Conformity to the power PC theory of causal induction depends on the type of probe question

P. W. Cheng's (1997) power PC theory of causal induction proposes that causal estimates are based on the power (P) of a potential cause, where P is the contingency between the cause and effect normalized by the base rate of the effect. Most previous research using a standard causal probe question has failed to support the predictions of the power PC model but recently Buehner, Cheng, and Clifford (2003) found that participants responded in terms of causal power when probed with a counterfactual test question, which they argued prompted participants to consider the base rate of the effect. However, Buehner et al. framed their counterfactual question in terms of frequency, a factor that has been demonstrated to decrease base rate neglect in judgements under uncertainty. In the experiment reported here, we sought to disentangle the influence of counterfactual and frequency framing of the probe question to determine which factor is responsible for encouraging responses in terms of causal power.     

Short article conformity to the power PC theory of causal induction depends on the type of probe question

P. W. Cheng's () power PC theory of causal induction proposes that causal estimates are based on the power (P) of a potential cause, where P is the contingency between the cause and effect normalized by the base rate of the effect. Most previous research using a standard causal probe question has failed to support the predictions of the power PC model but recently Buehner, Cheng, and Clifford () found that participants responded in terms of causal power when probed with a counterfactual test question, which they argued prompted participants to consider the base rate of the effect. However, Buehner et al. framed their counterfactual question in terms of frequency, a factor that has been demonstrated to decrease base rate neglect in judgements under uncertainty. In the experiment reported here, we sought to disentangle the influence of counterfactual and frequency framing of the probe question to determine which factor is responsible for encouraging responses in terms of causal power.     

因果力比较范式下对效力PC理论的检验

在用图形方式集中呈现信息的条件下,用因果力大小比较的实验范式检验效力PC理论。233名大学生被试对不同化学药物影响动物基因变异的能力做大小比较判断。结果发现,对单一因果关系因果力大小的比较判断具有以下3个特点：（1）不对称性：在预防原因条件下的因果力判断一般符合效力PC理论,而在产生原因条件下的因果力判断一般不符合效力PC理论;（2）在同时变化协变值DP和结果基率P(E|~C)的产生原因条件下,多数被试使用DP规则。这与概率对比模型的预测相一致,而不支持效力PC理论;（3）在固定协变值DP而只变化结果基率P(E|~C)的产生原因条件下,多数被试使用变异比RP规则。这是目前所有的因果推理理论都不能解释的现象。     

Is causal induction based on causal power? Critique of Cheng (1997)

The authors empirically evaluate P. W. Cheng's (1997) power PC theory of causal induction. They reanalyze some published data taken to support the theory and show instead that the data are at variance with it. Then, they report 6 experiments in which participants evaluated the causal relationship between a fictitious chemical and DNA mutations. The power PC theory assumes that participants' estimates are based on the causal power p of a potential cause, where p is the contingency between the cause and the effect normalized by the base rate of the effect. Three of the experiments used a procedure in which causal information was presented trial by trial. For these experiments, the power PC theory was contrasted with the predictions of the probabilistic contrast model and the Rescorla-Wagner theory. For the remaining 3 experiments, a summary presentation format was employed to which only the probabilistic contrast model and the power PC theory are applicable. The power PC theory was unequivocally contradicted by the results obtained in these experiments, whereas the other 2 theories proved to be satisfactory.     

Tests of the power PC theory of causal induction with negative contingencies

The power PC theory of causal induction (Cheng, 1997) proposes that causal estimates are based on the power p of a potential cause, where p is the contingency between the cause and effect normalized by the base rate of the effect. Previous tests of this theory have concentrated on generative causes that have positive contingencies with their associated outcomes. Here we empirically test this theory in two experiments using preventive causes that have negative contingencies for their outcomes. Contrary to the power PC theory, the results show that causal judgments vary with contingency across conditions of constant power p. This pattern is consistent, however, with several alternative accounts of causal judgment.     

