Judgement frequency, belief revision, and serial processing of causal information

Transcription

1 tion. - KEYED THE QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY, 2002, 55B (3), Judgement frequency, belief revision, and serial processing of causal information Andrés Catena, Antonio Maldonado, Jesús L. Megías, and Bettina Frese Universidad de Granada, Granada, Spain The main aim of this research was to study the cognitive architecture underlying causal/covariation learning by investigating the frequency of judgement effect. Previous research has shown that decreasing the number of trials between opportunities to make a judgement in a covariation learning task led to a higher score after an a or d type of trial (positive cases) than after b and c trials (negative cases). Experiment 1 replicated this effect using a trial-by-tria l procedure and examined the conditions under which it occurs. Experiment 2 demonstrated a similar frequency of judgement effect when the information was presented in the form of contingency tables. Associative or statistical single-mechanism accounts of causal and covariation learning do not provide a satisfactory explanation for these findings. An alternative belief revision model is presented. How people learn causal relationships between events has attracted the interest of scientists for centuries. Most of the current psychological research on causal learning is designed to answer questions such as under what input output covariation conditions does the participant infer causal input output relationships (Ahn, Kalish, Medin, & Gelman, 1995; Over & Green, 2001; White, 2000). Experiments in this field frequently involve a cue (S) and an outcome (O), which can be either present or absent on a given trial. Within such experiments, four types of trial can be distinguished: a trials, where the signal and the outcome are presented together; b trials, where the signal but not the outcome occurs; c trials, in which only the outcome is present; and d trials, when neither the signal nor the outcome occur. Typically, researchers have manipulated factors such as input output contingency (usually measured using DP, defined as the difference between the probability of the outcome given the cue and the probability of the outcome when the cue did not occur) and/or complexity (i.e., how many events make up the input/output conditions; see Allan, 1993; Shanks, 1993). Participants are asked about the magnitude of the covariation or correlation between the input and the output, and they mark their estimate on a bi- or unidirectional scale. The assumption is made that subjects Requests for reprints should be sent to Andrés Catena, Departamento de Psicología Experimental, Facultad de Psicología, Universidad de Granada, Campus de Catuja, s/n, Granada, Spain. acatena@ugr.es This research was supported by the Spanish Dirección General de Investigación Científica y Técnica (DGICYT) through grants PB to A. Catena and PB to A. Maldonado. We gratefully acknowledge the helpful comments of Anthony Dickinson and David R. Shanks. We also thank K. Shashok for help with the English. Ó 2002 The Experimental Psychology Society DOI: /

