5 ms·
Totally not a statistician, but I'll give it a shot. For the sake of the argument: test accuracy: exactly 99.0% accurate disease incidence: exactly 1 in 1
by dsp1234 11y ago
Totally not a statistician, but I'll give it a shot.
For the sake of the argument:
test accuracy: exactly 99.0% accurate
disease incidence: exactly 1 in 1 million
Calculation:
For the sake of simple calculations, let's assume we test exactly 1 million people.
tests positive = (1 * 0.99) + (999999 * 0.01)
tests positive = (.99) + (9999.99)
tests positive = 10000.98
We'll round up for the sake of argument to 10,001 positive results. And we know that only 1 person (remember that we're testing 1 million people) is actually sick. We have 1 actual sick in 10 thousand positives tests. So the probability that the positive test that is right in front of you is actually a truly sick person are 1 in 10 thousand.
- pif 11y agoBeware, you are making a strong assumption: that the test's accuracy is the same regarding false negatives and false positives. For example, a test may not find enough "anomaly" in an ill person to trigger the positive, thus yielding a false negative; at the same time, it may as well never find any "anomaly" in a sane person, and as a consequence never give any false positive. Back to your example, it's obvious that a test with a 0.01 probability to give a false positive is completely useless for an illness that affects 1e-6 of people.
- zdkl 11y agoSpot the domain-specific knowledge :) While true in the real world this wasn't part of the problem as written above!
- dspeyer 11y agoActual descriptions of medical tests routinely give both rates. They often call them "sensitivity" and "specificity". Good luck remembering which is which. But if only one rate is given, that indicates they're equal. If they're not, then it's reasonable to describe the documentation as incorrect.
- aidenn0 11y agoI have no trouble remembering which is which, as "sensitivity" is used in a way quite similar to its everyday use.