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Thursday, October 8. 2009

Fallacies of the Week: A quiz for ya

"We have a test for a rare disease (we’ll call it Jones Syndrome), and the test is 99% accurate, but it returns a false positive in 1% of those tested (that is, 1% of the time the test returns a positive, the disease is not present). If I test positive, what is the probability that I have Jones Syndrome?"


It's not a trick question, it's a question of simple logic - and that's why it's so easy to fool juries with this sort of thing.


OK, we'll add this data:


"How prevalent is Jones Syndrome, that is, what is the probability of my having it, irrespective of any test result? We’ll say that 1 in 10000 have Jones Syndrome, so your untested probability of having Jones Syndrome is 0.01%, or 0.0001."


Answer is below the fold.  Explanation at Right Wing Prof

Odds are 0.0989%, ie less than one tenth of 1% that I have the disease.
Posted by The Barrister in Fallacies and Logic, Our Essays at 10:19 | Comments (13) | Trackbacks (0)

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Given that it is a rare desease, i.e., it doesn't exist, I would say that that there is zero probabilty I have Jones Syndrome.

There's a missing bit of data: the prior probability that I have the disease. If everyone had Jones syndrome the probabilities would need to be revised accordingly.
#1 chuck on 2009-10-08 11:24 (Reply)
I watched a video a couple of weeks ago about this. Sorry I can't find it now but will try again later today. IIRC, it was a paper presented at a conference and it well worth the time.
#2 Retread on 2009-10-08 12:27 (Reply)
I know, I know... "ALBATROSS"!!!! Did I get it right?

You know, you could just have easily copied the full question, including the vital part:

"How prevalent is Jones Syndrome, that is, what is the probability of my having it, irrespective of any test result? We’ll say that 1 in 10000 have Jones Syndrome, so the probability of having Jones Syndrome is 0.01%, or 0.0001."

There I was spending 45 extra seconds (granted far less time than it takes to post this note, but wth) constipating on "wait a minute, did I read this right?", thrown off by the "It's not a trick question, it's a question of simple logic". Bet you're all full and satisfied with yourself. How clever you are. But of course, your purpose (and to some extent, the original author's) was to make a self-satisfying point. Actually, you had no quiz for us at all, since the answer as posted was undefined. Ruddy bastards.

Maybe I think 83% of people who pose misleading questions like this are annoying assholes. Upon later reflection, I find that I was wrong (e.g. false positive) 17% of the time. What are the odds that you are an annoying asshole? There, answer me that...it's not a trick question....
#3 KRW on 2009-10-08 13:02 (Reply)
What are the odds that we are annoying a'holes? Give 10 billion websites...
Heck, it was just to make a good statistical point, I think.
OK, I will add the prevalence data to the post!
#3.1 Bird Dog on 2009-10-08 13:08 (Reply)
Yeah, well maybe my "e.g." should be "i.e.". There, dammit, I'm human too. Well maybe just for the moment...
#3.1.1 KRW on 2009-10-08 13:21 (Reply)
"e.g" means an example follows and "i.e." means a clarification: e.g., I use at is to explain myslef, i.e. to use better words than I did the first time.
There's some high-falutin' Latin for each of them, but hey, the Romans are dead now.
#3.1.1.1 Geoff on 2009-10-08 16:20 (Reply)
The proper translations are these:

e.g. or "exempli gratia" = "for example"

i.e., or "id est" = "that is"
#3.1.1.2 ffarkle (Link) on 2009-10-08 16:37 (Reply)
The probability of Jones Syndrome in any one person - in the entire population - who takes the test and receives a true positive is, in fact, less than 1%.

But, the probability of Jones Syndrome in any person - who actually takes the test - and receives a true positive result is 99%.

Those are two very different questions. You asked the second and answered the first.
#4 Homer Jones on 2009-10-08 14:22 (Reply)
Uh, the "chance" of a person with a true positive having the disease is 100%. If they didn't have the disease they could not have a TRUE positive. I am missing the difference between your two questions.
#4.1 Paul (Link) on 2009-10-08 20:15 (Reply)
Howdy Homer
I kinda thought that was it and I find myself agreeing with you. A swat down could follow any moment from someone who understands stats better than I do.
BTW, annoying a*holes are how we get irritable bowel syndrome.
#5 Geoff on 2009-10-08 15:00 (Reply)
What an exercise. I read this knowing I could not get the answer as I am not good at this kind of thing, but I gave it a try. In less than thirty seconds Homer's remark flashed across my mind, and I instantly dismissed it knowing I had to be wrong. Then I moved on to the next post. I did eliminate the gratuitous garbage but still did not trust my smarter-than-I intuition.

I once talked with a guy who hired out to large companies to troubleshoot their computer systems. Arduous work at times, but he was so successful that he could not keep up with the demand for his services. I asked him about sequential thinking and the kind of logic required for the work, and he said this: "Don't tell anyone, but it's mostly intuition."
`
#6 Meta on 2009-10-08 18:32 (Reply)
The method used to calculate these things is called Bayesian statistics. It's related to the weak syllogism, which goes something like this:

All men are mortal.
Socrates is mortal.
Therefore, it is more likely that Socrates is a man.

Two things to note about the weak syllogism: it's backwards from the strong form and it is closer to how people reason about things in real life.
#7 chuck on 2009-10-08 23:57 (Reply)
Retread, I saw the viddy too. I think it was a TED talk but I haven't gone back to search for it.
I ... am lazy. 100% probability of sloth.
#8 BlogDog (Link) on 2009-10-09 09:10 (Reply)

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