Medical technology has developed numerous procedures for testing for various diseases, drug use, etc. All such procedures are prone to some error. There is therefore a real concern with the occurrence of “false positives” (saying a subject has the condition when s/he in fact doesn’t) and “false negatives” (saying the subject does not have the condition, when s/he actually does).
Suppose that a decision is made to test all driver’s license applicants for drug use (or: all college athletes for drug or steroid use; or: all prison inmates for AIDS). Let’s consider what the false positive rate might be, under a variety of circumstances.
a) Suppose first that everyone is tested for the condition, and that in reality two percent of the population has the condition. Suppose also that the test procedure used has 95% reliability — that is, whatever your condition, the test evaluates it correctly 95% of the time. What is the false positive rate? The false negative rate?
b) One way to lower the false positive rate is to modify the test in a way that will make it harder to get a “positive” reading, and easier to get a “negative” one. This will affect the reliability of the instrument. Let’s suppose such a modification is made, which increases to 97.5% the chance of correctly identifying a person without the condition, but which lowers to 90% the chance of correctly identifying a person with the condition. Now, what is the false positive rate for the problem in Part A? The false negative rate?
c) Another way to lower the false positive rate is only to test some members of the population — those deemed particularly “at risk,” or for whom there is some “probable cause” to suspect presence of the condition. Let’s suppose such a preliminary screening is done, eliminating much of the population from consideration. Of the remaining group, on whom the test is done, suppose that fully one-half have the condition of interest. Repeat Part A. Now, what are the false positive and false negative rates?
d) What are the relative costs of false positives and false negatives? What implications do these results have for various testing programs?
