Thinking and Deciding

ATTENTIONAL BIAS 187
Table 8.2: Incidence of symptom (S) and disease (D) for 100 patients
Disease present Disease absent
Symptom present 37 17
Symptom absent 33 13
From such a table, it is possible to determine whether a correlation exists between
the symptom and the disease. In this case, the symptom is not correlated at all with
the disease. Out of 54 patients who have the symptom, 37 have the disease, about
69%. Out of 46 patients who do not have the symptom, 33 have the disease, about
72%. A given patient has about a 70% chance of having the disease, whether this
patient has the symptom or not. The symptom is useless in determining who has the
disease and who does not, in this group of patients.
Nonetheless, 85% of the nurses said that there was a relationship between the
symptom and the disease. Smedslund presented the subjects with other kinds of relationships.
For example, by switching the 17 and the 13, a real (if weak) relationship
between symptom and disease was created. Here, the nurses were no more likely to
think there was a relationship than they were in the original case. Smedslund found
that the best predictor of the subjects’ judgment of relationship was the proportion
of the total number of cases in the upper left-hand cell. If the symptom and disease
were both frequently “present” (as indicated by high figures in that cell), subjects
tended to think that there was a relationship. Subjects seem to attend largely to this
cell, when they should (normatively) have been attending to the whole table.
As Nisbett and Ross point out (1980, p. 92), the reasoning exhibited by these
subjects is much like that of many laypeople when they discuss a proposition such
as “Does God answer prayers?”
‘Yes,’ such a person may say, ‘because many times I’ve asked God for
something, and He’s given it to me.’ Such a person is accepting the data
from the present/present cell as conclusive evidence for the covariation
proposition. A more sophisticated layperson may counter this logic by
asking for the data from the present/absent cell (i.e., prayers present,
positive outcome absent): ‘Have you ever asked God for something and
not gotten it?’
In fact (Nisbett and Ross point out), even these two cells are not enough. If positive
outcomes are just as likely to occur when we do not pray for them as when we do,
there is still no relationship. We need to know the absent/present and absent/absent
cells, the ones at the bottom of the table, as well as the two others.
Many other experiments have supported Smedslund’s general conclusion that
subjects tend to ignore part of the table. In asking whether a symptom predicts a