Signal Detection Theory and Procedures

Information and Criterion

In the previous example, there are two possibilities for the patient: either the “signal” (tumor in this case) is present or absent. There are also two possible decisions: either the decision maker (the radiologist in this case) thinks he or she sees the signal (the radiologist responds “yes”) or does not (the radiologist responds “no”). Thus, there are four possible outcomes. Two of these are correct: a correct reject (the tumor is absent and the radiologist says “no”) or a hit (the tumor is present and the radiologist says “yes”). The other two are incorrect responses: a miss (the tumor is present and the radiologist says “no”) or a false alarm (the tumor is absent yet the radiologist says “yes”).

The radiologist bases his or her decision on information. For example, healthy lungs have a characteristic shape. The presence of a tumor might distort that shape. Tumors may have different image characteristics: brighter or darker, or a different texture. With proper training, a doctor learns what to look for; with more practice and training, the doctor will be able to acquire more (and more reliable) information. Running another test (e.g., magnetic resonance imaging, MRI) can also be used to acquire more information. The effect of acquiring more information is to increase the likelihood of correct outcomes (a hit or correct rejection), while reducing the likelihood of errors (a false alarm or miss).

In addition to relying on information from medical tests, the medical profession encourages doctors to use their judgment. Different types of errors are not always equal. The doctor may feel that missing an opportunity for early diagnosis may mean the difference between life and death. A false alarm, on the other hand, may result only in a routine biopsy operation. Consequently, the doctor may choose to err toward “yes” (tumor present) decisions. However, other doctors under the same circumstances may feel that unnecessary surgeries (even routine ones) are bad (expensive, stressful, etc.), so they may chose to be more conservative and say “no” (no tumor) more often. They will miss more tumors, but they will be doing their part to reduce unnecessary surgeries. And they may feel that a tumor, if there really is one, will be picked up at the next checkup. These arguments are not about information. Two doctors, with equally good training, looking at the same CT scan, will have the same information. But they may utilize a different criterion. Indeed, the same doctor might use a different criterion for different patients. For example, the criterion might be shifted toward “no” responses for a patient with a higher risk of complications from a biopsy procedure. On the other hand, the criterion might be shifted toward “yes” responses for a patient with a family history of lung cancer.

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