Causal attribution from covariation information: the evidential evaluation model

Transcription

1 European Journal of Social Psychology Eur. J. Soc. Psychol. 32, (2002) Published online 3 July 2002 in Wiley InterScience ( DOI: /ejsp.115 Causal attribution from covariation information: the evidential evaluation model PETER A. WHITE* School of Psychology, Cardiff University, UK Abstract It is hypothesized that causal attributions are made by transforming covariation information into evidence according to notions of evidential value, and that causal judgement is a function of the proportion of instances that are evaluated as confirmatory for the causal hypothesis under test: this is called the evidential evaluation model. An experiment was designed to test the judgemental rule in this model by setting up problems presenting consensus, distinctiveness, and consistency information in which the proportion of confirmatory instances varied but the objective contingency did not. It was found that judgements tended to vary with the proportion of confirmatory instances. Several other current models of causal judgement or causal attribution fail to account for this result. Similar findings have been obtained in studies of causal judgement from contingency information, so the present findings support an argument that the evidential evaluation model provides a unified account of judgement in both domains. Copyright # 2002 John Wiley & Sons, Ltd. For more than forty years the idea that people make causal attributions by assessing covariation between candidate causes and effects has been a central theme of attribution research. Heider (1958) defined the covariation principle as follows: that condition will be held responsible for an effect which is present when the effect is present and absent when the effect is absent (p. 152). He derived this principle from the work of Cohen and Nagel (1934) who propounded a general view of a causal relation as a kind of invariant relation in which the cause is invariably connected with the effect (White, 2000a). The principle reflects Heider s view that people make causal attributions in the manner of naive scientists concerned primarily with the goals of understanding, prediction, and control. In accord with this he suggested that causal analysis is in a way analogous to experimental methods (p. 297). Kelley (1967, 1972, 1973) developed Heider s suggestion in a systematic way, using the covariation principle as the core of a model of causal attribution based on an analogy with the orthogonal manipulation of independent variables in analysis of variance designs. The aim of the model was to distinguish between three possible causal candidates. For example, where the effect to be explained is, John laughs at the comedian, the three candidates are the actor (John, the person who carries out the *Correspondence to: Peter A. White, School of Psychology, Cardiff University, PO Box 901, Cardiff CF10 3YG, Wales, UK. whitepa@cardiff.ac.uk Received 14 August 2001 Copyright # 2002 John Wiley & Sons, Ltd. Accepted 22 January 2002

2 668 Peter A. White behaviour in question), the target or object (the thing to which the behaviour is done, in this case the comedian), and the occasion or circumstances under which the behaviour is carried out. Causal attribution can, in principle, also be made to interactions between any two or all three of the candidates. To make a causal attribution people are presumed to seek information on three orthogonal dimensions. These are consensus, information about the behaviour of different actors with the same target under the same circumstances, distinctiveness, information about the behaviour of the same actor with different targets under the same circumstances, and consistency, information about the behaviour of the same actor with the same target under different circumstances. Covariation is assessed for each causal candidate across a sample of instances drawn from these three dimensions in a manner computationally equivalent to analysis of variance. The candidate that covaries with the effect is identified as the cause. If more than one candidate covaries with the effect then the cause is identified as an interaction between the covariates. Subsequently several other models of causal attribution from covariation information were proposed. Some of these were proposals about the kind of information that is sampled for purposes of causal attribution (Orvis, Cunningham, & Kelley, 1975; Pruitt & Insko, 1980; Forsterling, 1989; Cheng & Novick, 1990). Others have proposed different inductive rules in an attempt to provide a better account of the evidence from causal attribution experiments (Jaspars, 1983; Hilton & Slugoski, 1986; Hewstone & Jaspars, 1987; Cheng & Novick, 1990, 1992; Hilton, Smith, & Kim, 1995; Van Overwalle & Heylighen, 1995). The inductive rule that best describes the way in which people make causal attributions is the main concern of the present paper. Specifically, this research was designed to test the hypothesis that a model recently developed to account for the phenomena of causal judgement from contingency information accounts for phenomena of causal attribution as well, and that the two kinds of judgement are therefore made in the same way. Contingency information is information about the occurrence or nonoccurrence of a certain effect in the presence or absence of a certain causal candidate. The conventional identification of cells in a 2 2 contingency table is shown in Table 1: those conventions will be adopted herein. Studies of causal judgement from contingency information do not employ the verbal summary statements commonly used in causal attribution research. They present quantitative information, either summarised in a contingency table (e.g. Wasserman, 1990) or, more commonly, as a list of individual instances, either all available for scrutiny at once (e.g. White, 2000c, Making causal judgements from contingency information: the Evidential Evaluation model, submitted 2001) or in a trial-by-trial procedure in which each instance is removed and no longer available for scrutiny before the next one is presented (e.g. Shanks, 1987, White, 2000b, submitted 2001). The generally accepted objective measure of contingency is the P (delta P) rule (Jenkins & Ward, 1965; McKenzie, 1994; Ward & Jenkins, 1965). In terms of Table 1, P ¼ða=a þ bþ ðc=c þ dþ. More commonly it is represented as P ¼ pðe=cþ pðe= cþ ð1þ Table 1. Conventional identification of cells in the 2 2 contingency table Effect occurs Candidate cause Yes No Present a b Absent c d

