# brain sizes: Einstein's and women's

Bob LeChevalier lojbab at lojban.org
Wed Jul 17 16:21:17 EST 2002

```"John Knight" <johnknight at usa.com> wrote:
>> Bob LeChevalier wrote:
>> > "John Knight" <johnknight at usa.com> wrote:
>> > >Believe me, Parse, you don't need algebra or calculus to calculate the
>> > >statistical average for American girls in TIMSS math.  Even adjusting for
>> > >guesses doesn't require anything but some very basic probability theory.
>> > >
>> > >It's as simple as this:
>> > >
>> > >If you're asked a question which has four multiple choice answers, and you
>> > >haven't got a clue what the answer is, what is the probability of getting a
>> > >correct answer?  Since you have once chance in four of getting the right
>> > >answer, your probability is 0.25.  If you guess on two questions, your
>> > >probability is .5, and three it's .75, and four, it's 1.0.
>> > >
>> > >In other words, over the long run, or over millions of test takers, guessing
>> > >on such a question will yield 25% correct answers, or conversely, every
>> > >fourth answer will be correct.
>> >
>> > This makes the assumption that those who know nothing guess randomly. IN
>> > reality, we don't know that people guess randomly when faced with a test
>> > question they do not understand.  Indeed, we know that they do not.
>> >
>
>Wrong.  Dead wrong.  You could make that argument about one question, but
>when the pattern is repeated over and over again, then you can detect a
>pattern:  American girls scored lower on many questions than if they'd just
>guessed because they didn't have a clue about what the answer was.  Many of
>these questions had zero misses [read: 0% failed to provide an answer at
>all], which means you're nuts to even hint that "Indeed, we know that they
>do not"  "guess randomly".
>
>The ONLY time you could apply that argument is when a large percentage of
>them answered correctly, but even then, if 0% failed to respond at all, then
>some of them HAD to guess.

You have no logical basis to conclude that *any* kid guessed on *any*
question of TIMSS.  There is *no* statistical basis on which to conclude
same.  The number not responding is totally irrelevant.

The best evidence for guessing (which would not prove it, but it would be
evidence) would be if all of the answers, correct and incorrect, were chosen
with equal frequency within the expected margins to support a "random"
selection.  This would among other things require one to know how many girls
selected each answer, and those numbers are not published - only the numbers
for all American kids.  A couple of questions have approximately equal
distribution among the 4 answers, but not many.  And guessing does not
explain instances where more than half of each gender got the question
correct, nor D12 where fewer than 17% got the question correct.

>> Then the article makes the shockingly stupid conclusion that NONE of the
>> girls who got the answer right understood the problem!
>
>If guessing on a multiple choice question would yield 25% correct, but
>American girls only got 5% correct, then how would YOU calculate how many of
>them understood the problem?

You can't.  There is no data available to make such a calculation, and since
TIMSS was not trying to measure "understanding the problem", there is no
reason to fault them for not providing such data (Even if we had a clear
definition of what you mean by "understood the problem")

>> Isn't it odd that someone who is harping on math ability doesn't seem to
>> realize that 17 and 6 are both lower than 25? :)
>
>What's your point, J?  Who exactly do you think made the point that getting
>17% correct on a four part multiple guess problem is a lower score than if
>everyone just guessed?
>
>What part of that don't you understand (other than the typical and
>infinitely STUPID statement by lojbab that no students guessed)?

You haven't explained how 17% or 6% correct is even possible on a multiple
choice problem given the assumptions you made about guessing. This disproves
your assumptions about guessing.

lojbab

```

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