Statistical Analysis of Medical Tests
I finally figured out how to calculate the probability that you are positive if you tested positive on a medical test. To accomplish this, you have to have requisite data, as I have assumed I have in this hypothetical:
Assume that a test yields a false positive 2% of the time.
Assume that 10% of the test takers are actually positive.
You take the test and test positive.
Problem: What are the odds that you are positive?
Solution: Either you are positive and tested positive, or you are negative and tested false positive.
Assume 1000 people take the test.
Of the 100 who are actually positive, 98 test positive.
Of the 900 who are actually negative, 18 tested false positive.
So, of the 1,000 taking the test, you were one of 116 test takers who tested positive.
So the odds are 98 out of 116 that you were a true positive.
Therefore there’s a 83.05% chance that you are a true positive.