# brain sizes: Einstein's and women's--jet

John Knight johnknight at usa.com
Mon Jul 22 02:10:26 EST 2002

```"Bob LeChevalier" <lojbab at lojban.org> wrote in message
news:31emju068qnvgii9eihtqp690ua5nij8q1 at 4ax.com...
> "John Knight" <johnknight at usa.com> wrote:
> >Is it at *all* possible for you to understand the VAST difference between
> >the following two statements?  I really doubt if it is, since you were
> >obviously in that 50% of American boys who couldn't understand it either:
>
> And your evidence for this mythical 50% is?
>
> >> >> Jet wrote:
> >> >> Do you have numbers that are less than zero for the percentage of
> >> >> students with correct answers, monkey boy?
> >
> >She misinterpreted this from the following:
> >> >ps--this "math problem" actually is about as simple as many of the
TIMSS
> >> >questions where less than zero percent of American girls got the
correct
>
> What part of "less than zero percent of American girls got the correct
> answer" did you NOT intend, and how does it make any sense, so matter how
> much you "adjust it for guesses"?
>

Let's try to break this down into real simple pieces so American 12th grade
girls may be able understand it.

If you have a red straw, a green straw, a blue straw, and a white straw, and
you ask a student to pick one at random, then if they pick it randomly, the
probability of picking the red one is 0.25, and the green one is 0.25, and
the blue one is 0.25, and the White one is 0.25.

If you put all four straws back in your hand and ask them to pick them
randomly again, the probability is the same thing again.  If you do it two
more times, then the overall probability of picking each color is 1.0:  a
red one = 1.0, a green on = 1.0, a blue one = 1.0, and a white one = 1.0.

This doesn't mean that this is exactly what you'll get on the first set--but
if you were to do this a million times, you would have 250,000 red, 250,000
green, 250,000 blue, and 250,000 white, IF the student actually picked the
straws at random.

But if instead you were to end up with 333,000 red, 228,000 green, 251,000
blue, and 186,000 white straws, then you would know that there was some sort
of bias in the student's choice of straws.  To be specific, the student was
79% more likely to select red than white, 10.1% more likely to select blue
than green, etc.

Let's say that the green straw represents the correct answer on H04.  Where
probability would say that you would have 250,000 green straws, some sort of
bias against green, and ONLY this bias, caused you to have only 228,000.
With a large enough sample size (which TIMSS definitely was) this *bias
against* green [read: against the correct answer] is the ONLY way this can
happen.  To pick 32,000 fewer green straws than predicted by probability,
you *must* have something preventing a random selection of straws [read:

What bias do American 12th grade girls have against so many correct answers?

John Knight

```