3 Causal attribution 669 where p(e/c) is the probability that the effect occurs when the cause is present and p(e/ c) is the probability that the effect occurs when the cause is absent. Values of P fall in the range 1 (perfect negative contingency) to þ1 (perfect positive contingency). THE EVIDENTIAL EVALUATION MODEL The central proposition of the evidential evaluation model, which has been developed in a series of recent papers (White, 1998, 2000b, 2000c, 2002, in press, submitted 2001), is that instances of contingency information are treated as evidence with respect to a causal interpretation. In the case of causal attribution this means that instances of covariation information are treated as evidence with respect to whichever locus is being judged. When people are exposed to an instance of information they evaluate that instance in terms of its evidential value for the causal locus being judged. Judgement of a particular causal interpretation is determined by the proportion of instances in a sample that are evaluated as confirmatory for that interpretation. This is called the pci rule, where pci ¼ proportion of confirming instances. Normatively cells a and d are confirmatory, meaning that such instances increase the likelihood that the candidate being judged is the cause of the effect, and cells b and c are disconfirmatory. By this criterion the proportion of confirming instances would be the proportion of instances that fall into cells a and d. Most individuals conform to these normative evaluations for most cells but there are also frequent individual differences (Anderson & Sheu, 1995; White, 2000b). This implies the general model of the pci rule applied to the 2 2 contingency table format that is shown in equation (2) (White, submitted 2001, in press): W a a þ W d d J I ¼ ð2þ W a a þ W b b þ W c c þ W d d J I is the judgement of interpretation I and W a, W b, W c, and W d are weights assigned to cells a, b, c, and d respectively. Equation (2) is intended to accommodate individual differences in notions of evidential value by expressing them as cell weights. The general model therefore accommodates judges who assign equal weight to cells a and d, those who assign more weight to cell a than to cell d, and those who assign no weight to cell d at all. It can even accommodate those who assign counter-normative, disconfirmatory value to cell d if W d can take negative values. The model can accommodate a considerable range of individual differences, but White (2002, submitted 2001) observed that at the level of sample means it is over-inclusive, in other words capable of predicting tendencies that happen not to obtain as well as those that do. White (2002, submitted 2001) therefore proposed a more specific and predictively powerful version of the model that takes its form from two observations about causal judgement: most uses of contingency information conform to normative evidential evaluations, and individual differences in notions of evidential value are nonrandomly distributed (Anderson & Sheu, 1995; White, 2000b). The Pad Rule The finding that most uses of contingency information are normative implies that the unweighted version of the model provides a good approximation for predictive purposes at the level of sample means and should outperform other inductive rules. The unweighted rule is shown in J I ¼ a þ d ð3þ T

4 670 Peter A. White where T ¼ the total number of instances under consideration. This is called the Pad rule, referring to the Proportion of instances in cells a and d. Several experiments have found that Pad is a better predictor of causal judgements than P is. White (2002, submitted 2001) found that when Pad was manipulated and P was held constant causal judgements tended to vary with Pad, but when P was manipulated and Pad held constant, no significant differences were found. When p(c), the proportion of instances on which the candidate is present overall, ¼ 0.5, then values of P and Pad are isomorphic and generate identical ordinal predictions for causal judgement (White, submitted 2001). This is an important feature of the Pad rule. Many studies have shown that causal judgements conform closely to objective differences in P (Allan, 1993; Cheng, 1997; Shanks, 1995; Vallée-Tourangeau, Hollingsworth, & Murphy, 1998; Wasserman, Elek, Chatlosh, & Baker, 1993; White, 2000b). But in all these studies p(c) ¼ 0.5, and so the Pad rule fits that evidence as well as any other rule could. The only way to distinguish between Pad and P (and models based on P) isby using stimulus materials in which p(c) 6¼ 0.5. That was the approach taken by White (2002, submitted 2001), and the same strategy is used here. The Cause-present Effect The Pad rule is the main focus of the present research. However, the finding that individual differences in notions of evidential value are non-randomly distributed implies an important qualification to the Pad rule. White (2000b) found that cause-present information was consistently used according to normative notions of evidential value, but the evaluation of cause-absent information varied considerably between individuals, with some conforming to normative notions, others assigning it no evidential value, and others evaluating it in other idiosyncratic ways. This implies that causepresent information has a greater effect on mean tendencies in causal judgement than cause-absent information does, other things being equal. This will be called the cause-present effect. The causepresent effect will not be observed in every individual: it is an emergent property of the aggregation of individual tendencies in the evaluation of contingency information. To see how the cause-present effect works, suppose a set of instances in which P ¼þ0.5. If p(e), the proportion of instances under consideration in which the effect occurs, ¼ 0.5, then p(e/c) ¼ 0.75 and p(e/ c) ¼ However if p(e) ¼ 0.75, then p(e/c) ¼ 1.0 and p(e/ c) ¼ 0.5. No other values are possible without P changing. Both p(e/c) and p(e/ c) have increased by The increase in p(e/c) tends to raise causal judgement and the increase in p(e/ c) tends to lower it. However, under the cause-present effect the increase in p(e/c) raises judgement more than the increase in p(e/ c) lowers it, and so mean judgement tends to be higher at the higher value of p(e). Numerous studies have found effects of p(e) of this sort (Allan, 1993) and the explanation of this tendency in terms of the causepresent effect is directly supported by the findings of Wasserman et al. (1993) and White (2000b, submitted 2001). TESTING THE PAD RULE IN APPLICATION TO CAUSAL ATTRIBUTION The present experiment was designed to test the hypothesis that the Pad rule and the cause-present effect apply to causal attribution as they do to causal judgement from contingency information. In other words, the effect to be explained will be behavioural, as in other causal attribution studies, and the stimulus information concerns the three dimensions of consensus, distinctiveness, and consistency. The experiment has the same kind of design as previous tests of the evidential evaluation model

