PUZZLE
Suppose a disease effects 2% of the population.
Suppose you have a test that's 95% accurate (i.e., 95% of healthy people are diagnosed as healthy & 95% sick are diagnosed as sick).
If you are diagnosed as sick, what are the chances you're actually sick?
Hint: Not 95%
Suppose a disease effects 2% of the population.
Suppose you have a test that's 95% accurate (i.e., 95% of healthy people are diagnosed as healthy & 95% sick are diagnosed as sick).
If you are diagnosed as sick, what are the chances you're actually sick?
Hint: Not 95%
Hi. I forgot to post the answer: 27.94%.
The point is just because a test has a high degree of "accuracy" (95%) does not mean you are highly likely to be sick. Do a second test to be sure.
It helps to plug in numbers to see this, but you can just multiply percentages:
The point is just because a test has a high degree of "accuracy" (95%) does not mean you are highly likely to be sick. Do a second test to be sure.
It helps to plug in numbers to see this, but you can just multiply percentages:
In plain English. Given 1000 people & 2% are sick:
980 Healthy
20 Sick
Given 95% accurate test:
980*.95=931 healthy diagnosed HEALTHY
980*.05=49 healthy but diagn. SICK
20*.95=19 sick diagn SICK
20*.05=1 sick but diagn HEALTHY
Diagn. SICK:49+19=68
Actually sick:19
19/68=27.94%
980 Healthy
20 Sick
Given 95% accurate test:
980*.95=931 healthy diagnosed HEALTHY
980*.05=49 healthy but diagn. SICK
20*.95=19 sick diagn SICK
20*.05=1 sick but diagn HEALTHY
Diagn. SICK:49+19=68
Actually sick:19
19/68=27.94%
Here's the probability of actually being sick, as test accuracy increases from 75% to 100% accuracy.
h/t @E__Strobel
h/t @E__Strobel
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