2 268 CATENA ET AL. contingency/causality judgements are the indices of their covariation/causal learning (Shanks, 1985; see, e.g., Shanks, Holyoak, & Medin, 1996). In the search for the psychological mechanisms underlying contingency/causality judgements, the debate has focused on the relative merits of two types of mechanism one statistical (Cheng, 1997; Waldmann, 1996; Waldmann, Holyoak, & Fratianne, 1995) and the other associative (see Allan, 1993; Shanks, 1993). A consensus has yet to be reached concerning the outcome of this debate (see Lober & Shanks, 2000), not least because the predictions from both associative and statistical mechanisms are often equivalent at asymptote (e.g., those of DP and the delta rule, Chapman & Robbins, 1990). Moreover, Shanks (1991) has suggested that summarized presentation of information (e.g., in contingency tables) might result in the recruitment of a statistical mechanism, whereas trial-by-trial presentation might recruit an associative mechanism (see also, Price & Yates, 1995). In fact, trial-by-trial presentation is a very common procedure, and associative models appear to be well placed to explain different aspects of causality/covariation learning in this procedure (see, e.g., Dickinson & Burke, 1996; Shanks, 1987; Shanks, Darby, & Charles, 1998; Wasserman & Berglan, 1998). The results of recent studies, however, have undermined extant single-mechanism accounts of covariation judgements. For example, Catena et al. (1998) reported a series of experiments using trial-by-trial presentation within a symptom disease covariation task. In the first experiment they used a factorial procedure in which the factors were the frequency with which judgement was required (see later), symptom disease contingency, and type of the last trial in each block. Participants made a judgement after receiving information about eight patients (every eight trials) in the low-frequency condition, or after each patient or trial in the high-frequency condition. Objective contingency was set at.5 or 0.0 (defined by DP). Given the fact that associative and statistical models assume that the performance should be independent of the response mode (i.e., the frequency of judgement), both predict that the judgements should be similar in the two conditions. In contrast to these predictions, however, when the frequency of judgement increased, judgements became less accurate that is, less similar to the objective contingency, as defined by DP. The most important finding, however, was that this lack of accuracy in the high-frequency condition was determined and modulated by the type of trial that preceded the judgement. After an a or d trial, judgement scores were higher than after b or c trials. This frequency of judgement effect could not be attributed to interference, recency, or memory demands, and it seemed highly resistant to manipulation through instruction (see for a detailed discussion, Catena et al., 1998). Given the fact that single-mechanism models cannot explain this frequency of judgement effect, Catena et al. (1998) suggested an alternative model in which judgements depend on two mechanisms that operate in series (see also, Maldonado, Catena, Candido, & Garcia, 1999; Pennington & Hastie, 1992; Price & Yates, 1995): an information-computing mechanism that comes into play first and passes its output to an informating-integrating mechanism that then produces the judgement (see Figure 1). The information-integrating mechanism controls the updating of the judgement on trial n. This judgement is a function of the discrepancy between the new evidence and the judgement at trial n k, according to the following formula: n n - k n -k J = J + b( NewEvidence - J ) 1

3 SERIAL PROCESSING OF CAUSAL INFORMATION 269 Figure 1. The belief revision model: The serial, two-mechanism architecture for the causality/covariation judgement. where J stands for judgement on trial n (or n k), k is the number of trials since the last judgement, b is the revision rate parameter, and New Evidence refers to the amount of new information presented since the last judgement was made (i.e., between trial n k and trial n). This mechanism integrates information from two main sources: the causal knowledge and previous causal beliefs of the subject and the output of the information-computing mechanism (i.e., the new evidence). Previous beliefs, experience and task demands contribute to establish the value of the actualization rate parameter, b, and the weights (w j ; see later) of the type of trial (see Maldonado et al., 1999). The information-computing mechanism computes the new evidence with a statistical method such as a weighted delta D:

4 270 CATENA ET AL. w a + w b+ w c + w d NewEvidence = a + b+ c + d where a, b, c, and d are the number of each type of trial, and w j is the weight of each trial type. This mechanism is affected by factors related to the input such as number of causal agents. It is important to note that the information-computing mechanism is reset after every judgement, in order to be able to compute the new evidence between judgements. According to this model, the influence of the last trial on computation of new evidence will increase as the frequency of judgement increases. To illustrate this effect, let us assume that b =.5, w 1 = 10, w 2 = 7, w 3 = 7, and w 4 = 6. Consider the case in which the first block of eight trials has three a, one b, one c, and three d trials. The new evidence would be 3* * (- 7) + 1* (- 7) + 3* 6 = in the low-frequency condition. The judgement after the eighth trial would be J 1 = * = independently of the order of the trials. In the high-frequency condition, however, the eighth judgement (i.e., the judgement after the eighth trial) depends on the sequence of trials and on the type of the eighth trial. By way of an example, let us assume the sequence is a,d,d,a,c,d,b,a. According to the model, the eighth judgement will yield a value of However, the single interchange of the last two events (a b) will decrease the judgement to 0.20 with no change in the parameters. In the experiments described here we attempted to establish the generality of the frequency of judgment effect. Experiment 1 used a dual task procedure to examine further whether it is necessary to appeal to two mechanisms in order to understand the processes that underlie the learning of causal relationships. The crucial manipulation in this experiment was the presentation of two tasks (T1 and T2) in two groups (HL and LH). The tasks were presented in an alternating manner, and they differed in the frequency with which a causal judgement was required (high, H, and low, L). As we have shown, single-mechanism models do not predict that the frequency of judgement has any effect in covariant learning and, therefore, predict that the causal judgements will be equivalent in both H and L conditions. However, the belief-revision model assumes that the computational mechanism is reset after each judgement and that the new evidence is computed from the information that accumulates between consecutive judgements. Consequently, it predicts interference from the high-frequency task (H) upon the low-frequency one (L), because every time that the subjects make a judgement in task H, the computational mechanism is reset, preventing the accumulation of information in task L (cf., Catena et al., 1998, Experiment 3). Experiment 2 simply investigated whether it was possible to demonstrate a frequency of judgement effect when contingency tables were used. As we have indicated, the belief revision model predicts that such an effect should be apparent even when the information is presented in contingency tables. Overview of the experiments The two experiments had a similar design. Each participant was required to learn about and judge cause effect relationships in two problems (T1 and T2) involving the potential causes of