5 Causal attribution 671 Table 2. Stimulus materials for candidate C1, test of Pad rule Cell frequencies Problem a b c d Pad P p(e/c) p(e/ c) p(e) p(c) 1a þ b þ a þ b þ Mean of 1a þ 1b þ Mean of 2a þ 2b þ (White, 2000c, 2002, in press, submitted 2001). There is one test of the Pad rule which holds P values constant and one test of the P rule that holds Pad values constant. These will be described separately. The Test of the Pad Rule Control is a basic principle of experimental design, and in order to obtain an unambiguous test of the Pad rule it is necessary to control all other variables that might influence causal judgement. This control is achieved by comparing pairs of contingency tables, and the test of the Pad rule compares two such pairs. Basic information about these is shown in Table 2. The table shows cell frequencies and values of relevant variables for each of four problems. The critical information about the design is contained in the bottom two rows, which show mean values of each of the variables for each pair of problems: 1a þ 1b, and 2a þ 2b. This shows that the mean value of Pad differs between the two pairs but that the mean values of all other variables are held constant. Under the Pad rule it is predicted that the mean of the mean judgements for problems 2a and 2b will be higher than the mean of the mean judgements for problems 1a and 1b. If this difference is found, none of the other variables can account for it because the design controls them all. In effect the four problems constitute a 2 2 ANOVA design in which Pad value is one variable, and the main prediction is of a main effect of Pad. The other variable can be regarded as a same size manipulation of p(e/c) and p(e/ c): both variables change by the same amount, which they must if P is to be held constant. The fact that it is a same size manipulation warrants a second prediction for these four problems. Under the cause-present effect a change in value of p(e/c) has a greater influence on causal judgement than the same change in value of p(e/ c). Thus, if we compare problems 1a and 1b, p(e/c) and p(e/ c) are both greater by 0.5 in 1a than in 1b. The increase in value of p(e/c) tends to raise causal judgement and the increase in value of p(e/ c) tends to lower it, but under the causepresent effect the change in p(e/c) raises judgement more than the change in p(e/ c) lowers it, so the net effect should be higher judgement for 1a than for 1b. The same applies to the comparison between 2a and 2b. The general prediction is therefore a main effect of this manipulation with higher causal judgements at the higher combined values of p(e/c) and p(e/ c). The Test of the P Rule This test conforms to the same general principles: P is manipulated and Pad held constant across two pairs of problems. Basic information about these is shown in Table 3. The table shows cell frequencies

6 672 Peter A. White Table 3. Stimulus materials for candidate C1, test of P rule Cell frequencies Problem a b c d Pad P p(e/c) p(e/ c) p(e) p(c) 3a þ b þ a þ b þ Mean of 3a þ 3b 0.75 þ Mean of 4a þ 4b 0.75 þ and values of relevant variables for each of four problems. The critical information about the design is contained in the bottom two rows, which show mean values of each of the variables for each pair of problems: 3a þ 3b, and 4a þ 4b. This shows that the mean value of P differs between the two pairs but the mean values of Pad, p(e), and p(c) are held constant. Values of p(e/c) and p(e/ c) cannot be held constant because they are the determinants of P: if P varies, one or both of p(e/c) and p(e/ c) must vary too. This has two implications. One is that this design is different from that of the test of the Pad rule: one manipulated variable is P but the other has no clear identity. It will be termed a manipulation of p(e/c) and p(e/ c) because values of both variables are substantially higher in 3a and 4a than in 3b and 4b. The other implication is that differences between problems can be predicted from the cause-present effect. In particular, the mean value of p(e/c) is higher in 4b than in 3b, but there is no difference between 3a and 4a. On this basis it is predicted that causal judgements will be higher in 4b than in 3b and that there will be no significant difference between 3a and 4a, even though they differ in P value. The value of p(e/ c) is higher in 3a than in 4a and this might support a prediction of higher judgement in 4a than in 3a, but under the cause-present effect cause-absent information has only weak influence on causal judgement, so little or no difference is predicted. Thus, under the P rule both 4a > 3a and 4b > 3b are predicted, but under the cause-present effect only 4b > 3b is predicted. METHOD Participants The participants were 49 first-year undergraduate students at Cardiff University, participating in return for course credit. Fifty participants were originally run but one was excluded prior to data analysis for noncompliance with the instructions. Stimulus Materials Instructions to Participants Initial written instructions read as follows On the following pages you will see a series of judgemental problems all arranged in the same way. Each one starts with a sentence of the form: Somebody made a good score on such-and-such

