Diagnostic tests of medical conditions can have several types of results. The te

Question

Diagnostic tests of medical conditions can have several types of results. The test result can be positive or negative, whether or not a patient has the condition. A positive test (+) indicates that the patient has the condition. A negative test (?) indicates that the patient does not have the condition. Remember, a positive test does not prove the patient has the condition. Additional medical work may be required. Consider a random sample of 200 patients, some of whom have a medical condition and some of whom do not. Results of a new diagnostic test for the condition are shown.

Assume the sample is representative of the entire population. For a person selected at random, compute the following probabilities. (Enter your answers as fractions.)

(a) P(+ | condition present); this is known as the sensitivity of a test.


(b) P(? | condition present); this is known as the false-negative rate.


(c) P(? | condition absent); this is known as the specificity of a test.


(d) P(+ | condition absent); this is known as the false-positive rate.


(e) P(condition present and +); this is the predictive value of the test.


(f) P(condition present and ?).

Condition Present Condition Absent Row Total Test Result + 109 21 130 Test Result ? 25 45 70 Column Total 134 66 200

Explanation / Answer

a) p(+/condition present) = 109/134

b) p(-/condition present) = 25/134

c) p(-/condition absent) = 45/66

d) p(+/condition absent) = 21/66

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