Cultural Prescriptions and Statistical Reasoning

Cultural Prescriptions

A third factor that may contribute to the use of statistical heuristics is a cultural or subcultural prescription to reason statistically about events of a given kind. Statistical reasoning is the culturally prescribed way to think about randomizing devices in our culture, and this general approach undoubtedly trickles down to children. Similarly, statistical reasoning has become (or is becoming) the norm for experts in many fields – from insurance to medical diagnosis – and is rapidly becoming normative for the lay novice as well in such domains as sports and the weather. Models of statistical reasoning abound for sports in particular, as the following two examples indicate.

Baseball’s law of averages is nothing more than an acknowledgement that players level off from season to season to their true ability-reflected by their lifetime averages. A .250-hitter may hit .200 or .300 over a given period of time, but baseball history shows he will eventually level off at his own ability (“Law of Averages,” 1981).

The musky tends to be a deep-water fish. Most fishing success is in shallow water, but . . . this misleading statistic [is probably accounted for in part by the fact that] sheer statistical chance dictates that fish will come from the waters receiving the most man hours of fishing pressure. Shallow water fishing for muskies is very popular, and very few fishermen work them deep (Hamer, 1981).

The statistical spirit embodied in these quotations reaches many fans. Thus, it is commonplace to hear lay people endorse the proposition that, “On a given Sunday, any team in the NFL can beat any other team.” (Compare with “On a given Sunday, any parishioner’s altruism can exceed that of any other parishioner”!)

In our view, these three factors – clarity of the sample space and the sampling process, recognition of the role of chance in producing events, and cultural prescriptions to think statistically – operate individually, and perhaps more often, together to increase people’s tendencies to apply statistical heuristics to problems that require a statistical approach. If these factors are genuinely important determinants of people’s ability to reason statistically, then it should be possible to find support for the following predictions.

In cases in which the sample space is clear and the possibility of repetition is salient, people respond appropriately to statistical variables. In particular, in the task of generalizing from instances, in which the sample space is a clear dichotomy and the sampling process is just the observation of more members of a clearly defined population, (1) people generalize more cautiously when the sample size is small and when they have no strong prior belief that the sampled population is homogeneous, and (2) people can be influenced to generalize more or less readily by manipulations that emphasize the homogeneity or heterogeneity of the sampled population.

The following predictions should hold both for generalization and for other, more complex, inferential tasks:

1. Manipulations designed to encourage recognition of the chance factors influencing events should serve to increase statistical reasoning.

2. People who are highly knowledgeable about events of a given kind should be more inclined than less knowledgeable people to apply statistical reasoning to the events – because both the distributions of the events and the chance factors influencing the events should be clearer to such people.

3. People should be disinclined to reason statistically about certain kinds of events that they recognize to be highly variable and uncertain – notably social events – because the sample spaces for the events and the chance factors influencing the events are opaque.

4. Training in statistics should promote statistical reasoning even about mundane events of everyday life because such training should help people to construct distributional models for events and help them to recognize “error,” or the chance factors influencing events.