I see no disagreement. You are describing another way that the numbers could be presented so that it would be understood. I am not suggesting that doctors literally confuse the two ways of defining “false positive” but that the definition of false positive given is so far outside of experience, apparently, they are confused/mistaken about how to apply it correctly. My point is that if they actually needed it outside the exam once or twice (i.e., if the result was connected enough with experience to identify the correct or incorrect answer) they would readily learn how to do it.
You have asserted that the reason doctors can accurately tell patients their chances after a diagnostic test even if they perform poorly on the word problem is because they are confused about the term “false positive”. But the problem can be phrased without using the word “positive” at all, and people will still get it wrong if it’s phrased in terms of probabilities and get it right if it’s phrased in terms of relative frequencies. So the fact that doctors can tell patients their chances after a diagnostic test even if they perform poorly on the word problem has nothing to do with them being confused about false positives.
I see no disagreement. You are describing another way that the numbers could be presented so that it would be understood. I am not suggesting that doctors literally confuse the two ways of defining “false positive” but that the definition of false positive given is so far outside of experience, apparently, they are confused/mistaken about how to apply it correctly. My point is that if they actually needed it outside the exam once or twice (i.e., if the result was connected enough with experience to identify the correct or incorrect answer) they would readily learn how to do it.
You have asserted that the reason doctors can accurately tell patients their chances after a diagnostic test even if they perform poorly on the word problem is because they are confused about the term “false positive”. But the problem can be phrased without using the word “positive” at all, and people will still get it wrong if it’s phrased in terms of probabilities and get it right if it’s phrased in terms of relative frequencies. So the fact that doctors can tell patients their chances after a diagnostic test even if they perform poorly on the word problem has nothing to do with them being confused about false positives.