5 SERIAL PROCESSING OF CAUSAL INFORMATION 271 two fictitious diseases in a factory. In each problem, the participants received information about whether each worker in the factory had the disease, and whether the potential causal agent was present in each worker. The participants task was to estimate the degree of the relationships between the potential cause and the subsequent disease, in a legal suit brought against the factory by the workers. In both experiments there were two basic conditions. In the high-frequency condition (H) the participants were asked to provide a judgement after they had received each piece of information; results were obtained for either a single worker (Experiment 1) or as a single summary table for all workers (Experiment 2). In the low-frequency condition (L) participants provided their judgements after they had received every eight pieces of information (either eight workers or eight tables). The cause effect contingency, as measured by DP, was always set at.5. It is important to note that the information was presented on a trial-by-trial basis and that the participants knew from the beginning of training that they were to provide a judgement after a given number of trials. Only the judgement frequency differed between the two conditions. EXPERIMENT 1 In Experiment 1 all participants received two similar problems. In the high high (HH) and low low (LL) conditions, the same participant was asked to estimate the relationships between a possible cause and an effect in two tasks. Judgements made in each condition were expected to differ according to the belief revision model: Judgements made in the high-frequency condition would be less accurate and would be affected by the type of the last judgement. The next question was how people solve a high-frequency and a similar low-frequency task when they are intermixed in the high low (HL) and the low high (LH) conditions (i.e., H L H L H L H L in the HL condition and L H L H L H L H in the LH condition). The belief revision model (see Figure 1) proposes that the new evidence is based on information presented between two consecutive judgements. Accordingly, it predicts that the H task will interfere with the L task, because after each judgement the mechanism of computation of the new evidence is reset, and a new count begins. For example, let us suppose the sequence is a1a2d1d2b1b2a1a2d1d2c1c2d1d2a1a2, in which 1 and 2 represent the high- and low-frequency tasks in group LH, and a, b, c, and d represent the different trial types. Participants do not make a judgement in the low-frequency condition until after the last trial, but they do not accumulate evidence because the computation mechanism has been reset after each judgment that is made in the high-frequency task. With this assumption, and using the same parameters as before, the prediction for the high-frequency condition is that the judgement after Trial 8 (J 8 ) is as follows: J 8 = *( ) = where 2.58 is the judgement at Trial 7,b is.5, and 10 is the new evidence between trials 7 and 8. The prediction for the low-frequency condition is: J 8 = *( 10-0) = 5

