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Confusion of the Inverse In one study, physicians were
Chapter 4, Problem 35BB(choose chapter or problem)
Problem 35BB
Confusion of the Inverse In one study, physicians were asked to estimate the probability of a malignant cancer given that a test showed a positive result. They were told that the cancer had a prevalence rate of 1%, the test has a false positive rate of 10%, and the test is 80% accurate in correctly identifying a malignancy when the subject actually has the cancer. (See Probabilistic Reasoning in Clinical Medicine by David Eddy, Cambridge University Press.)
a. Find P (malignant | positive test result). (Hint: Assume that the study involves 1000 sub jects and use the given information to construct a table with the same format as Table.)
b. Find P (positive test result | malignant). (Hint: Assume that the study involves 1000 sub jects and construct a table with the same format as Table.)
c. Out of 100 physicians, 95 estimated P (malignant | positive test result) to be about 75%. Were those estimates reasonably accurate, or did they exhibit confusion of the inverse? What would be a consequence of confusion of the inverse in this situation?
Questions & Answers
QUESTION:
Problem 35BB
Confusion of the Inverse In one study, physicians were asked to estimate the probability of a malignant cancer given that a test showed a positive result. They were told that the cancer had a prevalence rate of 1%, the test has a false positive rate of 10%, and the test is 80% accurate in correctly identifying a malignancy when the subject actually has the cancer. (See Probabilistic Reasoning in Clinical Medicine by David Eddy, Cambridge University Press.)
a. Find P (malignant | positive test result). (Hint: Assume that the study involves 1000 sub jects and use the given information to construct a table with the same format as Table.)
b. Find P (positive test result | malignant). (Hint: Assume that the study involves 1000 sub jects and construct a table with the same format as Table.)
c. Out of 100 physicians, 95 estimated P (malignant | positive test result) to be about 75%. Were those estimates reasonably accurate, or did they exhibit confusion of the inverse? What would be a consequence of confusion of the inverse in this situation?
ANSWER: