The authors of the paper “Do Physicians Know when Their Diagnoses Are Correct?” (Journal of General Internal Medicine [2005]: 334– 339) presented detailed case studies to students and faculty at medical schools. Each participant was asked to provide a diagnosis in the case and also to indicate whether his or her confidence in the correctness of the diagnosis was high or low. Define the events C, I, and H as follows: C = event that diagnosis is correct I = event that diagnosis is incorrect H = event that confidence in the correctness of the diagnosis is high
a. Data appearing in the paper were used to estimate the following probabilities for medical students: P(C) = 0.261 P(I) = 0.739 P(H| C) = 0.375 P(H| I) = 0.073 Use the given probabilities to construct a “hypothetical 1000” table with rows corresponding to whether the diagnosis was correct or incorrect and columns corresponding to whether confidence was high or low.
b. Use the table to compute the probability of a correct diagnosis, given that the student’s confidence level in the correctness of the diagnosis is high.
c. Data from the paper were also used to estimate the following probabilities for medical school faculty: P(C) = 0.495 P(I) = 0.505 P(H| C) = 0.537 P(H| I) = 0.252 Construct a “hypothetical 1000” table for medical school faculty and use it to compute the probability of a correct diagnosis given that the faculty member’s confidence level in the correctness of the diagnosis is high. How does the value of this probability compare to the value for students computed in Part (b)?