6 272 CATENA ET AL. where 0 is the judgement at Trial 0. In both conditions, the new evidence is reduced to the computation of the last trial. It is important to note that, assuming no interference, the predicted judgement for this low-frequency condition would be 2.13 after this last block. Method Participants The participants were 128 University of Granada law faculty undergraduates; approximately 70% of the participants were female and all received extra course credits for their participation. The mean age was 22 years (range: 21 to 25). They had not participated in a previous psychological experiment. Design and procedure Each participant was seated alone at his or her classroom desk. They each received a booklet containing information about the tasks, and in which they were to record their judgements. The instructions described a fictitious lawsuit put forward by the factory workers. There were two different contingency problems, but in both the contingency was fixed at DP =.5. In the first task (hereafter T1), the disease was miltosis, and the potential causal agent was the inhalation of a gas in an industrial plant. In the second task (hereafter T2), the disease was a skin rash, and the potential cause was excessive overtime hours worked. The two tasks were presented as part of an expert report requested by a fictitious judge. In T1, information was given about 32 different workers who underwent medical examination. Participants received information about whether the workers had inhaled the gas and the subsequent development of the disease (miltosis). In T2, information was given about the time spent on the job by the workers and the development of the skin rash. Participants were instructed not to reread the pages already completed and to avoid writing notes in the booklet. In the high-frequency condition, each page contained the information about one worker followed by the judgement scale. In the low-frequency condition, the response scale appeared only after every eight workers. The response scale section was from 100 to +100 in 10-point increments, with the corresponding interpretations ( 100 stood for an extremely negative relationship; +100 represented the positive extreme; and 0 expressed no relationship at all). The question participants were asked to respond to was: Taking into account all the information you have seen until now, how strong do you think the relationship is between the disease and the potential cause? 1 Each participant received information about 32 fictitious workers in each task. There were four worker (trial) types: The a type had the potential cause and the disease; the b type had the cause but not the disease; the c type had the disease but not the cause; and the d type had neither the cause nor the disease. To study the influence of each type of trial, each participant received a different sequence of events, and the type of the last trial in each block was counterbalanced using an incomplete within-group sequence. For 8 participants, the last trial of the first, second, third, and fourth blocks of eight trials was a, b, d, and c, respectively; from the remaining 24 participants, 8 received each of the following sequences: b, c, a, d; c, d, b, a; and d, a, c, b. The sequence of the remaining trials in each block was randomly produced with the aid of a personal computer; however, within each block the objective contingency was.5. In each sequence, trials from one task (T1) were alternated with trials from the other task (T2). Participants in the HH group provided judgements in the high-frequency mode for both tasks (T1 and T2), whereas those in the LL group provided judgements in the low-frequency mode of response for both tasks. In groups LH and HL, one task (T1 or T2) was performed in the high-frequency judgement 1 This is the translation of the Spanish sentence: Teniendo en cuenta toda la información que se le ha presentado hasta el momento, hasta que punto cree que C causa E?

7 SERIAL PROCESSING OF CAUSAL INFORMATION 273 mode and the other in the low-frequency mode. The order of problem evaluation and of frequency of judgement conditions (high and low) was counterbalanced. Accordingly, half of the participants judged the gas miltosis relationship in a high-frequency mode and the relationship between hours spent on the job and the appearance of the skin rash in a low-frequency mode; for the remainder these assignments were reversed. Temporal parameters were undetermined because the test was self-paced. Results and discussion The judgements that were analysed were those after Trials 8, 16, 24, and 32 (i.e., after each block of eight trials) because these were the trials on which participants in both the high- and the low-frequency conditions made judgements. The data were ordered according to the type of the last trial in each block (called hereafter type-of-last trial analysis, see Figure 2). This makes it possible to look for interactions between the frequency of judgement and the type of the last trial in each block before that judgement. For all statistical analyses, the significance level was fixed at.05. Figure 2 shows mean causality judgements for each group and type of last trial, collapsed across T1 and T2. The results from groups HH and LL replicate the frequency of judgement effect: The mean judgement in group LL was the same across all trial types, whereas the judgements in group HH were dependent on the type of the last trial in the block. Judgements by participants in groups HL and LH showed the same pattern as that of group HH and thereby indicate that the high-frequency task influenced performance in the low-frequency task. The data were subjected to an analysis of variance (ANOVA), where the first factor was the treatment group (HH, HL, LH or LL), and the two within-subject factors were type of Figure 2. Experiment 1: Mean causality judgement as a function of judgement frequency (high, H; low, L) and type of the last trial (a, b, c, and d) in each of the four groups (LL, HH, LH, and HL).

