along with the fact that approximately 20% of the participants’ data was best fit by the optimal model suggests that approximately 60% of the participants in each condition were using the optimal decision criterion along orientation, but not length.
-------------------Table 4-----------------------------
5 Information-integration models (see Maddox & Ashby, 2004 for details) were also applied to the data, but these rarely provided the best account of the data and are not discussed further.

As outlined earlier, we predict that a promotion focus should lead to greater cognitive flexibility in the form of larger shifts in the decision criteria across trials when the goal is unattainable. Large shifts in the decision criteria across trials will result in a larger estimate of the noise parameter in the model. Thus, we predict larger noise estimates in the Promotion-Unattainable condition than in the other three conditions. In addition, we predict no difference in the noise estimates across these three remaining conditions. As a test of this hypothesis, we examined the parameters of the sub-optimal-length-orientation model. This model is the most general model, and thus, by definition must provide the best account of the data. In fact, during the final block of trials, this model accounted on average for 82%, 84%, 73% and 80% of the participants’ responses in the Promotion-Attainable, Prevention-Attainable, Promotion-Unattainable, and Prevention-Unattainable conditions, respectively. The estimated standard deviation of internal noise from the sub-optimal-lengthorientation model was subjected to a 2 regulatory focus x 2 goal state x 12 block mixed design ANOVA. All three main effects were significant [regulatory focus: [F(1, 99) = 5.20, p < .05, MSE = 2836.34; goal state: F(1,
99) = 8.69, p < .01, MSE = 630.38; block F(11, 1089) = 86.31, p < .001, MSE = 221.12], but none of the interactions were significant. Although the regulatory focus x goal state interaction was only marginally significant [F(1, 99) = 2.73, p = .10, MSE = 2836.34] we conducted follow-up analyses comparing the
Promotion-Unattainable condition noise values with those from the other three conditions. These data are depicted in Figure 5. As expected, we found that the standard deviation of internal noise was statistically equivalent across the two attainable goal and the Prevention-Unattainable goal conditions, but that there was significantly greater variability in the Promotion-Unattainable goal condition than in any other condition (all p’s
< .05). It is worth mentioning that an examination of the best fitting decision criteria yielded a similar result with larger deviations from the optimal values in the Promotion-Unattainable condition than in the other three conditions that yielded similar decision criterion values.
-------------------Figure 5-----------------------------
Discussion
Experiment 2 examined the effects of regulatory focus on four-category, conjunctive rule-based classification learning when the goal was easily attainable or unattainable. Because the two-dimensional nature of the rule was clear early in learning, and because noisy decision criteria had to be learned under unequal baserate conditions, we expected that classification learning would be best when the participant was under a motivational state conducive to gradual, incremental adjustment of the decision criteria, as opposed to a motivational state conducive to large shifts in the decision criteria. Our working hypothesis was that a promotion focus results in a high level of cognitive flexibility and thus is associated with large criterion shifts whereas a prevention focus results in low levels of cognitive flexibility and thus is associated with more gradual shifts in criterion. We predicted that this regulatory focus effect would only be observed when the goal was difficult to attain or was completely unattainable as in Experiment 2.
The results supported our prediction. Performance in the attainable goal condition was unaffected by regulatory focus, and was equivalent to performance in the unattainable goal condition when a prevention focus was induced. In contrast, performance was significantly worse in the unattainable goal condition when a promotion focus was induced. The model based analyses suggest that the locus of this performance deficit in the latter condition is due to poorer decision criterion placement and greater variability in the memory and placement of the decision criterion. Both of these problems are predicted from the cognitive flexibility hypothesis because large changes in the decision criteria will lead to poorer learning of the optimal criteria and, by definition, will be more variable.
General Discussion
This article aims to bridge the gap between research on motivation and cognition. In particular, we examined the effects of regulatory focus (Higgins, 1987) on perceptual classification learning. We assumed that a promotion focus supports more flexible cognitive processing than does a prevention focus. Thus, a promotion focus should be most beneficial in environments that call for flexibility.
We tested this proposal in two different classification learning settings. In Experiment 1, the participant needed to abandon a highly salient simple, uni-dimensional rule in favor of a more complex, conjunctive rule. A qualitative shift in strategy of this sort should be enhanced by greater cognitive flexibility and thus we predicted better performance under a promotion than under a prevention regulatory focus. This hypothesis was supported