7 Causal attribution 673 golf course under such-and-such circumstances, followed by the question why?. There are three possible reasons for the good score: something about the person (e.g. he might be a good player), something about the course (e.g. it might be an easy course), or something about the circumstances (e.g. they might have made it easy to get a good score). Each of these is listed under the question why? as follows: 1. Something about the person. 2. Something about the course. 3. Something about the circumstances. Any or all of these things might have been responsible for the good score: in the absence of any further information, each of them is equally likely to have been. Obviously, to work out why the good score occurred, you need additional information. So under the three possibilities you will see a lot more information about various people getting good or bad scores on various courses under various circumstances. Each line identifies a person, a course, the circumstances, and the score (good or bad). You should study this information and use it to help you make your three judgements. To make each judgement you should put a number from 0 (zero) to 100 by each of the three possibilities. 0 (zero) means that the thing in question was not at all responsible for the good score, and 100 means that the thing in question was totally responsible for the good score. The more you think a particular thing was responsible for the good score, the higher the number you should give that thing. Important: please make sure you put a number beside each of the three possibilities and don t miss any out. Problem Content There were eight problems identifed as 1a to 4b in Tables 2, 3, and 4. Each problem had a common format, illustrated by the example in the Appendix. As the example shows, each problem began with a description of an outcome to be explained. The outcome in all problems was got a good score and the description specified an actor, a target (a golf course), and circumstantial information. Under this the three causal candidates were listed. The crucial manipulations concerned just one candidate, which in any given problem could be either the actor or the target. The identity of this candidate was manipulated in a way described below: here, the candidate will be identified as candidate C1 (described by Tables 2 and 3), the other two being identified as candidates C2 and C3, respectively (described by Table 4). Table 4. Stimulus materials for candidates C2 and C3 Cell frequencies Problem a b c d Pad P 1a b a b a b a b

8 674 Peter A. White Under this was a list of information about other instances. This is the information about consensus, distinctiveness, and consistency. Each of the consensus instances identified a different actor with the same target and circumstances. Each of the distinctiveness instances identified a different target with the same actor and circumstances. Each of the consistency instances identified a different circumstance with the same actor and target. In the case of circumstance information, the nature of the circumstance varied across problems and included four time-related circumstances, months of the year (winter), months of the year (summer), days of the week, and times of day, and four object-related circumstances, make of golf club (fictitious), make of golf ball (fictitious), drink consumed prior to playing, and food consumed prior to playing. Each instance specified an actor, a target, a circumstance, and an outcome, either good or bad score. In each problem there were 16 randomly ordered instances. The content of these 16 instances was dictated by the cell frequencies in Tables 2, 3, and 4. To illustrate, the Appendix shows what the participants saw in the case of problem 1b. In this problem there were 6 instances in which a good score was obtained (sum of cells a and c in the row for problem 1b in Table 2 and Table 4) and 10 in which a bad score was obtained (sum of cells b and d ). In all of the 6 instances where a good score was obtained candidate C1 (in this case the actor) was present (cell a in Table 2), in 3 of them candidate C2 was present, and in 3 of them candidate C3 was present (cell a in Table 4). The contingency information stipulates how many instances of each kind are included in each problem: thus, in problem 1b there were four consensus instances (because Table 2 stipulates only four instances in which the actor is absent for this problem, the sum of cells c and d ), six distinctiveness instances and six consistency instances. A decision was taken to use identical matrices for candidates C2 and C3. With this decision and the orthogonal manipulation of causal candidates that is part of the logic of Kelleyan causal attribution, setting cell frequencies for candidate C1 fully determines the cell frequencies for the other two candidates. These cell frequencies and other relevant properties are described in Table 4. The stimuli have some interesting features. In particular, Pad and P values vary across matrices, but not in the same way. This yields a further possible discriminative test of the two models: judgements of candidates C2 and C3 should vary in accordance with Pad if the evidential evaluation model is correct and in accordance with P if models incorporating P are correct. P values for candidate C1 are in all cases positive and those for candidates C2 and C3 are in all cases negative. For this reason it was deemed unwise to make candidate C1 the same causal locus (actor, target, or circumstances) in all eight problems. Half of the participants received a set of materials in which candidate C1 was the actor for problems 1a to 2b and the target for problems 3a to 4b, and the other half received the opposite arrangement. Thus, the identity of the causal candidate was constant within each set of four problems, to rule out the possibility of contamination from scenariospecific effects. Procedure Participants took part in groups of two or three in a large and comfortably furnished office. They were presented with a booklet containing the instructions for the task on the first page followed by the eight problems in random order. A different random order was generated for each participant. Participants were invited to ask questions if anything in the instructions was not clear. None did so. When they had completed the questionnaire they were thanked and given course credit. They were not debriefed at this stage for fear of contaminating future participants, but at the conclusion of the research information about the study was made available.