8 274 CATENA ET AL. task (T1 or T2) and type of the last trial in each block (types a, b, c, or d). This analysis revealed significant effects of the type of task, F(1, 126) = 10.13, type of the last trial, F(3, 372) = 21.58, and an interaction between treatment group and type of the last trial, F(9, 378) = There were, however, no other significant effects or interactions. Simple effects analysis of the Group Type of Trial interaction showed first that there were significant differences between trial types in group HH, F(3, 93) = 3.85, group HL, F(3, 93) = 9.19, and group LH, F(3, 93) = 12.69, but not in group LL (F < 1). Post hoc least significant difference (LSD) tests in the HH, HL, and LH groups indicated that judgement scores after type a trials were higher than scores after b and c trials in all groups. The only difference between these three groups (HH, HL, and LH) was that judgement scores after type d trials were lower than scores following type a trials in group LH, somewhat lower (p.056) in group HL, and not significantly different in group HH, which suggests that subjects had some difficulty in evaluating such types of trial (see for discussion Catena et al., 1998). Second, there were significant differences between groups only on type b, F(3, 124) = 4.14, and type c, F(3, 124) = 5.37, trials. Post hoc LSD tests showed that group LL scores were higher than those of the other groups on both types of trial. The results from groups LL and HH replicated the frequency of judgement effect when two tasks were intermixed and the same judgement frequency was used (see Figure 2). The most noteworthy results were those obtained in the two groups in which the frequency of judgement conditions were intermixed (in groups HL and LH). This arrangement resulted in a pattern of judgements in the low-frequency condition that matched that observed in the high-frequency condition. This pattern of results is consistent with the belief revision model and is inconsistent with predictions derived from single-mechanism models in which performance in both conditions (H or L) should have been similar and close to the objectively defined contingency. To assess the generality of the influence of the frequency with which judgements are made, the next experiment used contingency tables to present the information about the relationship between potential causes and effects. In these conditions it is often assumed that a statistical mechanism operates. EXPERIMENT 2 Experiment 2 used a summarized data presentation format, instead of a trial-by-trial presentation, to provide information about the contingency between the potential cause and the effect. In each table the number of a type, b type, c type, or d type events in each cell was different (see Figure 3), whereas the contingency was held at DP =.5. A table was defined as a, b, c, or d to indicate that the value in each of these cells was the greatest (see Figure 3). In terms of the belief revision model, the new-evidence is different after each type of table (58, 46, 41, and 57 for table types a, b, c, and d, respectively; see NE in Figure 3), whereas the new evidence taking into account all tables was 52 (using the parameters for the belief revision model from Table 2, see later). In the low-frequency condition, participants provided a causality judgement after a block of eight tables. According to the belief revision model, that judgement will take into account all the information seen in the eight tables, and the model will predict no judgement differences after each of the four blocks, as the new evidence is the same. In the high-frequency

9 Figure 3. Type of table defined according to the relative frequency of each cell. P(e/c) is the conditional probability of the effect given the cause, and P(e/ c) is the probability of the effect given no cause. DP is the difference between these two conditional probabilities, and p is the causal power as defined by equation p = 1 P(e/c), where e represents effect, and c represents the absence of the cause. NE stands for the new evidence derived from the belief revision model. 275

