Guessing that everyone is T- results in a 100% false negative rate, which although not much better than a 99% false negative rate, might more than make up for a 1% decrease in the false positive rate.
If this is a real cancer test, and the researcher is optimizing a balance between false positives and false negatives, where would you prefer that he or she place that balance? A lot of medical tests have intentionally very low false negative rates even if that means they have proportionally much higher false positive rates (than they would if they were optimizing for a different balance).
THANK YOU! That’s the best explanation I’ve ever seen of the difference. I don’t know if it’s right; but at least it’s making a coherent claim.
Can you spell out how the computation is done with the priors in the Bayesian case?
Quibble:
Guessing that everyone is T- would have a lower error rate.
Guessing that everyone is T- results in a 100% false negative rate, which although not much better than a 99% false negative rate, might more than make up for a 1% decrease in the false positive rate.
If this is a real cancer test, and the researcher is optimizing a balance between false positives and false negatives, where would you prefer that he or she place that balance? A lot of medical tests have intentionally very low false negative rates even if that means they have proportionally much higher false positive rates (than they would if they were optimizing for a different balance).