by the data with faster, more accurate learning for promotion participants. Model based analyses suggested that the performance advantage that emerged late in learning for the promotion participants was due to a shift toward the more complex, conjunctive rule during the intermediate stage of learning. However, once a participant, whether promotion- or prevention-focused, abandons the uni-dimensional rule in favor of the conjunctive rule, learning progressed in a similar manner.
In Experiment 2 the two-dimensional nature of the optimal rule was apparent early in learning and so changing the decision criterion gradually was a better strategy than attempting a qualitative shift in strategy.
Under these conditions and when the goal is attainable, we predict no effect of regulatory focus because promotion participants will not chose to make big changes in their strategy and will behave similarly to prevention participants. On the other hand, when the goal is unattainable, the promotion participants, who have high levels of cognitive flexibility, will be more willing than low cognitive flexibility prevention participants to try large changes in strategy in an attempt to “find” the correct rule. Because the form of the correct rule is obvious early in learning, these large shifts in strategy will adversely affect promotion participant’s performance. Thus, we predicted that performance would be worst for promotion participants when the goal was unattainable, with no difference across the two attainable conditions. These predictions were supported by the accuracy data. In addition, and as predicted, the locus of the promotion-unattainable condition deficit appeared to be in worse memory and more variable placement of the decision criteria. Taken together, these data support Higgins’ regulatory fit hypothesis and extend it to the domain of classification learning. These data also provide support for our claim that a promotion regulatory focus leads to increased cognitive flexibility.
Implications for Research on Cognition
These data suggest that motivational focus can be manipulated easily within the framework of cognitive research, and, at least within the domain of classification learning, this simple manipulation can have a large and easily interpretable effect on performance. Our hope is that this work will stimulate other researchers to begin to examine the effects of motivation on cognition. One reason why it is important to explore the influence of regulatory focus on cognitive processing is that many studies in cognitive psychology have an implicit promotion focus that goes unrecognized. For example, in many studies experimental participants receive course credit or a monetary payment that is often accompanied by a bonus for good performance. In other cases, participants are told to complete a task and that they will be allowed to leave as soon as they achieve a certain performance criterion. Both of these situations induce a mild promotion focus. Although researchers generally use these procedures in an attempt to “motivate” participants to perform well, as the current data suggest, a promotion regulatory focus will only lead to better performance when flexibility in the task is beneficial. Thus, the bulk of our data in cognitive psychology may be drawn from conditions in which participants have a promotion focus.
Flexibility and Regulatory Fit
An important concept in current research on regulatory focus is the idea of regulatory fit (Avnet and
Higgins, 2004; Higgins, 2000). Initially, this work demonstrated that people’s perception of value can be influenced both by the worth of the item as well as by the degree to which the processes they use to obtain or use the item fit with their current regulatory focus (Higgins, Chen Idson, Freitas, Spiegel, & Molden, 2003; Lee
& Aaker, 2004). Thus, a person may value a product that prevents a disease more when they have a prevention focus than when they have a promotion focus, because of the fit between the nature of the product and their regulatory focus.
The concept of regulatory fit has two potential applications within the research program we pursue.
First, there may be a fit between the kinds of cognitive procedures supported by a regulatory focus and the domain in which cognition is taking place. For example, we suggested here that promotion focus leads to a relatively greater degree of cognitive flexibility than does a prevention focus. Furthermore, we found that when the task is constructed so that cognitive flexibility is advantageous, then promotion focused participants perform better than prevention focused participants. In contrast, when the task is constructed so that cognitive flexibility is not advantageous, promotion focused participants perform worse than prevention focused participants.
A related sense of regulatory fit can occur when an individual’s regulatory focus fits the structure of the rewards and payoffs in the environment. In the current studies, for example, participants were trying to gain points on each trial. Thus, promotion participants also had a regulatory fit between their promotion focus and the presence of rewards on each trial. Prevention participants actually had a regulatory mismatch between their regulatory focus and the presence of potential gains on each trial.
We examined this type of regulatory fit in a recent study (Markman, Baldwin, & Maddox, in press).
We asked participants to learn a difficult classification task with a noisy decision criterion. Participants given a

