brain sizes: Einstein's and women's
lojbab at lojban.org
Wed Jul 17 03:22:30 EST 2002
"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.
But the assumption becomes totally meaningless if in fact they know
SOMETHING. If 100% of them know something, but not enough to solve the
problem, then it is quite plausible that 100% of them will get the answer
wrong. Thus someone knowing Newtonian physics perfectly will get the wrong
answer on a question that uses special relativity theory. A good test
designer will know that the Newtonian approximation is a likely error, and
will include that answer among the incorrect alternatives.
>No algebra. No calculus. A bit of probability theory, and you already know
>that 25% of all students will get the correct answer if they only *guess* on
>a four part multiple choice question.
But you have no evidence that any kid "guessed" on any problem.
>Now here's the hard part:
>Question H04 on TIMSS had four multiple choice answers, so you would think
>that no country or age group or race or sex would answer less than 25% of
>them correct, right?
Wrong. I would think that if the question were difficult and well designed,
that this would be quite possible.
>How do you think that's possible?
>You can probably figure this out with no knowledge of algebra or calculus,
>and you already know all the probability theory that might be needed, so
>what is your explanation?
I've given an explanation, and mine explains how on question D12, both boys
and girls in the US scored less than 17% and South Africans scored only 6.4%
correct. You can look at the breakdown of the answers and see that the kids
did NOT guess randomly; they intentionally selected particular answers, which
were the wrong ones.
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