9 Causal attribution 675 Table 5. Means, Pad manipulation Problem Candidate 1a 1b 2a 2b C C C Table 6. Means, P manipulation Problem Candidate 3a 3b 4a 4b C C C Results Mean judgements for the Pad manipulation are shown in Table 5 and those for the P manipulation in Table 6. Each causal candidate was analysed separately. Candidate C1 Taking the Pad manipulation first, data were analysed with a 2 (levels of Pad, versus 0.875) 2 (high versus low p(e/c) and p(e/ c)) analysis of variance (ANOVA) with repeated measures on both factors. There was a significant effect of Pad, F(1, 48) ¼ 11.34, p < 0.01, with higher ratings at the higher level of Pad. This is the predicted effect of Pad. There was also a significant effect of the manipulation of p(e/c) and p(e/ c), F(1, 48) ¼ 60.33, p < 0.001, with higher ratings when p(e/c) and p(e/ c) were high. This was the tendency predicted under the hypothesis of the cause-present effect. The interaction between the two variables was not statistically significant, F(1, 48) ¼ 0.73, ns. Data from the P manipulation were analysed with a 2 (levels of P, þ0.33 versus þ0.67) 2 (high versus low p(e/c) and p(e/ c)) ANOVA with repeated measures on both factors. There was a significant effect of P, F(1, 48) ¼ 10.20, p < 0.01, with higher ratings at the higher level of P. The hypothesis of the cause-present effect led to a specific prediction of a difference between problems 3b and 4b but no difference between problems 3a and 4a. Simple effects analysis confirmed this prediction. For problems 3a and 4a there was no significant effect of P, F(1, 48) ¼ 0.27, ns; but for problems 3b and 4b there was a significant effect of P, F(1, 48) ¼ 6.28, p < The conclusion is that the main effect is not a true effect of P but is instead attributable to the cause-present effect, because the difference was specific to problems 3b and 4b. There was also a significant effect of the manipulation of p(e/c) and p(e/ c), F(1, 48) ¼ 46.97, p < 0.001, with higher ratings when p(e/c) and p(e/ c) were high. The interaction between the two variables was not statistically significant, F(1, 48) ¼ 2.52, ns.

10 676 Peter A. White Candidates C2 and C3 As Table 4 shows, the Pad and P manipulations on candidate C1 entailed a pattern of contingencies for candidates C2 and C3 that does not fall into a clear experimental design. Accordingly, it was decided to assess the effects of Pad and P on judgement by paired comparisons between means using the t-test for related means. For each candidate eight problems entail a total of 28 paired comparisons. For candidate C2 19 of the 28 t-tests produced a difference significant at the 0.05 level. All 19 were in the direction predicted by the Pad rule: in other words, the mean was higher for the problem with the higher value of Pad. Of the nine non-significant results, four were predicted on the grounds that the Pad values were identical. Another four showed non-significant trends in the predicted direction and one showed a non-significant trend in the other direction. 12 of the 19 significant results were in the direction predicted by P, five were in the opposite direction, and two were significant differences between problems with identical P values. Of the non-significant results, four were in the direction predicted by P and five were in the opposite direction. For candidate C3 13 of the 28 t-tests produced a difference significant at the 0.05 level. All 13 were in the direction predicted by the Pad rule. Of the 15 non-significant results, 10 showed trends in the direction predicted by the Pad rule, one was in the opposite direction, and four were predicted on the grounds that the Pad values were identical. Twelve of the 13 significant results were in the direction predicted by P and one was a significant difference between a pair of matrices with identical P values. Of the non-significant results, six were in the direction predicted by P, eight were in the opposite direction, and one was predicted on the grounds that the P values were identical. DISCUSSION The findings support the basic contention of the evidential evaluation model that causal attributions are predicted by the Pad rule and the cause-present effect. When Pad was manipulated and all other variables were controlled a significant effect of Pad was found. The manipulation of p(e/c) and p(e/ c) also yielded a significant difference in the direction predicted under the hypothesis of the cause-present effect. When P was manipulated and Pad and other variables were controlled a significant effect was found: however, the effect was specific to a pair of problems in which p(e/c) varied, and the result was therefore interpreted as evidence for the cause-present effect, not the P rule. The pattern of the results for the other two causal candidates also fitted closely with the pattern of differences in Pad values and did not fit so well with the pattern of differences in P values. Other Models The key finding, obtained in several experiments on causal judgement from contingency information (White, 2000c, 2002, in press, submitted 2001) and now in an experiment on causal attribution, is that causal judgements vary with Pad, or more generally pci, when P is controlled and do not vary significantly with P when Pad or pci is controlled. Any model of causal judgement or causal attribution must be capable of accounting for these results if it is to be considered viable. There are two main classes of competing models in the contingency judgement literature, namely inductive rule models such as the probabilistic contrast model (Cheng & Novick, 1990, 1992), the power PC theory (Cheng, 1997), and a weighted version of the P rule (Lober & Shanks, 2000) and associative learning models, which model causal judgement according to basic learning mechanisms

