So while i was waiting at the bus stop this morning i happened to read a sign on another bus that said:

One out of three kids who smoke will die prematurely.

Now, after that bus left my mind started churning away on that statement.  What's interesting is that no matter how hard i tried i kept coming up with some extremely bizarre conclusions to be drawn from their statement.  Specifically here's how i thought about it:

1. Dying is sort of like IQ, you have some average that you consider "normal" and then you have those who are under it and those who are over it.
2. So, you can twist the original claim a little to say "one in three kids who smokes will have a low IQ".
3. But, then that would be to me that "two in three kids who smoke do not have a low IQ".  i.e. "two out of three kids who smoke have an average or above average IQ".
4. Now, the average for IQ is 100, but that doesn't necessarily mean that there are equal number of people with an IQ over 100 as there are below 100.   You could have 1 person with a 150 IQ and 50 people with a 99 IQ and get that average.  But, say for the sake of argument it's somewhat close to around a 50/50 split for people above/below (+/- a few points or whatnot).
5. Now, what i can see is that there is a 66% chance if you're a smoker of having an average or above average IQ.
6. By smoking you've raised your chances far above what the norm would be, and you're actually in an elite group that has fooled people into thinking smoking is bad when it is in fact good.
7. Now, if we step back away from IQ and to lifetime expectancy, we can see that two out of three smokers will live up to or beyond an expected age of maturity.
8. Not bad at all, and for only a few bucks a day it seems like a reasonable tradeoff!
A perfect series of logical steps leading to an undeniable conclusions.   *snort*

Now, obviously my bleary hungover early saturday logic was rife with logical fallacies, and there are statisticians (as well as other rational minds) out there who are having trouble holding down their morning constitution after reading that.  It's also funny to me given that i was a math major and that learning and understanding how to reason about these things was something i have been trained to do since high school.  And yet, even with all that knowledge and experience it is so simple to make incorrect inferences and to let statistics cause you to think something that simply isn't the case.  I joke and make fun of people who do it when the media and politicians try to twist around their meaning to make you think something that isn't true, but in the end, i am just as susceptible.    What makes it so easy to get tripped up over these very simple scenarios we are presented with?  I really don't know.  My gut feeling tells me that it comes down to there being many vital, but easily misused, logical and mathematical tools out there and the differences between them are often to subtle to keep track of when your brain is moving along at 80 tps (thoughts per second).  You mistake what averages are supposed to mean.  Analogies are formed even when they are invalid for some reason.  All it takes is one mistake and the whole thign comes crashing down (and worse yet is that there are so many easy mistake to be made that in the end it's almost certain that something wrong will have happened and the conclusion is suspect).  However i know little about this and maybe there are some cognitive scientists out there who can shed some light as to why and how this happens.