10 276 CATENA ET AL. condition, however, participants were asked to estimate the relationship after each table. The belief revision model proposes that the computation of the new evidence is made considering only the information given in the last table, because the computation mechanism is reset after each judgement. Therefore, the predictions of the model for the high-frequency condition are that the judgement should be higher after an a type than after a c type or b type of table (see Figure 3; Table 2, see later). Method Participants The participants were 64 undergraduate students from the University of Granada law faculty. The sample had approximately the same composition and characteristics as that in Experiment 1. Design and procedure The general design of Experiment 2 was similar to that of Experiment 1 with the exception that only Task 1 was used (the potential causal agent was inhalation of a gas, and the disease was miltosis ). Instructions, stimuli, question, and judgement scale were the same as those used in Experiment 1 and similarly presented in a booklet. The only difference was that in each booklet a contingency table indicated the frequency of a, b, c, and d results of 32 fictitious workers (see Figure 3, for examples). Participants provided a judgement of causal relationship between the potential causal agent and the illness after every eight tables in the low-frequency group (L) and after each table in the high-frequency group (H). An incomplete counterbalanced matrix was used to control for the type of the last table of each block. It is important to note that all tables had the same contingency (DP = +.5, see Figure 3) obtained from different conditional probabilities: minimum p(e/c) =.625; maximum p(e/c) =.875; minimum p(e/ c) =.125, maximum p(e/ c) =.375. All other procedural details were the same as those in the previous experiment. Results and discussion Figure 4 shows the same patterns of results as those in Experiment 1 in both the high- and the low-frequency conditions. No difference was found between types of table in the low-frequency condition, whereas in the high-frequency condition, judgements were dependent on the type of table that had immediately preceded the judgement: Judgements are higher after an a table than after the other types of table. ANOVA with frequency of judgement and type of table as factors showed significant effects of frequency, F(1, 70) = 4.49, type of table, F(3, 210) = 6.48, and interaction between the two, F(3, 210) = A simple main effects analysis revealed a significant effect of type of the last table in the high-frequency group, F(3, 105) = Post hoc LSD tests showed that the mean score when type a tables were presented was higher than that when type b, c, d tables were used. However, in the low-frequency group there was no significant effect of the type of the last table, F(3, 105) = On the other hand, scores in the low-frequency (L) group were higher than in the high-frequency (H) group for type b, F(1, 70) = 6.09, and type c tables, F(1, 70) = These results were similar to those found in Experiment 1 with groups HH and LL, and they indicated that the frequency of judgement effect can be observed when information is presented in a table-by-table instead of a trial-by-trial format. The implications of these results are explored later.

11 SERIAL PROCESSING OF CAUSAL INFORMATION 277 Figure 4. Experiment 2: Mean causality judgement as a function of the judgement frequency (high, H; low, L) and table type (a, b, c, and d). GENERAL DISCUSSION The results of these experiments demonstrated a frequency of judgement effect, defined as an interaction between the frequency with which judgements are made and the type of the last trial in each block. This effect is robust: It was obtained with different formats for the presentation of information (trial-by-trial or contingency tables). Experiment 1 replicated the frequency of judgement effect when the participants made causal judgements in two similar tasks at the same time. When judgements in both tasks were made under a low-frequency (LL group) condition, the participants accurately detected the contingency regardless of the type of the last trial in each block. However, when judgements in both tasks (HH group) or in either one of the tasks (LH and HL) were made under a high-frequency condition, they were affected by the last trial. Experiment 2 demonstrated a similar frequency of judgement effect when a summarized procedure for data presentation was used. Again, the smaller the piece of information (i.e., the number of tables between two consecutive judgements), the greater the influence of the relative frequency of each cell in the contingency table. The results of Experiments 1 and 2 indicate that causal judgement accuracy is a function of two factors. First, it increases as the number of trials or pieces of information between two consecutive judgements increases that is, as the frequency of judgement decreases. Second, accuracy in the high-frequency conditions depends on the type of information given immediately before the judgement is made. The importance of these effects lies in their implications for theoretical accounts of contingency/causality learning.

