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Any statisticians here?
Posted: Mon Aug 26, 2024 10:48 pm
by 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!
Re: Any statisticians here?
Posted: Tue Aug 27, 2024 1:02 am
by Puja
Donny osmond wrote: ↑Mon Aug 26, 2024 10:48 pm
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
Re: Any statisticians here?
Posted: Tue Aug 27, 2024 6:21 am
by Donny osmond
Puja wrote: ↑Tue Aug 27, 2024 1:02 am
Donny osmond wrote: ↑Mon Aug 26, 2024 10:48 pm
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.
Re: Any statisticians here?
Posted: Fri Oct 18, 2024 12:01 pm
by Big D
Donny osmond wrote: ↑Mon Aug 26, 2024 10:48 pm
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.
Re: Any statisticians here?
Posted: Mon Nov 25, 2024 9:35 pm
by paddy no 11
I have looked at your answers
Initial thoughts are prevalence is irrelevant and he's 95% likely to have it?
Re: Any statisticians here?
Posted: Mon Nov 25, 2024 9:39 pm
by paddy no 11
Donny osmond wrote: ↑Mon Aug 26, 2024 10:48 pm
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!
I better quote somewhere or the answer above will never be seen