Statistics question, help please!?

Question

A test for a certain disease is found to be 95% accurate meaning that it will correctly diagnose the disease in 95 out of 100 people who have the ailment. The test also 95% accurate for a negative result, meaning that it will correctly exclude the disease in 95 out of 100 people who do not have the ailment. For a certain segment of the population, the incidence of the disease is 4%.

Now suppose the incidence of the disease is 49%. Compute the probability that the person actually has the disease, given that the test is positive.

dunkelblau · Accepted Answer

If we take a random population of 10000 @ 49% incidence,

    Person     Total     Positive     Negative
    Sick        4900       4655         245
    Healthy     5100        255        4845

Prob(Sick|Positive) for 49% incidence rate = 4655/(4655+255) = 94.8%

Now for your 4% general incidence rate

    Person     Total     Positive     Negative
    Sick         400        380          20
    Healthy     9600        480        9120

Prob(Sick|Positive) for 4% incidence rate = 380/(380+480) = 44.2%

There's an important point to this comparison-- when you're designing medical tests
for serious problems, the accuracy requirements tighten a lot for rarer diseases.
That 95% accuracy may sound good, but you'll end up with lots of false positives 
when the incidence rate is low-- and this may cause people to ignore a positive result.

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Statistics question, help please!?

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