Another hoary old chestnut but fun maybe for those to whom it is novel:
A test of a disease presents 5% false positives. The disease strikes 1/1000 of the population. People are tested at random without any evidence of predisposition or prior symptoms. A patient's test is positive. What is the chance he/she has the disease?
Quote from: En_Route on May 08, 2012, 08:19:54 PM
Another hoary old chestnut but fun maybe for those to whom it is novel:
A test of a disease presents 5% false positives. The disease strikes 1/1000 of the population. People are tested at random without any evidence of predisposition or prior symptoms. A patient's test is positive. What is the chance he/she has the disease?
95%. The prevalence of the disease in the population is irrelevant as this is post test.
If one were to take the same figures but say how many false positive per million of the population one would expect 1,000 cases but you'll have 1,050 as there are 5% false positives in the test to you'll get the 1,000 + 0.05*1000
Quote from: En_Route on May 08, 2012, 08:19:54 PM
Another hoary old chestnut but fun maybe for those to whom it is novel:
A test of a disease presents 5% false positives. The disease strikes 1/1000 of the population. People are tested at random without any evidence of predisposition or prior symptoms. A patient's test is positive. What is the chance he/she has the disease?
95%?
ETA: ooooh, Tank thought the same thing I did, so it MUST be right. Who's logical? Who's logical? A-li, A-li, A-li!!!! ;D
Quote from: Ali on May 08, 2012, 08:44:23 PM
Quote from: En_Route on May 08, 2012, 08:19:54 PM
Another hoary old chestnut but fun maybe for those to whom it is novel:
A test of a disease presents 5% false positives. The disease strikes 1/1000 of the population. People are tested at random without any evidence of predisposition or prior symptoms. A patient's test is positive. What is the chance he/she has the disease?
95%?
ETA: ooooh, Tank thought the same thing I did, so it MUST be right. Who's logical? Who's logical? A-li, A-li, A-li!!!! ;D
Don't count your non-infected chickens just yet my dear.
Quote from: En_Route on May 08, 2012, 08:19:54 PM
Another hoary old chestnut but fun maybe for those to whom it is novel:
A test of a disease presents 5% false positives. The disease strikes 1/1000 of the population. People are tested at random without any evidence of predisposition or prior symptoms. A patient's test is positive. What is the chance he/she has the disease?
"5% false positives"
5% of what?
a) 5% of all the positive results
b) 5% of all the people tested?
if b then 5% of 1000 people = 50 people however only 1 will have he disease
1 is 2% of 50
so a positive result gives a person a 2% chance of having the disease.
Trick question. The chances are 1/1000 as that is the rate provided for actually having the disease independent of testing.
Minor edit: Stevil's way makes sense too, really, depending on what the question is actually aimed at.
Quote from: Stevil on May 08, 2012, 10:39:16 PM
Quote from: En_Route on May 08, 2012, 08:19:54 PM
Another hoary old chestnut but fun maybe for those to whom it is novel:
A test of a disease presents 5% false positives. The disease strikes 1/1000 of the population. People are tested at random without any evidence of predisposition or prior symptoms. A patient's test is positive. What is the chance he/she has the disease?
"5% false positives"
5% of what?
a) 5% of all the positive results
b) 5% of all the people tested?
if b then 5% of 1000 people = 50 people however only 1 will have he disease
1 is 2% of 50
so a positive result gives a person a 2% chance of having the disease.
False positive rates are always expressed by reference to the number of tests. So 2% it is. What is interesting in an alarming but not very surprising way is that a lot of doctors got the answer wrong.
Quote from: Stevil on May 08, 2012, 10:39:16 PM
Quote from: En_Route on May 08, 2012, 08:19:54 PM
Another hoary old chestnut but fun maybe for those to whom it is novel:
A test of a disease presents 5% false positives. The disease strikes 1/1000 of the population. People are tested at random without any evidence of predisposition or prior symptoms. A patient's test is positive. What is the chance he/she has the disease?
"5% false positives"
5% of what?
a) 5% of all the positive results
b) 5% of all the people tested?
if b then 5% of 1000 people = 50 people however only 1 will have he disease
1 is 2% of 50
so a positive result gives a person a 2% chance of having the disease.
*Cocks head to the side like a spaniel. Thinks a long time. Re-reads explanation 3x* Nope, still don't understand why it's 5% of 1000 and only one will have the disease. *Shakes head. Goes back to playing Draw Something*
I think I get this one! Do I get a cookie? ;D
^ Your choice. 1 in 50 cookies contain strong laxatives and there are 31 cookies on the plate. All cookies were baked by a man with long hair.
...So there is a one in one chance of there being hair in it.
:( This reward does not feel very rewarding all of a sudden...
How's the man's hygiene?
Quote from: DeterminedJuliet on May 09, 2012, 02:21:16 PM
:( This reward does not feel very rewarding all of a sudden...
How's the man's hygiene?
He has a bath every month even if he doesn't need it.
Also, some dreads which he packs in a plastic bag before bathing, yes? :D
Errmmm. I may just purchase some cookies.
In the cookie emporium, the proprietor informs you that his prices are higher than average. You expostulate and announce your intention of searching farther afield. No point my dear he says in a dangerously patronising fashion; the same is true of 90% of all cookie emporiums. Could this be true?
*weeps helplessly*
Of course it could be true.
Even if you don't play with statistics more than you absolutely have to, 9 places have cookies at 10 dollars a pop. One place has cookies at 9 dollars a pop. Assuming prices do not get rounded up or down, the average is 9.90, meaning ninety percent of cookie joints actually sell for above average.