4 ms·

The ratio matters because the second type of error is significantly worse ie: it is much worse to have tuberculosis and be told you do not have tuberculosis. Th

The ratio matters because the second type of error is significantly worse ie: it is much worse to have tuberculosis and be told you do not have tuberculosis. They are looking at type 1 vs type 2 error. I think that they are saying three things 1) real tests aren't actually trying to minimize both types error of which is the opposite of the hypothesis "It might be natural to conclude that physicians seek to minimize both types of error" 2) illustrating with a very dangerous disease (to give the reader an idea of risk) the difference in types of error. 3) Demonstrating potential trade offs that occur, Type 1 error is so much less risky they are ok with 50x as much error.

jellicle 6y ago
Cynically, if doctors are financially rewarded for performing treatments, doctors may prefer a test with significant false positives over one with minimal false positives. (If your knee jerks and you start saying things like 'doctors never allow financial incentives to change their medical decisions!', let me respond by saying there are many studies that say that they do, and also you can replace 'doctors' with 'health-adjacent corporations' if you like.)
- kazinator 6y ago
  If nobody at all has tuberculosis, then even a test heavily biased toward false negative will still produce nothing but false positives. In that situation, only two kinds of test will avoid false positives: (1) a perfectly reliable test, or else (2) a broken tests that never reports a positive.
kazinator 6y ago
This does look like a clear misinterpretation/misuse of statistics, and a blemish on the otherwise fine article. Suppose we have a perfectly reliable test for tuberculosis, but we foul it into having an equal false positive or negative rate as follows: we perform the perfect test, the flip a fair coin, and if it is "heads" we invert the test's outcome. Then if we apply the test to a population in which the incidence of tuberculosis is low (which is actually the case), most of the false results will be false positive. In other words, a high false positive rate in a screening test relative to a low false negative rate does not prove that the test is biased toward false positive identification. Consider that if nobody at all has tuberculosis, the only kind of false result possible is a false positive.

jellicle 6y ago

Cynically, if doctors are financially rewarded for performing treatments, doctors may prefer a test with significant false positives over one with minimal false positives. (If your knee jerks and you start saying things like 'doctors never allow financial incentives to change their medical decisions!', let me respond by saying there are many studies that say that they do, and also you can replace 'doctors' with 'health-adjacent corporations' if you like.)

kazinator 6y ago
If nobody at all has tuberculosis, then even a test heavily biased toward false negative will still produce nothing but false positives. In that situation, only two kinds of test will avoid false positives: (1) a perfectly reliable test, or else (2) a broken tests that never reports a positive.

kazinator 6y ago

This does look like a clear misinterpretation/misuse of statistics, and a blemish on the otherwise fine article. Suppose we have a perfectly reliable test for tuberculosis, but we foul it into having an equal false positive or negative rate as follows: we perform the perfect test, the flip a fair coin, and if it is "heads" we invert the test's outcome. Then if we apply the test to a population in which the incidence of tuberculosis is low (which is actually the case), most of the false results will be false positive. In other words, a high false positive rate in a screening test relative to a low false negative rate does not prove that the test is biased toward false positive identification. Consider that if nobody at all has tuberculosis, the only kind of false result possible is a false positive.