In many studies of base-rate use (or neglect), human participants are asked to judge the likelihood of an event on the basis of information about past occurrences (base rates) and present diagnostic case cue information. Base rates and case cues are presented in a tabulated statistical format. As Barbey & Sloman (B&S) point out in the target article, and as has been found by various investigators, subjects are less likely to neglect base-rate information when data presentation is transparent with respect to the set relations involved. Natural frequency presentation is transparent in this way. In fact, in daily life humans experience base rates in terms of natural frequencies; however, they experience them one example at a time. We thought that an ideal way to assess people's sensitivity to base-rate information would be with a matching-to-sample (MTS) procedure (Stolarz-Fantino & Fantino Reference Stolarz-Fantino and Fantino1990). In the typical MTS procedure selection of the comparison stimulus that matches the sample is reinforced. But the procedure may be modified to vary the “accuracy” of the sample, that is, the degree to which it predicts the correct answer and the base rates (the proportion of correct answers assigned to each of the two comparison stimuli). This procedure is analogous to Tversky and Kahneman's “taxicab problem” (Tversky & Kahneman Reference Tversky, Kahneman, Kahneman, Slovic and Tversky1982a) and other problems of similar type. In the MTS analog, the sample stimulus corresponds to the witness in the taxi problem, or the case-cue information in other base-rate neglect problems; the probabilities of reinforcement for selecting the comparison stimuli correspond to the base rates, or incidence of taxi types.
Our procedure was simple. The sample in a MTS task was either a blue or green light. After the sample was terminated, two comparison stimuli appeared: these were always a blue and a green light. Participants were instructed to choose either. We could present subjects with repeated trials rapidly (from 150 to 400 trials in a less than one-hour session, depending on the experiment), and we could readily manipulate the probability of reinforcement for selecting either color after a blue sample and after a green sample. In one condition, the blue and green samples were equi-probable. Following a blue sample, selection of the blue comparison stimulus was reinforced on 67% of trials and selection of the green comparison stimulus on 33% of trials. Following a green sample, selection of the green comparison stimulus was reinforced on 33% of trials and selection of the blue comparison stimulus on 67% of trials. In other words, the sample in this case had no discriminative (or informative) function, just as the witness testimony has no function in the cab problem when the witness is 50% accurate. If our participating college students were responding optimally, they should have come to select the blue comparison stimulus on every trial, regardless of the sample color, thereby obtaining reward on 67% of trials. In this condition, participants showed a huge base-rate neglect, matching green on 56% of trials. In fact, our human participants showed significant base-rate neglect over hundreds of trials in this condition and in several others, in a series of studies conducted primarily by Adam Goodie (e.g., Goodie & Fantino Reference Goodie and Fantino1995; 1996; 1999). In contrast, Hartl and Fantino (Reference Hartl and Fantino1996) found that pigeons selected optimally in a comparable MTS task, with no evidence of base-rate neglect.
What might account for the drastic difference in the behavior of pigeons and college students? We have speculated that humans have acquired strategies for dealing with matching problems that are misapplied in our MTS problem (e.g., Stolarz-Fantino & Fantino Reference Stolarz-Fantino and Fantino1995). For instance, from early childhood we learn to match like shapes and colors at home, in school, and at play (e.g., in picture books and in playing with blocks and puzzles). If base-rate neglect is a learned phenomenon, we should be able to eliminate it by using sample stimuli that are physically unrelated to the comparison stimuli. Therefore, we repeated our earlier experiment (Goodie & Fantino Reference Goodie and Fantino1995) with a MTS procedure in which the sample stimuli were line orientations and the comparison stimuli were again the colors blue and green. This change eliminated base-rate neglect in keeping with the learning hypothesis (Goodie & Fantino 1996). Instead, participants' choices were well described as probability matching. To further assess the learning hypothesis, we next introduced a MTS task in which the sample and comparison stimuli were physically different but were related by an extensive history: The samples were the words “blue” and “green”; the comparison stimuli the colors blue and green. A robust base-rate neglect was reinstated. These and other experiments led us to conclude with some confidence that pre-existing associations contribute to the tendency to ignore or underweight base-rate information. Our human participants were not sensitive to the frequencies of reinforced choices, whereas pigeons, unfettered by prior associations, were appropriately sensitive to the same frequencies. However, Fantino et al. (Reference Fantino, Kanevsky and Charlton2005) have shown that pigeons will also neglect base-rate information if they are given sufficient prior MTS training with a 100% reliable sample – that is, a training history more similar to that of human subjects.
Whether or not we have evolved to process information in terms of frequencies, there is evidence that trial-by-trial presentation of information can be difficult for human participants to process. For example, Jenkins and Ward (Reference Jenkins and Ward1965) found that participants' judgments of contingency were more related to the number of successful trials (Response 1 followed by Outcome 1) than they were to the actual degrees of association between responses and outcomes. A second study (Ward & Jenkins Reference Ward and Jenkins1965) showed that, when statistical information was presented in summary form, many more participants based their contingency judgments on logical rules (75%) than when they received trial-by-trial information (17%).
Stolarz-Fantino et al. (Reference Stolarz-Fantino, Fantino and Van Borst2006) found that even with base-rate story problems (similar to the taxicab problem) in which statistical information was presented in a probability format, human participants attended appropriately to base-rate information under certain conditions. For example, when they made likelihood judgments on a series of problems, their estimates of likelihood varied appropriately with base-rate and case-cue values; this was not the case when participants judged single problems. And when the case-cue information was unreliable (as when the “witness” was described as being correct 50% of the time), many participants ignored the case cue in favor of the base rate.
Presumably, trial-by-trial experience emphasizes associative processes (System 1), whereas information presented in tabulated statistical form can cue associative and/or rule-based (System 2) activity. A challenge for future research will be to learn more about how information learned through experience becomes the subject of rule-based reasoning. Like Goodie and Fantino's (1996) participants, people typically have more immediate experience with case-cue information than with base rates; appreciating the effect of base rates usually means integrating information over a period of time. In tasks involving tabulated statistical information, base-rate and case-cue information are available simultaneously; however, in life, as pointed out by Fiedler (Reference Fiedler2000), the base rates of many important events are unknown. Therefore, past experience may lead people to put more emphasis on case cues even when base-rate information is available.
As the target article suggests, there is more to performance on base-rate problems than the question of whether information is presented in the form of probabilities or frequencies. In fact, other variables may dwarf the effects of presentation.
