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TABLE 2.2 Decision-Making Under Uncertainty
The Facts
Our Decision
No difference.
No difference.
Drug is better.
Type I error
:
Manufacturer wastes money
developing ineffective drug.
Drug is better.
Type II error
:
Manufacturer misses
opportunity for profit.
Public denied access to
effective treatment.
TABLE 2.3 Decision-Making Under Uncertainty
The Facts
Fears et al.'s Decision
Compound not a
Not a carcinogen.
Compound a carcinogen.
carcinogen.
Type I error
:
Manufacturer misses
opportunity for profit.
Public denied access to
effective treatment.
Compound a
Type II error
:
carcinogen.
Patients die; families suffer;
Manufacturer sued.
an error. We also make an error if we decide there is no difference and the
new drug really is better. These decisions and the effects of making them
are summarized in Table 2.2.
We distinguish the two types of error because they have the quite differ-
ent implications described in Table 2.2. As a second example, Fears,
Tarone, and Chu [1977] use permutation methods to assess several stan-
dard screens for carcinogenicity. As shown in Table 2.3, their Type I error,
a false positive, consists of labeling a relatively innocuous compound as
carcinogenic. Such an action means economic loss for the manufacturer
and the denial to the public of the compound's benefits. Neither conse-
quence is desirable. But a false negative, a Type II error, is much worse
because it would mean exposing a large number of people to a potentially
lethal compound.
What losses are associated with the decisions you will have to make? Specify
them now before you begin.
DECISIONS
The hypothesis/alternative duality is inadequate in most real-life situa-
tions. Consider the pressing problems of global warming and depletion of
the ozone layer. We could collect and analyze yet another set of data and
