Perceiving a strong causal relation in a weak contingency: Further investigation of the evidential evaluation model of causal judgement

Contingency information is information about the occurrence or nonoccurrence of a certain effect in the presence or absence of a candidate cause. An objective measure of contingency is the δP rule, which involves subtracting the probability of occurrence of an effect when a causal candidate is absent from the probability of occurrence of the effect when the candidate is present. Causal judgements conform closely to δP but deviate from it under certain circumstances. Three experiments show that such deviations can be predicted by a model of causal judgement that has two components: a rule of evidence, that causal judgement is a function of the proportion of relevant instances that are judged to be confirmatory for the causal candidate, and a tendency for information about instances in which the candidate is present to have greater effect on judgement than instances in which the candidate is absent. Two experiments demonstrate how this model accounts for some recently published findings. A third experiment shows that it is possible to use the model to predict the occurrence of high causal judgements when the objective contingency is close to zero.     

Accounting for occurrences: An explanation for some novel tendencies in causal judgment from contingency information

Contingency information is information about empirical associations between possible causes and outcomes. In the present research, it is shown that, under some circumstances, there is a tendency for negative contingencies to lead to positive causal judgments and for positive contingencies to lead to negative causal judgments. If there is a high proportion of instances in which a candidate cause (CC) being judged is present, these tendencies are predicted by weighted averaging models of causal judgment. If the proportion of such instances is low, the predictions of weighted averaging models break down. It is argued that one of the main aims of causal judgment is to account for occurrences of the outcome. Thus, a CC is not given a high causal judgment if there are few or no occurrences of it, regardless of the objective contingency. This argument predicts that, if there is a low proportion of instances in which a CC is present, causal judgments are determined mainly by the number of Cell A instances (i.e., CC present, outcome occurs), and that this explains why weighted averaging models fail to predict judgmental tendencies under these circumstances. Experimental results support this argument.     

Causal judgement as evaluation of evidence: The use of confirmatory and disconfirrnatory information

There are four kinds of contingency information: occurrences and nonoccurrences of an effect in the presence and absence of a cause. In two experiments participants made judgements about sets of stimulus materials in which one of these four kinds had zero frequency. The experiments tested two kinds of predictions derived from the evidential evaluation model of causal judgement, which postulates that causal judgement depends on the proportion of instances evaluated as confirmatory for the cause being judged. The model predicts significant effects of manipulating the frequency of one kind of contingency information in the absence of changes in the objective contingency. The model also predicts that extra weight will be given to one kind of confirmatory information when the other kind has zero frequency, and to one kind of disconfirmatory information when the other kind has zero frequency. Results supported both sets of predictions, and also disconfirmed predictions of the power probabilistic contrast theory of causal judgement. This research therefore favours an account of causal judgement in which contingency information is transformed into evidence, and judgement is based on the net confirmatory or disconfirmatory value of the evidence.     

Causal judgement from contingency information: Judging interactions between two causal candidates

In two experiments participants judged the extent to which occurrences and non-occurrences of an effect could be attributed to an interaction between two causal candidates A and B. In Experiment 1 judgements were influenced by the proportion of instances normatively evaluated as confirmatory for the interaction interpretation, when the objective contingency was held constant. Information about instances in which both candidates were present and the effect occurred was more influential than information about instances in which both candidates were absent and the effect did not occur. In Experiment 2 the occurrence rate of the effect when both candidates were present, when A alone was present, when B alone was present, and when both were absent was manipulated. Interaction judgements were mainly determined by occurrence rate when both were present. There was also a significant effect of occurrence rate when both were absent, but the other two occurrence rates had no significant effect. These results are interpreted as supporting a general model in which causal judgements are made according to the proportion of instances evaluated as supporting the interpretation being judged.     

Making causal judgments from the proportion of confirming instances: the pCI rule

It is proposed that causal judgments about contingency information are derived from the proportion of confirmatory instances (pCI) that are evaluated as confirmatory for the causal candidate. In 6 experiments, pCI values were manipulated independently of objective contingencies assessed by the deltaP rule. Significant effects of the pCI manipulations were found in all cases, but causal judgments did not vary significantly with objective contingencies when pCI was held constant. The experiments used a variety of stimulus presentation procedures and different dependent measures. The power PC theory, a weighted version of the deltaP rule, the Rescorla-Wagner associative learning model (R. A. Rescorla & A. R Wagner, 1972), and the deltaD rule, which is the frequency-based version of the pCI rule, were unable to account for the significant effects of the pCI manipulations. These results are consistent with a general explanatory approach to causal judgment involving the evaluation of evidence and updating of beliefs with regard to causal hypotheses.     

Judgement of two causal candidates from contingency information: II. Effects of information about one cause on judgements of the other cause

When judgements are being made about two causes there are eight possible kinds of contingency information: occurrences and nonoccurrences of the outcome when both causes are present, when Cause 1 alone is present, when Cause 2 alone is present, and when neither cause is present. It is proposed that contingency information is used to some extent to judge proportionate strength, which is the proportion of occurrences of the outcome that each cause can account for. This leads to a prediction that judgements of one cause will be influenced by information about occurrences, but not nonoccurrences, of the outcome when only the other cause is present. In six experiments consistent support was found for this prediction when the cause being judged had a positive relation with the outcome, but no consistent tendency was found when the cause being judged had a negative relation with the outcome. The effects found for causes with positive contingency cannot be explained by the Rescorla-Wagner model of causal judgement nor by the hypothesis that causal judgements are based on conditional contingencies.     

