Figure 171

Estimated probability in the taxi-cab problem that a Blue cab was responsible for the accident in causal and control conditions. Data from Tversky and Kahneman (1980).

Thus, the odds ratio is 12:17, meaning that there is a 41% probability that the taxi cab was Blue versus a 59% probability that it was Green.

Neglecting base rates

What we have done so far is to describe how people's estimates of the probability of certain hypotheses might vary in the light of new evidence. In fact, people often take much less account of the prior odds or the base-rate information than they should if they were following the principles of Bayes' theorem. Base-rate information was defined by Koehler (1996, p. 16) as "the relative frequency with which an event occurs or an attribute is present in the population." There are many situations in which participants seem to neglect base rates. For example, consider the taxi-cab problem discussed earlier. Tversky and Kahneman (1980) found that most participants ignored the base-rate information about the relative numbers of Green and Blue cabs. They concentrated on the evidence of the witness, and maintained that there was an 80% likelihood that the taxi was Blue rather than Green (see Figure 17.1). In fact, as we have seen, the correct answer based on Bayes' theorem is 41%.

Tversky and Kahneman (1980) also used an alternative condition in which people did take base-rate information into account. They changed the (a) part of the problem to:

Although the two companies are roughly equal in size, 85% of cab accidents in the city involve Green cabs, and 15% involve Blue cabs.

In this version of the problem, a clear causal relation is drawn between the accident record of a cab company and the likelihood of there being an accident. In the original version of the problem, in contrast, the population difference for the two cab companies is given no causal significance. Thus, the base-rate information was predicted to be of more significance in this new problem, and to play a greater part in participants' assessments. This prediction was confirmed, with most participants producing estimates of a 60% likelihood (see Figure 17.1). It appears that base rates may be ignored, but various factors (e.g., the presence of a causal relation) can partially reverse this behaviour.

Additional evidence about the circumstances in which people do and do not use base-rate information emerges from studies by Casscells, Schoenberger, and Graboys (1978) and by Cosmides and Tooby (1996).

Casscells et al. (1978) presented the following problem to members of staff and to students at Harvard Medical School:

If a test to detect a disease whose prevalence is 1/1000 has a false positive rate of 5%, what is the chance that a person found to have a positive result actually has the disease, assuming that you know nothing about the person's symptoms or signs?

The base-rate information is that 999 people out of every 1000 do not suffer from the disease. However, 50 out of every 1000 people tested would give a false positive finding (5% is the false positive rate). Thus, 50 times as many people give a false positive result as give a true positive result (the one person in 1000 who had the disease), and so there is only a 2% chance that a person testing positive actually has the disease. The correct answer was given by 18% of the participants, but 45% ignored the base-rate information and gave the wrong answer of 95%.

Cosmides and Tooby (1996) used a rather similar problem. However, they emphasised the frequencies of individuals in the various categories relevant to the problem. In addition, they told the participants to construct an active pictorial representation. More specifically, the participants had to colour in different squares to represent those individuals with and without the disease. In these circumstances, 92% used the base-rate information and gave the correct answer.

Evaluation

Koehler (1996) reviewed findings on use of baserate information. He concluded that this literature, "does not support the conventional wisdom that people routinely ignore base rates. Quite the contrary, the literature shows that base rates are almost always used and that their degree of use depends on task structure and representation" (P. 1).

Koehler (1996) argued that there are three main reasons for not concluding that base-rate information is typically ignored. First, the most common finding is that individuals pay less attention than they should to base-rate information. However, it does have some influence on their decision making, and so cannot be said to have been ignored altogether.