promotion focus could earn an entry into a monetary drawing by exceeding a performance criterion, while participants given a prevention focus had to achieve a performance criterion in order to keep their entry into a monetary drawing. In addition to the regulatory focus manipulation, we manipulated the nature of the payoffs associated with correct and incorrect responses. In the “gains” condition, participants earned points regardless of the correctness of their response, but earned more points for being correct, and more points for being correct for category A than for category B. In the “losses” condition, participants lost points regardless of the correctness of their response, but lost fewer points for being correct, and fewer points for being correct for category A than for category B. Markman et al. (in press) hypothesized that a promotion focus would lead to better learning in the gains condition than in the losses condition, and that prevention focus would lead to better learning in the losses condition than in the gains condition. This hypothesis was motivated by a regulatory fit notion and was supported by the data.
If we apply this notion of regulatory fit between an individual’s regulatory focus and the reward structure of the environment, we see that the present studies had a fit only in the promotion conditions. That is, people could receive points for their response, but could never lose points. Because the current study did not include “loss” conditions, it is impossible to determine whether a promotion focus leads to increased cognitive flexibility in general or whether a promotion focus leads to increased cognitive flexibility when it is paired with
“gains”. A critical test would require that Experiments 1 and 2 be replicated under an all loss situation. If a promotion focus always leads to increased cognitive flexibility, then the pattern of results observed in the current experiments should replicate with all loss conditions. In contrast, if increased cognitive flexibility results from a “fit” between an individual’s regulatory focus and the nature of the payoffs in the task, then we would predict the results to reverse. On this view, a prevention focus would “fit” with the loss payoffs leading to greater cognitive flexibility. (Obviously, whether cognitive flexibility leads to good task performance would still depend on whether the task domain itself was one for which cognitive flexibility was advantageous.) Future work should address this issue.
Summary
In summary, the present article provides two studies that support the conjecture that promotion focus supports flexible cognitive processing. When the task is suited to flexible processing (as in Experiment 1), people with a promotion focus outperform those with a prevention focus. In contrast, when the task is suited to more conservative cognitive processing (as in Experiment 2), people with a prevention focus outperform those with a promotion focus. Finally, the present studies illustrate the importance of testing theories of motivation with data that support modeling. The accuracy data in our studies were not sufficient to conclude that people performed more flexibly when they had a promotion focus than when they had a prevention focus. However, the model fits provided clear evidence for this flexibility. In Experiment 1, these model fits demonstrated that people with a promotion focus shifted from a unidimensional rule to a conjunctive rule faster than did people with a prevention focus. In Experiment 2, the model fits demonstrated that people with a promotion focus exhibited significantly more variability in their decision criteria than did those with a prevention focus.
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Table 1. Category Distribution Parameters for Experiment 1.
_______________________________________________________
Category
A
A
1
2
A
3
A
4
A
5
A
6
A
7
A
8
A
9
A
10
 l
42 42 12
42 114 12
42
42
114 42 12
114 114 12
114
114
 o
186
258
186
258
 l
12
12
12
12

12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12 o cov
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 lo
A
11
A
12
B
B
1
2
B
3
B
4
186 42 12
186 114 12
258
258
42
114
12
12
186 186 12
186 258 12
258
258
186
258
12
12
Note: The orientation units were transformed into radians by multiplying each value by

/500. The horizontal position for Category A items were sampled from a univariate normal distribution with mean = 253 and standard deviation =75, whereas the Category B items were sampled from a univariate normal distribution with mean = 397 and standard deviation =75.

CJ
UD-Pos
UD-L or UD-
O
Table 2. Proportion of Promotion and Prevention Focus Participants for which a Conjunctive, Uni-dimensional
Position, Uni-dimensional Length or Uni-dimensional Orientation model Provided the Best Account of the Data
Along with the Average Accuracy Rates Obtained for those Participants.
Block
Promotion
Model
Percentage
Proportion
Correct
Model
Percentage
1
37
2
27
3
33
4
40
5
53
6
50
7
60
8
60
9
57
10
63
11
67
12
63
0.87 0.84 0.90 0.91 0.89 0.87 0.91 0.92 0.94 0.95 0.94 0.96
Prevention
Promotion
Prevention
Proportion
Correct
Model
Percentage
Proportion
Correct
Model
Percentage
Proportion
Correct
40 20 27 30 27 33 40 37 43 43 53 53
0.85 0.88 0.89 0.89 0.92 0.91 0.93 0.91 0.92 0.92 0.91 0.92
37
0.85 0.82 0.84 0.83 0.83 0.86 0.87 0.82 0.82 0.85 0.82 0.84
33
50
57
53
50
47
63
47
60
50
60
37
53
40
60
37
53
37
57
33
47
37
43
0.85 0.81 0.81 0.84 0.78 0.81 0.83 0.85 0.84 0.83 0.81 0.82
Promotion
Model
Percentage
Proportion
Correct
Model
Percentage
27 23 13 13 0
0.73 0.75 0.69 0.71 NA
0 3 0 7 0
NA 0.73 NA 0.61 NA
27 23 23 7 13 7 7 3 3 0
0
NA
0
0
NA
3
Prevention
Proportion
Correct 0.67 0.70 0.74 0.79 0.75 0.73 0.85 0.88 0.77 NA NA 0.58
Note: CJ = conjunctive rule model; UD-Pos = Uni-dimensional Position model; UD-L = Uni-dimensional
Length model; UD-O = Uni-dimensional Orientation model; Promo = Promotion focus; Prev = Prevention focus; Model Prop = The proportion of participants best fit by the relevant model class; Acc = the Accuracy rate for the participants in the relevan odel class; NA = not applicable.

