People's beliefs about the causal structure of the world impact a variety of cognitive processes. For instance, features that cause other features are given more weight in categorization than in similarity judgments (Ahn & Dennis, 1997), so that people tend to categorize tadpoles with frogs on the basis of both groups having the same DNA, although that DNA causes tadpoles to be more similar to minnows. An important question for cognitive psychology, therefore, concerns the processes involved in making causal inferences. Two classes of models are currently popular that explain causal reasoning (see Cheng, Park, Yarlas, & Holyoak, 1995; Price & Yates, 1995). In this dissertation, I propose to discover and explore a new phenomenon, involving the effect of the order of evidence in causal induction. Neither of the two dominant models (at least, as they are currently interpreted) can explain this phenomenon; in the course of my investigations, I hope also to provide support for a third, alternative model that can make accurate predictions about order effects.

One class of model is based on statistical contingency. According to this class of model, people compute the strength of possible causes based on the frequency of co-occurrence between an effect and a candidate cause of that effect (Ward & Jenkins, 1965). More formally, the strength of a candidate cause may be expressed as DP=P(E|C)-P(E|~C), where DP is the causal strength and P(E|C) and P(E|~C) are the conditional probabilities of the effect (E) occurring given the presence (C) or absence (~C) of the cause. This rule may also be expressed in terms of the frequency of co-occurrence between the cause and the effect.

	Cause present	Cause absent
Effect present	Cell A	Cell B
Effect absent	Cell C	Cell D

Table 1.

A more sophisticated version of the contingency model has been suggested by Cheng and colleagues (Cheng, 1997; Cheng, Park, Yarlas, & Holyoak, 1995). In this conditionalized contingency model, the contingencies are conditioned on other possible causes, so that DP is weighted by the probability of the effect occurring given the presence of alternative causes.

Although rule-based models can successfully predict causal judgments after asymptotic learning (e.g. Cheng, 1997), they do not provide adequate descriptions of the processes involved in inference. One common complaint against them (e.g. Price & Yates, 1995) is that they require all of the inference to occur at the time of judgment; that is, after as many training instances have been as possible have been observed. After all, the models themselves are framed in terms of the frequency of co-occurrence observed up to the point of judgment. Phenomena occurring prior to judgment simply are not covered. In other words, these models seem to propose that training instances are processed simultaneously at the end of learning (cf. Gallistel, 1990).

The problem is that causal reasoning often deals with sequential information. That is, we see events one at a time, and oftentimes try to figure out whether one event causes another. We rarely have the luxury, however, of storing all of those instances (in memory, on paper, or in a computer) and only later summarizing them to make a causal inference. It seems reasonable, therefore, to assume that people continuously update probabilities based on learning instances.

The second class of models takes account of sequential processing, through appeal to the formation of associations between causes and effects. Currently, the dominant associationist model in the field of causal induction is the Rescorla-Wagner model (Rescorla & Wagner, 1972; Wagner & Rescorla, 1972). This model defines the change in associative strength between a cue and an outcome (in this case, a cause and an effect) as a function of the salience of both cue and outcome, and the total strength of previously trained associations. The strength of association is computed between each cue and the outcome. Note that the applications of the Rescorla-Wagner model in the causal learning literature (e.g. Baker, Mercier, Vallée-Tourangeau, Frank, & Pan, 1993; Price & Yates, 1995; Shanks & Lopez, 1996; Wasserman, Elek, Chatlosh, & Baker, 1993) assume that the strength of the association between cue and outcome is interpreted to be equivalent to a subject's estimate of causal strength. The Rescorla-Wagner model has two aspects which have proven to be important for causal induction: causes compete with one another for association with a given effect. This competition implies that at asymptote a weak cause (i.e. one that covaries less with the effect) will be "discounted" in favor of a strong cause (i.e. a cause that covaries more with the effect). The model also can make predictions about the effects of order, based simply on strength of association, during the learning sequence.

For humans, however, the order of evidence may have an additional effect: events that occur earlier during learning may affect the interpretation of later events. The third kind of model, which serves as the basis for this dissertation, makes the assumption that subsequent information is interpreted in light of previous information. In other words, people use later learning trials to update beliefs formed during previous learning. One current model of belief updating (Hogarth & Einhorn, 1992) proposes that initial trials serve to form an anchoring value, which is then adjusted sequentially with each new piece of evidence. For instance, a physician may investigate the probability that a patient has contracted a certain disease by ordering a set of tests. The initial symptoms that the patient presented helped to anchor the subjective probability of the disease; the result of each test will allow the physician to revise her estimate of that subjective probability upward or downward.

Belief-updating models, as exemplified by Hogarth and Einhorn (1992), have usually been applied only to constructs such as impression formation. I propose that causal learning also occurs through a process of belief formation and updating. In this view, the information that a person receives at the beginning is used to construct a model about possible causal relationships. This initial belief then helps to determine the final judgment, for example, by providing an anchor point for future adjustments (Hogarth & Einhorn, 1992). Thus, I hypothesize that if the initial evidence suggests a generative causal relationship, then people will prefer to focus on the evidence that confirms that relationship: Cells A and D in Figure 1. In constrast, if the evidence initially suggests an inhibitory relationship, then people will tend to focus on evidence that confirms that relationship (Cells B and C). In other words, I predict a primacy effect, in that presenting evidence of a generative causal relationship (i.e. Cell A and D cases) first will lead to higher causal strength ratings, than will presenting evidence of a null, or even inhibitory, relationship (Cell B and C cases).

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