Second, there are typically major differences between the laboratory and the real world in terms of how we obtain base-rate information. In the laboratory, this information is generally provided directly by the experimenter. In the real world, in contrast, such information is typically obtained indirectly (if at all) via numerous experiences. There is some evidence suggesting that this difference is important. For example, consider the real-world research carried out by Christensen-Szalanski and Bushyhead (1981). They found that doctors were sensitive to the predictive value of various symptoms associated with pneumonia, and argued that the doctors were sensitive to base rates. However, of those patients estimated by the doctors to have a 90% chance of having pneumonia, under 20% actually had pneumonia (Clare Harries, personal communication). Thus, the doctors were not actually very sensitive to base-rate information.

The notion that doctors typically make effective use of base-rate information was disproved by Bergus, Chapman, Gjerde, and Elstein (1995). Doctors were presented with the case history of a man who reported a 1-hour episode of weakness in the right arm and leg. Some of the doctors were informed initially that he had had treatment for lung cancer, whereas the others were only told this at the end of the experiment. Those who were told initially about the lung cancer gave a mean probability of 48% that the correct diagnosis was brain cancer that had spread from the lungs. In fact, however, the correct probability is 99.5%, and so their estimate of the base rate was incorrect. All the doctors were then told that the patient had been given a CAT scan which had not revealed any abnormality. This additional information reduces the likelihood that the correct diagnosis is brain cancer spreading from the lungs to 93%. Those who had just learned of the previous lung cancer produced an average probability estimate of 79%, compared to only 11% for those doctors who had been given that information initially. Thus, the doctors were more likely to neglect information relevant to base rate if it had been provided some time previously.

The effects of experience on usage of baserate information can be complex. For example, Gluck and Bower (1988) carried out a study in which the participants had 250 learning trials. On each trial, combinations of four symptoms were displayed, and the participants had to decide which of two diseases was present. One disease was present 75% of the time and the other disease was present 25% of the time. The participants' performance on the last 50 trials indicated that they were using base-rate information about the relative frequencies of the diseases. However, when asked questions at the end of the experiment, their answers did not reflect accurate knowledge of baserate information. According to Spellman (1996), base-rate information that has been acquired via implicit learning (complex learning in the absence of conscious recollection of what has been learned) can be accessed more readily on implicit memory tests (e.g., performance) than on explicit memory tests (e.g., direct questioning).

To return to the third of Koehler's points, in most real-world situations, base-rate information is either unavailable or of limited usefulness. According to Koehler (1996, p. 14), "When base rates in the natural environment are ambiguous, unreliable, or unstable, simple normative rules for their use do not exist. In such cases, the diagnostic value of base rates may be substantially less than that associated with many laboratory experiments." There are often several competing base rates in the real world. Suppose you are trying to work out the probability that a given professional golfer will score under 70 in his next round on a given course. What is the relevant base rate? Is it his previous scores on that course during his career, or his general level of performance that season, or his performance over his entire career, or the average performance of other professionals? As Connolly (1996, p. 19) pointed out, "In any reasonably complex informational environment, it is essentially arbitrary to select some part of the information as relevant to the estimation of a base rate." As a result of these uncertainties, our everyday experiences may have indicated that there is little value in base-rate information, and so we are reluctant to make use of such information when it is available.

Representativeness heuristic

Why do we often fail to make much use of baserate information? Tversky and Kahneman and their associates argued that we typically utilise a simple heuristic or rule of thumb known as the representativeness heuristic. When people use this heuristic, "events that are representative or typical of a class are assigned a high probability of occurrence. If an event is highly similar to most of the others in a population or class of events, then it is considered representative" (Kellogg, 1995, p. 385). The representativeness heuristic is studied in situations in which people are asked to judge the probability that an object or event A belongs to a class or process B. If someone is given a description of an individual and asked to guess the probability that this individual has a certain occupation, it is typically found that they judge probabilities in terms of the similarity of the individual to their stereotype for that occupation. In a study by Tversky and Kahneman (1974), the participants were given the following description of Steve:

.very shy and withdrawn, invariably helpful, but with little interest in people, or in the world of reality. A meek tidy soul, he has a need for order and structure and a passion for detail.

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Business Correspondence

Business Correspondence

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