A test for a disease correctly diagnoses a diseased person as having the disease with a probability of .85. The test incorrectly diagnoses someone without the disease with a probability of .1
The Correct Answer and Explanation is:
This problem seems to be related to the concepts of sensitivity and specificity in medical testing.
Key Definitions:
- Sensitivity (True Positive Rate): The probability that the test correctly identifies a person with the disease. In this case, it is given as 0.85 or 85%. This means that if a person actually has the disease, the test will correctly identify them as positive 85% of the time.
- False Positive Rate: The probability that the test incorrectly identifies a healthy person as having the disease. This is given as 0.1 or 10%, meaning if a person is healthy, there’s a 10% chance they will be incorrectly diagnosed as diseased.
Explanation:
- The true positive rate (sensitivity) of 0.85 tells us that 85% of the diseased people will be diagnosed correctly by the test.
- The false positive rate of 0.1 tells us that 10% of the healthy people will be incorrectly diagnosed as diseased by the test.
Now, you may also want to know other performance metrics, such as specificity, which is the probability of correctly identifying a healthy person as not having the disease. It can be found by subtracting the false positive rate from 1: Specificity=1−False Positive Rate=1−0.1=0.9\text{Specificity} = 1 – \text{False Positive Rate} = 1 – 0.1 = 0.9Specificity=1−False Positive Rate=1−0.1=0.9
This means the test will correctly identify 90% of healthy individuals as being healthy.
Additionally, if you wanted to calculate the overall accuracy of the test, you would need more information, such as the prevalence of the disease in the population being tested. However, for now, based on the provided probabilities, we know that the test is fairly accurate at detecting the disease (85% sensitivity) and has a moderate chance of falsely diagnosing healthy individuals (10% false positive rate).
Understanding these metrics is crucial in evaluating the effectiveness of a medical test in diagnosing diseases.