11 Causal attribution 677 (Allan, 1993; Shanks, 1993, 1995; Shanks & Dickinson, 1987; Van Hamme & Wasserman, 1994; Wasserman, Kao, Van Hamme, Katagiri, & Young, 1996). White (submitted 2001) has shown that none of these can account for the key finding. The inductive rule models uniformly fail to predict the tendency of causal judgements to vary with Pad when P is controlled. Associative learning models also fail to predict this tendency, though the extent of the failure depends on assumptions about learning rates (White, submitted 2001). Since the logic of the design of the present experiment was the same as in White (submitted 2001), the inductive rule and associative learning models have the same failings. This can be illustrated with two of the inductive rule models, the power PC theory (Cheng, 1997) and the weighted P model (Lober & Shanks, 2000). A full account of these models can be found in the respective cited publications: for the sake of brevity, this discussion concentrates on the rules used to predict judgements. In the power PC theory the inductive rule for a single causal candidate is P modified by information about the rate of occurrence of the effect when the causal candidate is absent. The version of this rule that applies when 0 is shown in p ¼ P=1 pðe= cþ ð4þ In equation (4), p stands for causal power. As for the weighted P model, Lober and Shanks (2000) proposed that the best fit to the data could be found if P was modified such that p(e/c) was weighted W 1 ¼ 1.0 and p(e/ c) was weighted W 2 ¼ 0.6. Values of p and weighted P, P W, for the eight problems in the present experiment are shown in Table 7. Both p and P W predict some features of the means quite well, particularly the tendency for problems 1a, 2a, 3a, and 4a to receive higher judgements than the other four, the finding interpreted here as showing the cause-present effect. However the key finding is the main effect of Pad and both models fail to predict this. The mean values of p and P W for the two pairs 1a þ 1b and 2a þ 2b are the same, þ0.75 and þ0.60 respectively, so neither model predicts any difference between the different values of Pad. The same inadequacy was found by White (submitted 2001). Both P and p have the further drawback that they require both p(e/c) and p(e/ c) to be computed. This means that they require samples of both cause-present and cause-absent information, and that they can be unreliable if one or other sample is of small size. For example if there is a large sample of cause-present information but only three instances of cause-absent information p(e/ c) ¼ 0.33 if two of the three are cell d and p(e/ c) ¼ 0.67 if two of the three are cell c. Changing just one instance therefore makes a substantial difference to P. Pad can be computed even if there is no cause-absent Table 7. Test of power PC theory and weighted P rule against mean judgements of candidate C1 Cell frequencies Problem a b c d Pad p P w Mean 1a þ b þ a þ b þ a þ b þ a þ b þ Note: p ¼ causal power (equation (4)); P w ¼ weighted P.

12 678 Peter A. White information, when it effectively becomes a/(a þ b). It is not significantly affected by small sample size of one kind of information because it aggregates across all four cells rather than just two at a time: the three cause-absent instances in the above example are combined with the cause-present instances when Pad is computed, so changing just one of the cause-absent instances has little effect on the value of Pad. Other models of causal judgement have been proposed, including simpler judgemental rules (Allan, 1993; Kao & Wasserman, 1993; Smedslund, 1963), linear combination models (Schustack & Sternberg, 1981), and information integration models (Anderson, 1981, 1982; Busemeyer, 1991). Numerous published studies have shown that these do not adequately account for the phenomena of causal judgement (Allan, 1993; Cheng, 1997; Wasserman et al., 1996). To illustrate, Busemeyer s (1991) information integration model was tested by Wasserman et al. (1996). Wasserman et al. (1996) obtained causal judgements from participants after each instance of information. They determined cell weights empirically from participants final judgements and then entered the obtained weights into the information integration model to generate predictions for judgements after each trial. These predictions proved less accurate than those of an associative learning model. In particular, on several problems predictions for the early trials were too extreme compared to observed means, and only converged on observed mean judgements towards the end of the series (Wasserman et al., 1996, Figure 3). Existing models of causal attribution are similarly unable to account for the present results. In most cases this is because the models are not equipped to deal with quantitative information. Most of them offer a definition of what will be identified as a cause, and a causal attribution is made only to a locus that conforms to the definition. Models of this kind are not equipped to predict differences between causal judgements of different objective contingencies of the sort obtained here. This applies to models based on the covariation principle such as Kelley s original ANOVA model (Kelley, 1967), the template-matching model (Orvis et al., 1975), and the true ANOVA model (Forsterling, 1989), to the inductive logic model (Jaspars, 1983; Hewstone & Jaspars, 1987), the abnormal conditions focus model (Hilton & Slugoski, 1986), and models based on Mill s Methods of Experimental Inquiry (Mill, 1843/1973; Hilton et al., 1995; Van Overwalle & Heylighen, 1995). In fact the only model of causal attribution that is equipped to deal with quantitative information is the probabilistic contrast model (Cheng & Novick, 1990). In this model the basic rule of judgement is P computed for a defined focal set of instances. As we have already seen, this model fails to predict the key finding of judgements varying with Pad when P is controlled. One class of models that may be able to account for the present findings is that based on connectionist principles (Read & Marcus-Newhall, 1993; Read & Montoya, 1999; Van Overwalle, 1998; Van Overwalle & Van Rooy, 2001). The feedforward connectionist model proposed by Van Overwalle (1998) and Van Overwalle and Van Rooy (2001) has two layers of nodes: input nodes, which represent possible causes, and output nodes, which represent effects. In a feedforward network activation spreads only from input to output nodes. When a cause is present its input node is activated and that activation spreads to the output nodes in proportion to the weight of the connections. The weight of an input output connection is adjusted in accordance with the delta algorithm (McClelland & Rumelhart, 1988). The weight is adjusted upward when the effect is underestimated and downward when it is overestimated. Research by Van Overwalle and Van Rooy (2001) shows that this model successfully predicts incremental changes in causal judgement over a series of trials. By adjusting learning rates for individual causes and context factors it is possible for a simulation of the feedforward model to produce output that is highly correlated with the mean judgements observed in the present research. 1 The feedforward connectionist model can therefore be viewed as a competitor 1 I am indebted to Frank Van Overwalle for this information.