12 278 CATENA ET AL. Single-mechanism models Single-mechanism models assume that judgement is mapped from the outcome of only one mechanism either statistical (Cheng, 1997) or associative (Shanks, 1993). Models based on an associative mechanism (Allan, 1993; Markman, 1989; Van Hamme & Wassermann, 1994) appear to be well suited to account for trial-by-trial presentation. However, these models do not anticipate the results of Experiments 1 and 2 (see also, Catena et al., 1998). These models could yield different predictions, however, if they assumed that the judgement frequency affects learning rate parameters. This change might, for example, explain the differences frequently found at the end of a given period of training (i.e., a response mode effect, Catena et al., 1998), as performance reached will depend on these parameters (Allan, 1993). After a non-exhaustive search in the learning rate parameter space to fit the data for group HH and group LL in Experiment 1, we found that Markman s (1989) model predicted significant differences between a and d versus b and c trials not only in the high- but also in the low-frequency conditions (see Table 1). Furthermore, this type of model does not provide a ready account for the results obtained when each of the two tasks was estimated in either the high- or the low-frequency mode. According to single-mechanism models, the judgements should be accurate in both tasks. However, there was a clear interaction between the two tasks: The pattern of the results in the low-frequency task was less consistent with DP and similar to that of the high-frequency task. Finally, the associative approach is less suited to accommodate the results of Experiment 2, where a similar effect of judgement frequency was observed when contingency tables were used. Let us now return to the statistical models. According to these models, the factors that affect the computation of the rule (DP or causal power p) should also affect causality judgements. However, judgement frequency was not considered to be one of these factors. In Experiments 1 and 2, delta P and p were the same in the high- and low-frequency conditions. Therefore the estimations in both conditions should not have differed. It could be argued that TABLE 1 Markman (1989) and belief revision model predictions, and mean causality judgement in Experiment 1 as a function of type of trial and judgement frequency Type of trial a b c d RMSE Markman model L H Belief revision model L H Causality judgement L mean judgement H mean judgement Note: Predictions for the belief revision model were obtained assuming the same parameters used in Catena, Maldonado, and Candido (1998): w 1 = 100; w 2 = 70; w 3 = 70; w 4 = 60; high-frequency b =.3; low-frequency b =.9. Learning rates in the Markman model were: high-frequency a =.45; low-frequency a =.2. RMSE = root mean square error of prediction. Causality judgements were calculated by collapsing the first and the second task estimations in groups LL and HH in Experiment 1.

13 SERIAL PROCESSING OF CAUSAL INFORMATION 279 TABLE 2 Causal power (p) and belief revision model predictions, and mean causality judgement in Experiment 2 as a function of table type and judgement frequency Table type a b c d RMSE Power PC model Accumulated p 100 (LF) Nonaccumulated p 100 (HF) Belief revision model L H Causality judgement L mean judgement H mean judgement Note: Predictions for the belief revision model were obtained assuming the following parameters: w 1 = 100; w 2 = 60; w 3 = 60;w 4 = 80; trial-by-trial b =.5; block-by-block b =.9. RMSE = root mean square error of prediction. participants in the high-frequency condition computed the contingency or causal power piece by piece (i.e., trial by trial in Experiment 1 or table by table in Experiment 2, see Figure 3), and that the power would thus be different in the high- and in the low-frequency condition. Table 2 presents the predictions of the power PC model and the mean judgements under each experimental condition. Participants might (or might not) accumulate the information from table to table (see Table 2); the cumulative predictions fitted the low frequency condition quite well, but not the high-frequency condition. The problem with a non-cumulative causal power analysis is that it is unable to predict the judgements in either the H or L condition (see Table 2). Moreover, this account does not provide a ready account for why the frequency of judgement effect interacts with the frequency with which judgements are made or the interference found when the two tasks are estimated under different frequency conditions (see Experiment 1). A two-mechanism model The models that are currently used to explain causal/covariation learning assume that the products of the processing mechanism are directly translated into judgements. In other words, the processing mechanism is continuously active, and the judgement is an index of the current state of that process. The belief revision model (Catena et al., 1998; Maldonado et al., 1999) proposed that covariation detection and causal learning may be better explained by assuming that the mechanism that produces the judgement is not the same as the mechanism that processes the causal information. According to this model, these two functions are carried out by two mechanisms at different levels in the serial-information-processing hierarchy (see Figure 1). The first mechanism (whether statistical or associative) is thought to compute the information obtained since the last estimation made by the subject. Its function is thought to be to store information about individual events or categories of events or types of trial. This mechanism would be affected by variables related to the input, such as the contingency, the intervals, and other variables whose influence on causal judgements have been extensively demonstrated. The final judgement is thought to depend on the operation of a second mechanism that

