ERRORS OF JUDGMENT AND CHOICE----Episode 3

    THE ERRONEOUS MEANS WE UTILIZE WHEN MAKING
    DECISIONS AND CHOICES 

   Here's an example of using totally uninformative descriptions to make decisions :

   Dick is a 30-year-old man. He is married with no children. A man of high ability and high motivation, he promises to be quite successful in his field. He is liked by his colleagues. 

   This description was intended to convey no information relevant to the question of whether Dick is an engineer or a lawyer. Consequently, the probability that Dick is an engineer should equal the proportion of engineers in the group, as if no description had been given. The subjects, however, judged the probability of Dick being an engineer to be .5 regardless of whether the stated proportion of engineers in the group was .7 or .3. Evidently people respond differently when given no evidence and when given worthless evidence. When no specific evidence is given, prior probabilities are properly utilized ; when worthless evidence is given, prior probabilities are ignored. 

Insensitivity to sample size .  To evaluate the probability of obtaining a particular result in a sample drawn from a specified population, people typically apply the representativeness heuristic. That is, they assess the likelihood of a sample result, for example, that the average height in a random sample of ten men will be 6 feet, by the similarity of this result to the corresponding parameter [that is, to the average height in the population of men] . The similarity of a sample statistic to a population parameter does not depend on the size of the sample. Consequently, if probabilities are assessed by representativeness, then the judged probability of a sample statistic will be essentially independent of sample size. Indeed, when subjects assessed the distributions of average height for sample of various sizes, they produced identical distributions. For example, the probability of obtaining an average height greater than 6 feet was assigned the same value for samples of 1,000, 100, and 10 men. Moreover, subjects failed to appreciate the role of sample size even when it was emphasized in the formulation of the problem.  Consider the following question : 

     A certain town is served by two hospitals. In the larger hospital about 45 babies are born each day, and in the smaller hospital about 15 babies are born each day. As you know, about 50% og all babies are boys. However, the exact percentage varies from day to day. Sometimes it may be higher than 50%, sometimes lower. 
     For a period of 1 year, each hospital recorded the days on which more than 60% of the babies born were boys.  Which hospital do you think recorded more such days ? 
     The large hospital [21]
     The smaller hospital [21]
     About the same [that is, within 5% of each other [53] 
The values in parentheses are the number of undergraduate students who chose each answer. 
    Most subjects judged the probability of obtaining more than 60% boys to be the same in the small and in the large hospital, presumably because these events are described by the same statistic and are therefore equally representative of the general population. In contrast, sampling theory entails that the expected number of days on which more than 60% of the babies are boys is much greater in the small hospital than in the large one, because a large sample is less likely to stray from 50%. This fundamental notion of statistics is evidently not part of people's repertoire of intuitions. 


   A similar insensitivity to sample size has been reported in judgments of posterior probability, that is, of the probability that a sample has been drawn from one population rather than from another. Consider the following : 

     
     imagine an urn filled with balls, of which 2/3 are of one color and 1/3 of another. One individual has drawn 5 balls from the urn, and found that 4 were red and 1 was white. Another individual has drawn 20 balls and found that 12 were red and 8 were white. Which of the two individuals should feel more confidant that the urn contains 2/3 red balls and 1/3 white balls, rather than the opposite ? What odds should each individual give ? 

   In this problem, the correct odds are 8 to 1 for the 4:1 sample and 16 to 1  for the 12:8 sample, assuming equal prior probabilities. However, most people feel that the first sample provides much stronger evidence for the hypothesis that the urn is predominantly red, because the proportion of red balls is larger in the first than in the second sample. Here again, intuitive judgments are dominated by the sample proportion and are essentially unaffected by the size of the sample, which plays a crucial role in the determination of the actual posterior odds. In addition, intuitive estimates of posterior odds are far less extreme than the correct values. The underestimation of the impact of evidence has been observed repeatedly in problems of this type. It has been labeled "conservatism." 


    MORE TO COME.