# brain sizes: Einstein's and women's

mat mats_trash at hotmail.com
Mon Jul 22 06:30:14 EST 2002

```>
> No, Mat, it's not, and if you'd have answered a TIMSS question this way, you
> would have been just as wrong as almost 100% of American girls were on some
> of these probability and statistics questions.
>
> The statement is that the probability is 1.0 that you'll get one answer
> correct if you just guess on four different questions with four multiple
> choice answers.  That's much different than you are "CERTAIN to get one

No, the limits of probability (0 and 1) are defined as certain that a
particular event will not occur or definitely will occur,
respectively.  If you flip a coin you have a probability of getting a
head of 0.5 and similarly for the other side (tails in the UK).  Thus
your probability of getting either a head OR a tails (which I hope
you'll agree is certain) = 0.5 + 0.5 = 1.  According to your analysis
if I flip a coin twice then I am guaranteed to get, say, a head which
I would hope you'll agree is damned idiotic.

>
> Obviously you were never taught probabilities and statistics.

Actually I have very good grades in math

> This is the
> most basic principle possible.

Maybe of your "probability theory" but not that of everyone else

> No, it doesn't happen that way EVERY time,

But that is what P(event)=1 means.

> but over a long series of questions and answers, it will eventually end up
> this way.

That is the relative frequency, and yes over a large sample, if people
guess randomly, then the correct answers should equal 25% since
answering each question is indepedent of any other.  However you
working in getting to that conclusion is totally wrong.

>
> If zero percent get a four part multiple choice question wrong, then they're
> scoring 25% lower than if they'd just guessed, in which event might conclude
> that there's a high probability that they were taught the wrong thing if
> everyone selected just one wrong answer.  The other extreme is if 50% get
> other three answers, then this *is* an indication that 50% understood the
> problem [50% guessed wrong, x = total percent who guessed, .25x = the total
> number who guessed correctly, .75x = the percent who guessed incorrectly, x
> = 66.67 percent = total guesses, .25x = 16.7 percent = percent who guessed
> correctly, and .75x = 50 percent].
>
> So at 50% correct, guesses don't influence the score,

What? you;ve just worked out that 16.7% guessed, how does this "not
influence the score"?

So you apply your 'analysis' when it suits the conclusions you wish to
draw,  given that it clearly leads to erroneous results at the
extremes. Lets say that 10% of questions were answered correctly, this
means that 90% guess incorrecly and thus, by your method, that 120% of
people guessed (90 = 0.75x where x is the number of guessers..)  God
knows how many people actually take the test!  So you see at any
percentage below 25, caluclating the 'correct guessers' from the
number of incorrect answers will surely lead to a number of guessers
greater than the number taking the test.  I hope you will conclude
that that is idiotic.  Given then that 22.8% (<25%) of american girls