Any statisticians here?

[Donny osmond]

I've been amused by "a simple question" that is apparently given to doctors to test their understanding of "basic statistics"...

The Question:
If a test to detect a disease whose prevalence is 1/1000 has a false positive rate of 5%, what is the chance that a person found to have a positive result actually has the disease?


Show your working, please!

[Puja]

I've been amused by "a simple question" that is apparently given to doctors to test their understanding of "basic statistics"...

The Question:
If a test to detect a disease whose prevalence is 1/1000 has a false positive rate of 5%, what is the chance that a person found to have a positive result actually has the disease?


Show your working, please!

My initial reaction was to assume that the false positive percentage was calculated over the total number of tests, which would lead to the false positives for 1000 tests being 50, meaning that the chances of a positive result means actually having the disease is 1/51.

However, that didn't pass the common sense check, because that sounded like a shit test for that disease, so a very brief google tells me false positives rates are calculated from the positive tests only, which would mean that the answer is 95% (or 19/20, if you prefer).

Is that right?

Puja

[Donny osmond]

I've been amused by "a simple question" that is apparently given to doctors to test their understanding of "basic statistics"...

The Question:
If a test to detect a disease whose prevalence is 1/1000 has a false positive rate of 5%, what is the chance that a person found to have a positive result actually has the disease?


Show your working, please!

My initial reaction was to assume that the false positive percentage was calculated over the total number of tests, which would lead to the false positives for 1000 tests being 50, meaning that the chances of a positive result means actually having the disease is 1/51.

However, that didn't pass the common sense check, because that sounded like a shit test for that disease, so a very brief google tells me false positives rates are calculated from the positive tests only, which would mean that the answer is 95% (or 19/20, if you prefer).

Is that right?

Puja

Exactly what I thought, and a lot of others, but no that's not right.

Your first instinct was closer, and actually gives - I think?? - the right answer, but I can't explain why.

[Big D]

I've been amused by "a simple question" that is apparently given to doctors to test their understanding of "basic statistics"...

The Question:
If a test to detect a disease whose prevalence is 1/1000 has a false positive rate of 5%, what is the chance that a person found to have a positive result actually has the disease?


Show your working, please!

My thoughts were it ends up being 1/51 like you say.

I asked co-pilot and it came up with using Baye's Theorem which gives the probability of 0.0196 which is 1/51.