Thinking and Deciding

180 HYPOTHESIS TESTING
Table 7.2: Z ray test results and incidence of umphitis in 100 patients
Test result Umphitis No umphitis
Positive Z ray 50 0
Negative Z ray 30 20
All patients 80 20
Table 7.3: Z ray test results and incidence of umphitis in 100 patients
Test result Umphitis No umphitis
Positive Z ray 50 0
Negative Z ray 20 30
All patients 70 30
of what we will do for each outcome of the test. We realize that, for either outcome,
we will treat umphitis. Regardless of the outcome of the test, we will treat the same
eighty patients correctly that we would have treated otherwise.
The test would have some value if the situation were as shown in Table 7.3. Here,
if we do the test and it is positive, we would treat umphitis and be correct every time.
If we do the test and it is negative, this time we would not treat umphitis, and we
would be correct 60% of the time (30 out of 50 patients). Overall, if we do the test,
we would treat 80 out of 100 patients correctly. If we do not do the test, however,
we would treat umphitis, and we would be correct only 70% of the time; we would
treat correctly only 70 out of 100 patients. Therefore, in a group of 100 patients, we
would treat 70 correctly if we do not do the test, and we would treat 80 correctly
if we do the test. This is because the test result makes a difference; it affects the
action we would take. Overall, the expected utility of the test is .8 − .7, or.1.This
corresponds to the 10 extra patients out of 100 who would be treated correctly only
if the test is done.
In sum, a test has some expected utility only if it can affect the action we would
take. Subjects in experiments, however, show a bias in which they seek information
even when it cannot affect action. This information bias can occur elsewhere: in
medical practice, in organizations, and in daily life. What is not worth knowing is
not worth knowing.
We can apply the same kind of analysis to compute the relative value of different
possible tests or questions. Consider the water example on p. 174, which showed a
congruence bias, a preference for questions that yield a positive answer if the favored