Causal attribution from covariation information: the evidential evaluation model

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.     

Accounting for occurrences: a new view of the use of contingency information in causal judgment

When people make causal judgments from contingency information, a principal aim is to account for occurrences of the outcome. When 2 causes are under consideration, the capacity of either to account for occurrences is judged from how likely the cause is to be present when the outcome occurs and from the rate at which the outcome occurs when that cause alone is present, which gives an estimate of the strength of the cause. These propositions are formalized in a weighted averaging model, which successfully predicted several judgmental phenomena not predicted by other models of causal judgment. These include a tendency for judgment of one cause (A) to be reduced as the number of occurrences of when only the other one (B) increases and a tendency for A to receive higher judgments than B if A is better able to account for occurrences than B is even if B has a higher contingency with the outcome than A does. Overshadowing, a tendency for judgments of B to be depressed if A has a higher contingency, is weak or absent when B is better able to account for occurrences than A. Results of several experiments support these and related predictions derived from the accounting for occurrences hypothesis.     

Causal judgement from information about outcome magnitude

Information was presented in which a candidate cause was either present or absent, and the outcome variable (number of spots on a patient's skin) could take any of four nonzero values. It was found that cause-absent information carried greater weight than cause-present information. This is contrary to the usual finding for contingency information about binary outcome variables. Judgement was influenced more by extreme values of the outcome variable, and larger outcome values tended to have more effect on judgements than smaller outcome values. The hypothesis that participants compute linear correlation is disconfirmed by these results. Instead, the results show that participants focus disproportionate attention on some kinds of events and neglect others.     

Contingency proportion systematically influences contingency learning

In the color-word contingency learning paradigm, each word appears more often in one color (high contingency) than in the other colors (low contingency). Shortly after beginning the task, color identification responses become faster on the high-contingency trials than on the low-contingency trials—the contingency learning effect. Across five groups, we varied the high-contingency proportion in 10% steps, from 80% to 40%. The size of the contingency learning effect was positively related to high-contingency proportion, with the effect disappearing when high contingency was reduced to 40%. At the two highest contingency proportions, the magnitude of the effect increased over trials, the pattern suggesting that there was an increasing cost for the low-contingency trials rather than an increasing benefit for the high-contingency trials. Overall, the results fit a modified version of Schmidt’s (2013, Acta Psychologica, 142, 119–126) parallel episodic processing account in which prior trial instances are routinely retrieved from memory and influence current trial performance.     

The influence of the number of relevant causes on the processing of covariation information in causal reasoning

Research on causal reasoning has focused on the influence of covariation between candidate causes and effects on causal judgments. We suggest that the type of covariation information to which people attend is affected by the task being performed. For this, we manipulated the test questions for the evaluation of contingency information and observed its influence on both contingency learning and subsequent causal selections. When people select one cause related to an effect, they focus on conditional contingencies assuming the absence of alternative causes. When people select two causes related to an effect, they focus on conditional contingencies assuming the presence of alternative causes. We demonstrated this use of contingency information in four experiments.     

The influence of temporal distributions on causal induction from tabular data

Two experiments investigated the joint influence of statistical and temporal information on causal inference from tabular data. Participants were presented with unambiguous data sets containing information about relative effect frequencies in cause-present and cause-absent situations. In addition to contingency information, the stimuli also revealed information about the temporal distribution of effects. The participants took this information into account when making causal judgments, so that the mere advancing or postponing of the effect in time was attached with causal significance, even when the cause did not increase the overall probability of the effect. These results cannot be reconciled with standard contingency accounts of causal induction.     

Judgement of two causal candidates from contingency information: Effects of relative prevalence of the two causes

In four experiments participants made judgements about two possible causes of an effect. The prevalence of the causes was manipulated independently of their degree of contingency with the effect. Significant effects of the prevalence manipulation were obtained: In particular, ratings of the unmanipulated candidate tended to decline as the prevalence of the other candidate increased, and there was also a significant but smaller effect on judgements of the latter. These tendencies were independent of the order in which the two candidates were judged. These results were replicated under two stimulus presentation procedures, the instance list procedure (Experiments 1 and 2) and the trial-by-trial procedure (Experiment 3). It was hypothesized that people judge, to some degree, the proportionate strength of the candidates, in other words the proportion of occurrences of the effect in the presence of each, and that the cause prevalence effect is a consequence of this tendency. This hypothesis was supported by the results of Experiment 4: Those participants whose judgements of one candidate were negatively correlated with the frequency of occurrence of the effect in the presence of the other candidate showed a significantly stronger cause prevalence effect than the remainder.     

