Selective Application of Statistical Reasoning

Selective Application of Statistical Reasoning

The foregoing work indicates that nonstatistical heuristics play an important role in inductive reasoning. But it does not establish that other heuristics, based on statistical concepts, are absent from people’s judgmental repertoire. Indeed, if one begins to look for cases of good statistical intuitions in everyday problems, it is not hard to find some plausible candidates.

Even when judgments are based on the representativeness heuristic, there may be an underlying stratum of probabilistic thinking. In many of the problems studied by Kahneman and Tversky, people probably conceive of the underlying process as random, but they lack a means of making use of their intuitions about randomness and they fall back on representativeness. In the maternity ward problem, for example, people surely believe that the number of boys born on any particular day is a matter of chance, even though they rely on representativeness to generate their subjective sampling distributions. But consider the following thought experiment: If someone says, “I can’t understand it; I have nine grandchildren and all of them are boys,” the statement sounds quite sensible. The hearer is likely to agree that a causal explanation seems to be called for. However, imagine that the speaker says, “I can’t understand it; I have three grandchildren and all of them are boys.” Such a statement sounds peculiar, to say the least, because it seems transparent that such a result could be due just to chance – that is, there is nothing to understand. Such an intuition is properly regarded as statistical in our view.

The contrast between the statistical intuition in our anecdote and subjects’ use of the representativeness heuristic in the maternity ward problem illustrates the selectivity with which people apply statistical concepts. The failure to do so in the maternity ward problem may be due to the use of “60%” in the problem, which evokes comparison between 60% and 50% and thence the dependence on the similarity judgment in choosing an answer. It may also be due to lack of concrete experience in thinking about samples in the range 15–45. As Piaget and Inhelder (1951/1975) put it, people seem to have an intuitive grasp of the “law of small large numbers,” even though they may not generalize the intuition to large numbers.

People also seem to have an ability to use base rates for selected kinds of problems. Consider the concepts of easy and difficult examinations. People do not infer that a student is brilliant who received an A+ on an exam in which no one scored below A−, nor that the student is in trouble who flunked a test that was also failed by 75% of the class. Rather, they convert the base-rate information (performance of the class as a whole) into a location parameter for the examination (easy, . . . difficult) and make their inference about the particular student in terms of the student’s relative position compared to the difficulty of the exam. Indeed, laboratory evidence has been available for some time that base rates are readily used for causal attributions for many kinds of abilities and achievements (Weiner et al., 1972).

As Nisbett and Ross (1980) suggested, one suspects that many lay concepts and maxims reflect an appreciation of statistical principles. It seems possible, for example, that people sometimes overcome sample bias by applying proverbs such as, “Don’t judge a book by its cover” or, “All that glitters is not gold.” Perhaps people sometimes even manage to be regressive in everyday predictions by using concepts such as “beginner’s luck” or “nowhere to go but up/down.”

There is one inductive reasoning task in particular for which there is good reason to suspect that statistical intuitions are very frequently applied. This is generalization from instances – perhaps the simplest and most pervasive of everyday inductive tasks. People surely recognize, in many contexts at least that when moving from particular observations to general propositions, more evidence is better than less. The preference for more evidence seems well understood as being due to an intuitive appreciation of the law of large numbers. For example, we think that most people would prefer to hold a 20-minute interview rather than a 5-minute interview with a prospective employee, and that if questioned, they would justify this preference by saying that 5 minutes is too short a period to get an accurate idea of what the job candidate is like. That is they believe that there is a greater chance of substantial error with the smaller sample. Similarly, most people would believe the result of a survey of 100 people more than they would believe that of a survey of 10 people; again, their reason would be based on the law of large numbers.

As we shall see, there is reason to believe that people’s statistical understanding of the generalization task is deeper still. People understand, at least in some contexts, that the law of large numbers must be taken into account to the degree that the events in question arc uncertain and variable in a statistical sense. Thus they realize that some classes of events are very heterogeneous; that is, the events differ from one another, or from one occasion to another, in ways that are unpredictable, and it is these classes of events for which a large sample is particularly essential.