Table 3. Category Disribution Parameters for Experiment 2.


 l
 o
lo
A
A
2
A
A
4
B
B
2
B
B
4
C
C
2
C
C
4
D
D
2
D
1
3
1
3
1
3
1
3
D
4
105 105 15
105
135
105
135
165
195
165
195
135
135
195
195
135
135
195
195
15
135 105 15
15
105 165 15
15
135 165 15
15
165 105 15
15
195 105 15
15
165 165 15
15
195 165 15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Note: The orientation units were transformed into radians by multiplying each value by

/500.
Table 4. Percent of Participants (averaged across blocks) for which Each of the Four Models Provided the Best
Account of the Data Along with the Average Accuracy Rates Obtained for those Participants.
Attainable Unattainable
Promotion Prevention Promotion Prevention
Optimal
Sub-Optimal-Orientation
Sub-Optimal-Length
Sub-Optimal-Both
Model Percentage
Proportion Correct
Model Percentage
Proportion Correct
Model Percentage
Proportion Correct
Model Percentage
Proportion Correct
22
0.69
16
0.71
43
0.70
19
0.69
26
0.68
12
0.73
38
0.69
25
0.71
23
0.60
15
0.62
36
0.63
26
0.61
27
0.70
13
0.69
38
0.67
22
0.70

Figure 1. Scatter-plots of the stimuli along with the optimal decision bounds from the two-category conjunctive, rule-based category structure from Experiment 1. Plus signs denote stimuli from category A. Open circles denote stimuli from category B.

0.80
0.60
0.40
0.20
0.00
1.00
0.90
0.80
0.70
1
1
Promotion
Prevention
2 3
2 3
4 5
Block (48 trials/block)
4 5
A
6 7
B
6 7
C
8 9 10 11 12
8 9 10 11 12
Block (48 trials/block)
0.80
0.60
0.40
0.20
0.00
1 2 3 4 5 6 7 8 9 10 11 12
Block (48 trials/block)
Figure 2. (a) Proportion of participants who exceeded the performance criterion in Experiment 1. (b) Proportion correct (averaged across observers) from Experiment 1 along with standard error bars. (c) Proportion of participants whose data was best fit by a conjunctive model.

90
80
70
60
50
40
30
20
10
0
50 100 150
Length (pixels)
200 250
Figure 3. Scatter-plots of the stimuli along with the optimal decision bounds from the four-category conjunctive, rule-based category structure from Experiment 2. Open squares denote stimuli from category A.
Filled squares denote stimuli from category B. Filled triangles denote stimuli from category C. Open triangles denote stimuli from category D.

(a)
1.00
0.90
0.80
0.70
0.60
0.50
0.40
1 2 3 4 5 6 7 8 9 10 11 12
Block (48 trials/block)
Promotion-Attainable
Promotion-Unattainable
Prevention-Attainable
Prevention-Unattainable
(b)
1.00
0.90
0.80
0.70
0.60
0.50
0.40
Promotion
Prevention
Attainable Unattainable
Goal State
Figure 4. (a) Proportion correct (averaged across observers) from the Experiment along with standard error bars.
(b) Proportion correct (averaged across observers and blocks) from the Experiment along with standard error bars.

50
45
40
35
30
Promotion
Prevention
25
Attainable Unattainable
Figure 5. Average internal noise standard deviation from the sub-optimal-both model (averaged across observers) along with standard error bars.