13 Causal attribution 679 to the evidential evaluation model. This is a surprising result, however. As Van Overwalle and Van Rooy (2001) observed, weight adjustment with the delta algorithm is formally identical to acquisition of associative bonds in the Rescorla Wagner model of animal learning (Rescorla & Wagner, 1972). It is a well-established property of this model that its asymptotic output matches P (Allan, 1993), and it must therefore be assumed that the same is true of a feedforward connectionist model that utilises the delta algorithm. As we have seen, however, the P rule fails to predict the tendencies observed in the present research. Asymptotic output of the Rescorla Wagner model does deviate from P when the learning rate for reinforced trials (i.e. those on which the effect occurs) is different from that for nonreinforced trials (on which the effect does not occur). However several simulations run by White (submitted 2001) have shown that no combination of learning rates yields output that matches the observed effects of Pad manipulations. This led White (submitted 2001) to conclude that the Rescorla Wagner model failed to account for the findings. The same would be the case here because the same kind of manipulation was employed. The feedforward connectionist model may be superior to the Rescorla Wagner model in this respect, but the explanation for its superiority remains to be elucidated. Furthermore there are reasons for thinking that a feedforward model may not be the most appropriate connectionist model of causal judgement (Read & Montoya, 1999). On the other hand, one advantage of connectionist models, which they share with associative learning models such as the Rescorla Wagner model, is that they can model the development of causal judgement over a series of trials (Van Overwalle & Van Rooy, 2001). The Psychological Meaning of the Evidential Evaluation Model This research has concentrated on the capacity of a simple mathematical formulation, the Pad rule, to account for observed tendencies in causal judgement. However the Pad rule is not just a mathematical model of judgement. The rule is a mathematical instantiation of notions of evidential value. In essence, people seek a causal interpretation of an event or set of events. Different possible causal interpretations function as hypotheses about the event or events to be explained. Hypotheses are tested by gathering evidence. The status of a given interpretation is assessed by the proportion of relevant evidence that is deemed to be confirmatory for that interpretation. The Pad rule expresses this idea. This point deserves emphasis because research on causal judgement from contingency information can appear to be abstract and far removed from the problems of coping with information about causality in the natural environment, in its utilisation of the formal structure of the 2 2 contingency table. In the power PC theory a natural substrate of competence at causal judgement is assumed (Cheng, 1997), which effectively includes the conceptual framework of the 2 2 contingency table. This framework is not assumed in the Pad rule: all one has to assume is that judges encode individual instances of information as confirmatory or disconfirmatory for the causal candidate or hypothesis under consideration. The Pad rule is a specific version of the general pci principle of judging from the proportion of confirmatory instances, specific to contingency information about a single causal candidate. But the pci rule is capable of predicting causal judgement from any kind of information, given only that instances of that kind are encoded as confirmatory or disconfirmatory (or irrelevant) by the judge. This makes it, in principle, both flexible and applicable to naturally occurring forms of causal judgement. This approach differs from those of its main competitors in the contingency judgement literature at the most fundamental level. Those models treat causal judgement as an outcome of basic learning mechanisms (Shanks, 1993, 1995; Shanks & Dickinson, 1987; Wasserman et al., 1996) or innate inductive rules (Cheng, 1997). In both cases causal judgement is a matter of passively registering

