Re: IQ and Testosterone?
Stephen Barnard (steve@megafauna.com)
Wed, 04 Sep 1996 07:05:15 0800
Larry Caldwell wrote:
>
> In article <322B7F01.F70@megafauna.com>,
> Stephen Barnard <steve@megafauna.com> wrote:
>
> > Statistics show that male teenagers are far more likely to have automobile
> > accidents than, for example, women over the age of forty. Therefore insurance
> > companies charge *much* more to insure a male teenager than they charge to
> > insure his mother. They are making a perfectly understandable judgement that
> > the teenager is more likely to be an unsafe driver than is his mother. This is
> > what actuarial science is all about. It extends to every kind of insurance 
> > life, medical, accident, whatever. The result is that actions are taken with
> > respect to individuals based on statistical information.
>
> You did just fine until your last sentence. Actions are taken with respect
> to a *population* based on statistical information.
Tell that to the 16yearold who is trying to get insurance for the first time. When
he finds out that he has to pay a fortune he will have the definite impression that
someone making an inference about him as an individual based on statistical
information.
> Insurance companies are
> quite aware that individual variation exists. That's why they base rates
> on driving record, and require medical exams before writing life insurance.
> If you have cystic fibrosis, nobody is going to write your life insurance
> policy no matter what your stats say.
Here you are "loading the dice." A probabilistic statement about an individual (for
example, that his expected lifespan is 72 years) assumes that *no other information*
is available beyond the information that the individual is a member of a particular
population (not a sample). As soon as additional information is available that can
be used modify the statement. (Bayes Law is often useful in that case.)
>
> Another example is group medical insurance. There is a minimum group size
> at which point the risk becomes unacceptably large. Actuaries understand
> this very well.
>
Of course they do. But given an adequate sample the insurance companies go right
ahead and charge certain people certain premiums.
> > There are many other arenas in which more or less the same thing goes on 
> > compiling mailing lists for political contributions, targeted mass mailing,
> > focus groups, etc.
>
> To be sure, statistics can be useful. They just don't apply to individuals.
>
I didn't say that statistics apply to individuals. I said that statistics allow one
to make wellfounded probabilistic statements about individuals. There's a
difference.
> If you have studied statistics you have doubtless encountered methods of
> calculating sample variance. The existance of these formulas leads many
> people to assume that they are valid in all circumstances. In fact,
> statistics textbooks are careful to point out that sample distribution
> is only predictable if your sampling technique is invariant. No matter
> how much data you have about a population, it does not extend to an
> unsampled individual outside that population.
The purpose of a sample is to representative of a much larger population.
Information deduced from the sample is extrapolated to the population, and by
extension to members of the population. If what you are saying were true  that
statistical information were only valid over the sample  then political pollsters
would have to survey every single voter to draw a conclusion.
> You don't even know if
> their response will fall within the previously tested range.
>
>  Larry
I well aware of the concepts of probability and statistics. I've published papers on
topics such as Monte Carlo algorithms and Markov Random Fields. It is perfectly
acceptable to make probabilistic statements about individuals. In one sense, that's
the whole point of statistics, or at least one the major motivations.
Steve Barnard
