[Guest]

Say a new deadly disease sweeps the country. Let's call it Sudden Dumb Idiot Ailment, or SDIA for short. One of its symptoms are going to BrainDen.com and posting lots of "brain teasers" that people have posted months ago.

Luckily, right now, very few people have SDIA. Let's assume for the sake of argument that only 2% of the population has this disease (although looking at what's on reality television shows, you'd think it higher).

Suppose there's a test that checks to see if you have SDIA. Because the goal is to find people with SDIA (so they can't pass it on to other unsuspecting folks), the goal is to create a test with very few false negatives. One of the side effects of creating a test with very few false negatives is it creates false positives.

Say this test correctly identifies people who DO have SDIA 99.9% of the time. Say this test correctly identifies people who DO NOT have SDIA 98.5% of the time.

You are worried that you have SDIA (you got stumped on 3 "giterdone" riddles in a row), so you go in to take a test. The next day you get a phone call.... the test came back positive! Uh oh!

What are the chances that you actually do have SDIA???

By the way, the answer illustrates the situation with other types of disease testing.

[Guest]

Say a new deadly disease sweeps the country. Let's call it Sudden Dumb Idiot Ailment, or SDIA for short. One of its symptoms are going to BrainDen.com and posting lots of "brain teasers" that people have posted months ago.

Luckily, right now, very few people have SDIA. Let's assume for the sake of argument that only 2% of the population has this disease (although looking at what's on reality television shows, you'd think it higher).

Suppose there's a test that checks to see if you have SDIA. Because the goal is to find people with SDIA (so they can't pass it on to other unsuspecting folks), the goal is to create a test with very few false negatives. One of the side effects of creating a test with very few false negatives is it creates false positives.

Say this test correctly identifies people who DO have SDIA 99.9% of the time. Say this test correctly identifies people who DO NOT have SDIA 98.5% of the time.

You are worried that you have SDIA (you got stumped on 3 "giterdone" riddles in a row), so you go in to take a test. The next day you get a phone call.... the test came back positive! Uh oh!

What are the chances that you actually do have SDIA???

By the way, the answer illustrates the situation with other types of disease testing.

Okay, I'll try this, though I'm not at all good at math puzzles.

there is a .1% chance that it is a false negative.

There is a 1.5% chance that it is a false positive.

So, it is more likely that the test is true than false. It's pretty likely that you have SDIA.

[Nikyma]

Say a new deadly disease sweeps the country. Let's call it Sudden Dumb Idiot Ailment, or SDIA for short. One of its symptoms are going to BrainDen.com and posting lots of "brain teasers" that people have posted months ago.

Luckily, right now, very few people have SDIA. Let's assume for the sake of argument that only 2% of the population has this disease (although looking at what's on reality television shows, you'd think it higher).

Suppose there's a test that checks to see if you have SDIA. Because the goal is to find people with SDIA (so they can't pass it on to other unsuspecting folks), the goal is to create a test with very few false negatives. One of the side effects of creating a test with very few false negatives is it creates false positives.

Say this test correctly identifies people who DO have SDIA 99.9% of the time. Say this test correctly identifies people who DO NOT have SDIA 98.5% of the time.

You are worried that you have SDIA (you got stumped on 3 "giterdone" riddles in a row), so you go in to take a test. The next day you get a phone call.... the test came back positive! Uh oh!

What are the chances that you actually do have SDIA???

By the way, the answer illustrates the situation with other types of disease testing.

Love the question, very funny!

If I answer incorrectly, does that mean I'm infected?

99.2%?

[bonanova]

about 58%

[Guest]

about 58%

Bonanova is correct! Meaning, that if you got a positive test result back, it is more likely than not you do have SDIA, but there's a very good chance you don't. Many disease tests are like this; ALWAYS get a second test.

There's a 98% chance you don't have SDIA, and 1.5% chance that if you don't, you get a positive result. Multiply, and this situation happens 1.47% of the time. There's a 2% chance you have SDIA, and a 99.9% chance you'd get a positive test with that, so multiply, and this situation occurs 1.9998% of the time.

We don't care about the chances of getting a negative test, only a positive. So, in this combined 3.468% of the time, 1.998% of it, you would have SDIA. Divide it out, and you get 57.61% of the time that a positive test means you have this disease, and just over 40% of the time you don't.

[bonanova]

Out of a population of 100,000 persons who have a 2% likelihood of infection,

2000 have the disease, and will test 1998+ and 2-.

98000 do not have the disease and will test 1470+ and 96530-.

Of the 3468 who test positive, 2000 [57.67%] are true positives.

Your likelihood jumps from 2% to about 58%.

Here are some other cases ...

Suppose the initial likelihood of having the disease is 50%

Out of a population of 2000 such persons,

1000 will have the disease, and will test 999+ and 1-.

1000 will not have the disease, and will test 15+ and 985-.

Of the 1014 who test positive, 1000 [98.62%] are true positives.

Your likelihood jumps from 50% to 98.62% of having the disease.

Suppose the initial likelihood of having the disease is 90%. That's reasonable for Brainder's.

Out of a population of 10000 such persons,

9000 have the disease, and will test 8991+ to 9-.

1000 don't have the disease, and will test 15+ and 985-.

Of the 9006 who test positive, 9000 [99.93%] are true positives.

Your likelihood jumps from 90% to 99.93% of having the disease.

But suppose they just picked you off the street and your initial likelihood of having the disease is .01% [generous estimate.]

Out of a population of 10,000,000 such persons,

1000 have the disease, and will test 999+ and 1-.

9,999,000 don't have the disease, and will test 149985+ and 9849015-.

Of the 150984 who test positive, 1000 [0.66%] are true positives.

Your likelihood inches up from .01% to .66% of having the disease.

That's right: .66%. Not 66%.

The reliability of such a test on the general population is basically nil.