14 280 CATENA ET AL. integrates information. This second mechanism combines the information from different sources such as instructions, previous beliefs, and task expectations, and information received by the statistical mechanism. In addition, it is considered to hold operative control over the computation mechanism via two kinds of effect. The first effect is to reset this mechanism after each judgement, which defines the amount of information that will be summarized. The second effect is to select the computation subtype (associative or statistical) that will be applied. We also assume that cognitive variables (such as causal beliefs, evaluation of the task demands, previous experience with the task, cognitive strategies, instructions, and so on; see Maldonado et al., 1999), as well as emotional and motivational factors (incentives, value of the consequences, and so on; see Reed, 1994) influence this mechanism. Summary The main aim of this paper was to demonstrate the generality of the frequency of judgement effect. This effect implies that making a judgement is a crucial determinant of judgement accuracy (Catena et al., 1998; Maldonado et al., 1999). We submit that various singlemechanism theories cannot account for this effect and instead propose an account that includes two mechanisms that operate in a serial manner: The first of these computes the statistical relationship, and the second one integrates this information with any other information or beliefs about the task. This model provides a successful account of causal judgements whether information is presented in summarized or trial-by-trial format, and it predicts similar frequency of judgement effects in both procedures. REFERENCES Ahn, G., Kalish, C.K., Medin, D.L., & Gelman, S.A. (1995). The role of covariation versus mechanism information in causal attribution. Cognition, 54, Allan, L.G. (1993). Human contingency judgements: Rule based or associative? Psychological Bulletin, 114, Catena, A., Maldonado, A., & Cándido, A. (1998). The effect of frequency of judgement and the type of trials on covariation learning. Journal of Experimental Psychology: Human Perception and Performance, 24, Chapman, G.B., & Robbins, S.J. (1990). Cue interaction in human contingency judgement. Memory and Cognition, 18, Cheng, P. (1997). From covariation to causation: A causal power theory. Psychological Review, 104, Dickinson, A., & Burke, J. (1996). Within-compound associations mediate the retrospective revaluation of causality judgements. Quarterly Journal of Experimental Psychology: Comparative and Physiological Psychology, 49B, Lober, K., & Shanks, D.R. (2000). Is causal induction based on causal power? Critique of Cheng (1997). Psychological Review, 107, Maldonado, A., Catena, A., Cándido, A., & García, I. (1999). The belief revision model: Asymmetrical effects of noncontingency in human covariation learning. Animal Learning & Behavior, 27, Markman, A.B. (1989). LMS rules and the inverse base-rate effect: Comment on Gluck and Bower (1988). Journal of Experimental Psychology: General, 118, Over, D.E., & Green, D.W. (2001). Contingency, causation, and adaptive inference. Psychological Review, 108, Pennington, N., & Hastie, R. (1992). Explaining the evidence: Tests of the Story Model for juror decision making. Journal of Personality and Social Psychology, 62, Price, P.C., & Yates, J.F. (1995). Associative and rule-based accounts of cue interaction in contingency judgement. Journal of Experimental Psychology: Learning, Memory, and Cognition, 21, Reed, P. (1994). Influence of the cost of responding on human causality judgements. Memory and Cognition, 22,

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