单结果多原因情况下的因果判断研究

本研究以直接呈现每种因果类型的频次的方式考察单结果多原因情况下影响因果判断的因素,同时检验概率对照模型,效力PC理论和因果模型理论。结果发现：（1）影响因果判断的因素有：事件原因与促进条件的性质差异,原因的熟悉度,原因和结果的共变程度;（2）同题抽象性对因果判断没有影响;（3）概率对照模型和因果模型理论在一定的情况下适用,但是都不能解释所有的情况。     

Causal Induction in the Presence of a Perfect Negative Cue: Contrasting Predictions from Associative and Statistical Models

Two experiments on human causal induction with multiple candidate causes are reported. Experiment 1 investigated the influence of a perfect preventive cause on the ratings of a less contingent cause. Whereas the Rescorla-Wagner model (RWM) and Cheng's probabilistic contrast model predict that the less contingent cause should be completely discounted, the Pearce model predicts, in most cases, an enhancement of that cause's perceived importance. Results corresponded more closely tothe predictions of the Pearce model.The predictions of both the RWM and the Pearce model rely on a constant context cue acquiring associative strength, yet no such cue was explicitly identified in the task scenario employed in Experiment 1. Experiment 2 replicated a number of key conditions of Experiment 1 with a task scenario that afforded ratings of the causal importance of the context in which the effectiveness of the discrete candidate causes was evaluated. In addition, the number of trials was increased to test the possibility that the ratings in Experiment 1 were the product of incomplete learning. The results of the first experiment were replicated and the ratings of the effectiveness of the context cue were anticipated by both the RWM and the Pearce model. Overall, the Pearce model offers a more comprehensive account of the causal inferences recorded in this study.     

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.     

Distinguishing genuine from spurious causes: a coherence hypothesis

Two opposing views have been proposed to explain how people distinguish genuine causes from spurious ones: the power view and the covariational view. This paper notes two phenomena that challenge both views. First, even when 1) there is no innate specific causal knowledge about a regularity (so that the power view does not apply) and 2) covariation cannot be computed while controlling for alternative causes (so that the covariation view should not apply), people are still able to systematically judge whether a regularity is causal. Second, when an alternative cause explains the effect, a spurious cause is judged to be spurious with greater confidence than otherwise (in both cases, no causal mechanism underlies the spurious cause). To fill the gap left by the traditional views, this paper proposes a new integration of these views. According to the coherence hypothesis, although a genuine cause and a spurious one may both covary with an effect in a way that does not imply causality at some level of abstraction, the categories to which these candidate causes belong covary with the effect differently at a more abstract level: one covariation implies causality; the other does not. Given this superordinate knowledge, the causal judgments of a reasoner who seeks to explain as much as possible with as few causal rules as possible will exhibit the properties that challenge the traditional views. Two experiments tested and supported the coherence hypothesis. Both experiments involved candidate causes that covary with an effect without implying causality at some level, manipulating whether covariation that implies causality has been acquired at a more abstract level. The experiments differed on whether an alternative cause explains the effect.     

Strategy selection in causal reasoning: when beliefs and covariation collide.

The present study investigated how people combine covariation information (Cheng & Novick, 1990, 1992) with pre-existing beliefs (White, 1989) when evaluating causal hypotheses. Three experiments, using both within- and between-subjects designs, found that the use of covariation information and beliefs interacted, such that the effects of covariation were larger when people assessed hypotheses about believable than about unbelievable causal candidates. In Experiment 2, this interaction was observed when participants made judgments in stages (e.g., first evaluating covariation information about a causal candidate and then evaluating the believability of a candidate), as well as when the information was presented simultaneously. Experiment 3 demonstrated that this pattern was also reflected in participants' metacognitive judgments: Participants indicated that they weighed covariation information more heavily for believable than unbelievable candidates. Finally, Experiments 1 and 2 demonstrated the presence of individual differences in the use of covariation- and belief-based cues. That is, individuals who tended to base their causality judgments primarily on belief were less likely to make use of covariation information and vice versa. The findings were most consistent with White's (1989) causal power theory, which suggests that covariation information is more likely to be considered relevant to believable than unbelievable causes.     

Why Causation Need Not Follow from Statistical Association: Boundary Conditions for the Evaluation of Generative and Preventive Causal Powers

In experimental design, a tacit principle is that to test whether a candidate cause c (i.e., a manipulation) prevents an effect e, e must occur at least some of the time without the introduction of c. This principle is the preventive analogue of the explicit principle of avoiding a ceiling effect in tests of whether c produces e. Psychological models of causal inference that adopt either the covariation approach or the power approach, among their other problems, fail to explain these principles. The present article reports an experiment that demonstrates the operation of these principles in untutored reasoning. The results support an explanation of these principles according to the power PC theory, a theory that integrates the previous approaches to overcome the problems that cripple each.     

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.     

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.     