14 680 Peter A. White contingencies in an automatic process. Under the evidential evaluation model, although the possibility of an innate substrate of competence is not repudiated, causal judgement is a relatively sophisticated activity drawing on acquired notions of evidential value, and assessing causal interpretations that gain much of their meaning from a framework of acquired causal concepts (White, 1995, 2000c). White (2000b) has shown that notions of the evidential value of different types of contingency information vary between individuals, and that individuals reports of their notions of evidential value are better predictors of their causal judgements than normative models such as P. This approach is consistent with the consensus of developmental research, that competence at causal judgement from contingency information is a relatively late development (Kuhn, 1989; White, 1988, 1995). It is also consistent with previous research showing that people adopt a hypothesis testing approach to causal attribution (Hansen, 1980; Lalljee, Lamb, Furnham, & Jaspars, 1984; Shaklee & Fischhoff, 1982). The mathematical aspect of the model links the fundamental constituents of causal understanding, causal concepts, to the manifest phenomena of the world by means of notions of evidential value. To understand causal judgement and attribution it is necessary to understand the meaning that contingency and covariation information have for judges: that meaning is evidential value. Scope of the Model Kelley s original model specified three dimensions of information for causal attribution, consensus, distinctiveness, and consistency. Those dimensions were retained in the present research for the specific purpose of demonstrating the conformity of judgements to Pad with the traditional format. However the pci rule is not confined in application to those dimensions. In principle the rule can be applied to any kind of information so long as there is a clear proposition about the evidential value of that information, either for an individual judge or for a mean tendency across a sample of judges. It can therefore generate predictions for the extra dimensions postulated by Pruitt and Insko (1980) and Cheng and Novick (1990). Indeed, it does not even require covariation information. Because cell a information is consensually treated as confirmatory and cell b information as disconfirmatory, the model can generate predictions for sets of information in which there is no cause-absent information. White (2000c) found that, under some circumstances, people gave higher causal judgements to factors present in all instances in a set (i.e. factors about which no cause-absent information was presented) than to factors that correlated moderately with the effect. The Pad rule can generate a causal judgement for any dimension or format of information, so long as the evidential value of each kind of information is known. Having said that, the Pad rule is a model of asymptotic judgement only. It does not model the acquisition of causal judgement over a series of individual instances or trials. Because the rule is proportional, it predicts essentially the same judgement at all stages of acquisition so long as the proportion of confirmatory evidence does not vary significantly over the course of a sequential presentation. Many other rules, such as the P rule and p, have the same property. In fact it is well known that causal judgement does change over trials until at some point asymptote is reached (Shanks, 1987; White, 2000b). Several classes of models can explain many of the findings on acquisition, including associative learning models (Shanks, 1987, 1995), connectionist models (Read & Marcus- Newhall, 1993; Read & Montoya, 1999; Van Overwalle, 1998; Van Overwalle & Van Rooy, 2001), and belief revision models (Catena, Maldonado, & Cándido, 1998; Hogarth & Einhorn, 1992). One possibility is that the evidential evaluation model can be integrated with a belief revision model to form a comprehensive account of causal judgement, because these two kinds of models both conceptualise causal judgement as involving the treatment of evidence in a cognitive process. However the viability of such an integration remains to be ascertained.

15 Causal attribution 681 CONCLUSION Heider (1958) propounded a view of ordinary people as naive scientists, primarily concerned to understand the world and the events that take place in it as best they can. For Heider this implied a methodological orientation aimed at extracting invariant (dispositional) properties from the flow of events, and in later models of causal attribution it came to mean an equally methodological concern with sampling and rules of inference. Whether people should be regarded as naive scientists or not, they share with science a concern with hypotheses and the evaluation of evidence with respect to hypotheses. A large body of developmental research has been interpreted along these lines (Kuhn, 1989), and this view is consistent with the founding principles of the evidential evaluation model. One cannot afford to be too particular about methodology in a world where controlled experimental designs are rarely practicable, so it is unlikely that a model that stipulates the gathering of evidence on particular orthogonal dimensions could account for everyday causal attribution. But an attitude of concern with hypotheses and evidence that yields an inductive rule flexible enough to cope with the vagaries of information availability in the real world can perhaps be regarded as both scientific and practical. The pci rule does not specify dimensions from which information must be sampled: all it requires is that people assess the evidential value of any piece of information they come across. It is therefore both practical, in its applicability under real world conditions, and scientific, in its concern with hypothesis and evidence. It has been shown that the evidential evaluation model predicts judgemental tendencies equally well in both causal judgement from contingency information (White, 2000c, 2002, in press, submitted 2001) and causal attribution (the present experiment). This supports a contention that these two areas of research can be unified under a single explanatory account. The possibility of such unification may have been partly obscured by differences in methodology, particularly the traditional use of verbal summaries as stimulus information in the causal attribution literature. The future use of information about single instances as stimulus information, which has been common practice in the contingency judgement literature, should be a valuable adjunct to the further theoretical and experimental integration of these two important bodies of research. REFERENCES Allan, L. G. (1993). Human contingency judgements: rule based or associative? Psychological Bulletin, 114, Anderson, J. R., & Sheu, C.-F. (1995). Causal inferences as perceptual judgments. Memory and Cognition, 23, Anderson, N. H. (1981). Foundations of information integration theory. New York: Academic Press. Anderson, N. H. (1982). Methods of information integration theory. New York: Academic Press. Busemeyer, J. R. (1991). Intuitive statistical estimation. In N. H. Anderson (Ed.), Contributions to information integration theory (Vol. 1, pp ). Hillsdale, NJ: Erlbaum. Catena, A., Maldonaldo, A., & Cándido, A. (1998). The effect of the frequency of judgment and the type of trials on covariation learning. Journal of Experimental Psychology: Human Perception and Performance, 24, Cheng, P. W. (1997). From covariation to causation: a causal power theory. Psychological Review, 104, Cheng, P. W., & Novick, L. R. (1990). A probabilistic contrast model of causal induction. Journal of Personality and Social Psychology, 58, Cheng, P. W., & Novick, L. R. (1992). Covariation in natural causal induction. Psychological Review, 99, Cohen, M. R., & Nagel, E. (1934). An introduction to logic and scientific method. New York: Harcourt, Brace.