其它可能原因的呈现方式在因果判断中的作用

研究使用不同方式呈现了其它可能原因,研究了这种不同的呈现方式对被试使用共变信息和经验信息进行因果判断的影响。研究结果表明:(1)其它可能原因的呈现方式对于因果判断有着一定的影响。当这一信息在待判断原因与结果的共变中出现、且永远存在时,被试会排除这一其它可能原因的作用,从而增强判断的信心;(2)当其它可能原因出现于待判断原因与结果的共变中、且永远存在时,被试会在一定程度上忽视经验信息的作用,更多地依赖共变信息做出判断。     

Cue interaction effects in causal judgement: An interpretation in terms of the evidential evaluation model

In judging the extent to which a cue causes an outcome, judgement can be affected by information about other cues that are correlated with the one being judged. These cue interaction effects have usually been interpreted in terms of associative learning processes. I propose that a different model of causal judgement, the evidential evaluation model, offers a viable alternative interpretation of cue interaction phenomena. Under the evidential evaluation model, instances of contingency information are interpreted as evidence, which is confirmatory, disconfirmatory, or irrelevant for the cue being judged. When two cues co-occur in a set of instances the evidential value of the instances for one of them is determined by three factors: the proportion of confirming instances in the set; disambiguation value, which concerns the relation between the set of information and prior beliefs about the co-occurring cue; and confirmation value, which concerns the relation between the set of information and prior beliefs about the cue being judged. Any previous judgement of the cue is then modified in the light of these. It is shown that this model can account for all the cue interaction phenomena that have been investigated in studies of human causal judgement. The model also generates novel predictions, and the results of three experiments give support to these predictions. It is also shown that several other current models of causal judgement fail to predict a key result from Experiment 3.     

The Parallel Episodic Processing (PEP) model: Dissociating contingency and conflict adaptation in the item-specific proportion congruent paradigm

The present work introduces a computational model, the Parallel Episodic Processing (PEP) model, which demonstrates that contingency learning achieved via simple storage and retrieval of episodic memories can explain the item-specific proportion congruency effect in the colour-word Stroop paradigm. The current work also presents a new experimental procedure to more directly dissociate contingency biases from conflict adaptation (i.e., proportion congruency). This was done with three different types of incongruent words that allow a comparison of: (a) high versus low contingency while keeping proportion congruency constant, and (b) high versus low proportion congruency while keeping contingency constant. Results demonstrated a significant contingency effect, but no effect of proportion congruence. It was further shown that the proportion congruency associated with the colour does not matter, either. Thus, the results quite directly demonstrate that ISPC effects are not due to conflict adaptation, but instead to contingency learning biases.     

Belief-based and covariation-based cues affect causal discounting.

Causal discounting occurs when the perceived efficacy of a putative cause is reduced by the presence of a stronger causal candidate. Previous studies of causal discounting have defined the strength of causal candidates in terms of the degree to which the cause and the effect covary (e.g., Baker, Mercier, Vallee-Tourangeau, Frank, & Pan, 1993). In contrast, in the present study, causal strength was defined in terms of both covariation- and belief-based cues. Seventy-two participants made causality judgments for a fictional causal candidate both in isolation and when paired with either a stronger or a weaker cause. The results demonstrated that the degree to which a causal candidate is discounted depends not only on the degree to which an alternative cause covaries with the effect, but also on whether the alternative is a believable or unbelievable candidate. Indeed, it was observed that a highly believable alternative will produce the discounting effect, even if it is a weaker covariate than the original candidate. These findings suggest the need to incorporate both belief-based and covariation-based cues into models of causal attribution.     

情境特异比例一致变化对冲突效应的影响

采用Hedge和Marsh任务与比例一致性操纵相结合,分别以刺激的空间位置和形状作为比例一致操纵的情境线索,考察刺激-反应联结学习与注意调节在比例一致效应中的作用。结果发现,在情境比例一致操纵下,冲突效应的效应量受到比例一致操纵的影响产生反转。表明刺激-反应联结学习在情境特异比例一致效应中起到主要作用。     

Implicit contributions of context to recognition

Studies of the impact of context on remembering have not focused on the influence of contextual contingency on subsequent recognition in the condition in which the contingency cannot be verbalized. In two experiments, we analyzed the effect of an implicitly encoded position contingency involving location and semantic category on both hit and false alarm recognition judgments after 1 day and 1 week delays. We vigorously probed for what participants could say about the contingency. We found context effects for both hits and false alarms, whether or not participants could verbalize any knowledge they might have of contingency. These results suggest that people may use contextual information when making a recognition judgment even if they are not aware of this information.     

Strategy changes in human contingency judgments as a function of contingency tables.

Judgment strategies of 169 undergraduate students on problems to judge the contingency between two binary events were identified by the method of rule-based analysis to clarify whether or not the strategies the subjects used would be affected by the concrete nature of the contingency table. Problems were constructed along two factors: total cell frequency and width of range of objective contingencies. Although the factor of total cell frequency had no effect on subjects' strategies, the number of subjects who changed strategies corresponding with problem instances increased when the objective contingencies were set closer to zero or when problems became more difficult. These results are discussed in the context of previous studies of this issue in the literature.