Re: What is the probability and significance of this chance encounter?

Before we get started, I want to point out an important double meaning
behind the word "significance".  While we can work out the rough
probability of this coincidence, which roughly translates to significance
in the statistical sense, significance can also be interpreted as "meaning"
and this you will have to figure out for yourself.

Ah, the joys of a posteriori coincidence.  There are several statistical
topics to address here, not least of which is the self fulfilling prophecy.
 If you want to find things in common, you will find things in common.  By
analogy, fortune tellers are able to work their amazing magic by providing
vague prophecies which true believers can bend to fit their experience.
Thus, there are remarkably few fortunes told which involve being hit by a
blue late model Buick at the intersection of Pine and James streets on June
15th, 2001.

Secondly, we can look at the non-intuitive nature of statistics.  I once
dated a woman with the same birthday as mine, which seems like quite a
coincidence and was terribly significant (at the time).  Of course, she was
the woman I broke up with to date my wife, so it wasn?t destiny.  I can
recall dating roughly 10 women in high school and college, so the
probability that I would have the same birthday as at least one of them is
p=1-(1-1/365)^10=0.027.  By convention this is statistically significant
(p<0.05), but in the grand scheme of things it really isn't all that
unlikely.  In my set of 10 close friends, assuming that each of them dated
roughly the same number of people that I did, the probability that at least
one of us dated a person with the same birthday is p=1-(1-.027)^10=0.24.
Thus, unless one of my buddies has also had this experience (informally,
none of them did) it's not all that unlikely.

Third, we can look at confounding variables: some things go together, like
high IQ and attending college, blonde hair and light eyes, and high IQ and
left-handedness.  The association is stronger for some of these patterns
than others: not many people familiar with the US population would dispute
that blonde hair and light eye color are associated, while the association
between handedness and IQ is weak enough that it?s still under debate
today. The strength of each association between variables also depends on
external factors.  The association between high IQ and college is better in
the ivy league than in most community colleges, because the ivy league is a
self selected group of people with high IQ.

So let's get started.  First let us look at physical characteristics.  Here
are some raw stats I pulled from the 1999 Statistical Abstract of the US:
80.3% of the population is Caucasian, and 46% of the 18-21 year old
Caucasian population is enrolled in college.  The 46% doesn't really
matter: you met her at college, therefore it was pretty darn likely that
she?d be enrolled in college, too.  Assuming that the racial composition of
your university mirrors the general US population there would be an 80.3%
chance that she's Caucasian.  Of course, this assumption is a big one: at
UC Berkeley the probability that she's caucasian is more like 50%, and at
some southern schools the probability would be even lower.

Given that she's Caucasian, the probability of blonde hair depends on age,
region of origin and peroxide.  In a Danish sample, 67% of adults were
blonde, although this is almost certainly one of the blondest populations
available.  So let's say that 20% of US Caucasian adults are blonde, or at
least pretend to be.  The correlation between blonde hair and light eye
color is well known, although the widely disseminated notion of strict
Mendelian inheritance for these traits is bogus.  While you mention
Blue-green (hazel) eye color, the fact is that light colored irides tend to
have yellow, blue and grey flecks.  Thus, the match in eye color you
perceive probably reflects a bias on your part where you want to see
similarities rather than differences.  As for "reflecting" colors you wear,
it's a common assertion in fashion circles re: light eyes, but I'm not
aware of any science to back it up.

Another factor which could tie together some of the similarities would be
if you guys are both swimmers.  The swim team tends to be composed of
academic overachievers with an athletic build and chlorine bleached hair.
However, you didn't mention aquatics so I won't pursue this.

Stats concerning other factors: the standard deviation of IQ is reportedly
around 16, so at 140ish you are approximately two standard deviations above
the mean.  This places you in the top 2.5% of the population.  However, it
also means that you are probably at a school for clever people, so the
match in IQ is less important than you think.  I've heard that SAT scores
correlate well with standard IQ test results, and your college almost
surely uses the SAT in admitting applicants.  Fact is, the match in subject
area is also strongly confounded with IQ: some subject areas attract people
with higher IQ as measured on the standard tests (math, physics, english
literature, not underwater basket weaving).

So here's my estimate of the probabilities that you would meet someone
similar to you in the traits listed, if these were the only traits you
looked at: 80% of the US is Caucasian, 20% of adult caucasians are fair
haired with light eyes, 10% of the population is lefty, 2.5% of the
population has an IQ over 140, and 0.5% of the US population has a chemical
dependency (so given 2 parents, ~1% of kids have a parent with a chemical
dependency.)  Multiplying out, I get 4X10^-6 (or 4 in a million), providing
that these traits are independent.  Pretty good, huh?  Well, it all depends
on how many other traits you compared before you discovered these 5.  Do
you share a birthday?  Do you both loathe macaroni and cheese?  Are you
both big fans of Michael Jordan?  My point is that you could probably find
an equivalent match of 5 relatively frequent traits with virtually anyone
(Your dad is a birdwatcher, too?!) to yield a similarly biased probability
estimate.

As an aside, I've got a high IQ (probably over 140), am right handed with
ambidextrous ability in pool, tennis, and racquetball, don't really have an
athletic build anymore, if ever, have sandy blonde hair and blue green eyes
with yellow rims around the pupil (which my sister assures me reflect blue
and green shirts magnificently), and had an opposite sex great grandparent
with a chemical dependency.  Even more astonishingly, I work at a
university and I'm the oldest child of two.  See my point?

Anyhow, as I mentioned at the beginning, even if this coincidence isn't
statistically significant, there are other meanings to significant...

	Chris
	peterpan@mbt.washington.edu