From covariation to causation: a test of the assumption of causal power

How humans infer causation from covariation has been the subject of a vigorous debate, most recently between the computational causal power account (P. W. Cheng, 1997) and associative learning theorists (e.g., K. Lober & D. R. Shanks, 2000). Whereas most researchers in the subject area agree that causal power as computed by the power PC theory offers a normative account of the inductive process. Lober and Shanks, among others, have questioned the empirical validity of the theory. This article offers a full report and additional analyses of the original study featured in Lober and Shanks's critique (M. J. Buehner & P. W. Cheng, 1997) and reports tests of Lober and Shanks's and other explanations of the pattern of causal judgments. Deviations from normativity, including the outcome-density bias, were found to be misperceptions of the input or other artifacts of the experimental procedures rather than inherent to the process of causal induction.     

因果判断中经验与共变信息的结合及各自作用

研究使用相继呈现信息的方法控制了被试获得信息的顺序,从而将经验和共变信息在因果判断中所起到的作用分离了出来。结果表明：（1）个体综合两种信息进行因果判断的过程既不是简单的相加操作,也不是使用经验信息控制共变信息的进入,而是先判断经验信息,再判断共变信息是否与之一致,当出现不一致的情况时又重新考虑经验信息。（2）在改变先前判断的过程中,经验信息所起的作用更大,其中又以当其证明待判断原因不可信时所产生的改变更大。     

Interaction between previous beliefs and cue predictive value in covariation-based causal induction

The main aim of this work was to show the impact of preexisting causal beliefs on causal induction from cause-effect co-occurrence information, when several cues compete with each other for predicting the same effect. Two different causal scenarios -- one social (a), the other medical (b) -- were used to check the generality of the effects. In Experiments 1a and 1b, participants were provided information on the co-occurrence of a two-cause compound and an effect, but not about the potential relationship between each cause by its own and the effect. As expected, prior beliefs -- induced by means of instructions -- strongly modulated the causal strength assigned to each element of the compound. In Experiments 2a and 2b, covariation evidence was provided, not only about the predictive value of the two-cause compound, but also about one of the elements of the compound. When this evidence was available, prior beliefs had less impact on judgments, and these were mostly guided by the relative predictive value of the cue. These results demonstrate the involvement of inferential integrative mechanisms in the generation of causal knowledge and show that single covariation detection mechanisms -- either rule-based or associative -- are insufficient to account for human causal judgment. At the same time, the fact that the power of new covariational evidence to change prior beliefs depended on the availability of information on the relative (conditional) predictive value of the target candidate cause suggests that causal knowledge derived from information on causal mechanisms and from covariation probably share a common representational basis.     

样例学习条件下的因果力估计

在逐个呈现因果样例的条件下,考察单一因果关系因果力估计的特点,同时检验联想解释,概率对比模型,权重DP模型,效力PC理论和pCI规则。实验让65名大学生被试估计不同化学药物影响动物基因变异的能力。实验结果表明：（1）对产生原因的因果力估计符合权重DP模型;（2）对预防原因的因果力估计较多符合效力PC理论;（3）因果力估计具有复杂多样性,难以用统一的模式加以描述和概括。     

Driven by power? Probe question and presentation format effects on causal judgment

It has been proposed that causal power (defined as the probability with which a candidate cause would produce an effect in the absence of any other background causes) can be intuitively computed from cause-effect covariation information. Estimation of power is assumed to require a special type of counterfactual probe question, worded to remove potential sources of ambiguity. The present study analyzes the adequacy of such questions to evoke normative causal power estimation. The authors report that judgments to counterfactual probes do not conform to causal power and that they strongly depend on both the probe question wording and the way that covariation information is presented. The data are parsimoniously accounted for by an alternative model of causal judgment, the Evidence Integration rule.     

Selecting explanations from causal chains: Do statistical principles explain preferences for voluntary causes?

We investigate whether people prefer voluntary causes to physical causes in unfolding causal chains and whether statistical (covariation, sufficiency) principles can predict how people select explanations. Experiment 1 shows that while people tend to prefer a proximal (more recent) cause in chains of unfolding physical events, causality is traced through the proximal cause to an underlying distal (less recent) cause when that cause is a human action. Experiment 2 shows that causal preference is more strongly correlated with judgements of sufficiency and conditionalised sufficiency than with covariation or conditionalised covariation. In addition, sufficiency judgements are partial mediators of the effect of type of distal cause (voluntary or physical) on causal preference. The preference for voluntary causes to physical causes corroborates findings from social psychology, cognitive neuroscience and jurisprudence that emphasise the primacy of intentions in causal attribution processes. Copyright © 2009 John Wiley & Sons, Ltd.