"mat" <mats_trash at hotmail.com> wrote in message
news:43525ce3.0207180723.642fd8f9 at posting.google.com...
> >
> > 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.
>> So you are certain to get a correct answer if you guess on four
> questions? and you claim to understand probability?!
>> P(one questions correct given 4 choices and if guessing) = 0.25
> P(two questions correct) = 0.25 x 0.25 = 0.0625
> P(three questions correct) = 0.25 x 0.25 x 0.25 = 0.015625
> .
> .
> .
> P(n questions correct) = 0.25^n
>> its essentially the same as asking the probability of getting a one
> (or any specified number) on sequential throws of a dice. Overall you
> expect to get 1/6 (the relative frequency), but getting four ones in a
> row is equal to 1/(6^4)
>
Nice try, "mat", but you're way off. Thanks for giving it a try, though.
P1 = P2 = P3 = P4 = 0.25
In other words, the probability of getting one question right by guessing at
a 4 part multiple choice question is 0.25
But to figure the probability of getting four of the same questions right,
not the *same* answer on each question, but the *correct* answer, you must
add them up, which is P1 + P2 + P3 + P4 = 1.0
>> Your assumptions are also further invalid in that you calculate the
> number 'guessed correctly' by assuming that all who got it wrong
> 'guessed incorrectly'. Not only is this illogical in that you are
> characterising one group of students on the basis of another group but
> it also leads to strange conclusions such as if 70% answer correctly,
> 10 of this 70% of this is accounted for by correct guesses, whereas if
> 100% answer correctly no-one guessed, since there are no incorrect
> answers.
>
No. The assumption is valid, particularly since the percent correct is
lower than if they had just all guessed, and when all of the questions are
answered. It's true that some of the questions might reflect some bad
instruction in the classroom, but when the responses are spread across the
spectrum like they were, and still the score was lower than pure guesses,
then the only conclusion can be that they guessed on most of the questions.
> > 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. http://christianparty.net/timssh04.htmshows
> > that American girls answered only 22.8% of them correct.
> >
> > They scored 2.2% lower than if they'd just guessed.
>> Which should tell you something about your analysis rather than
> something about the intelligence of girls
>> You are doing much too basic an analysis. For example such a figure
> of 22.8% may well gloss over the fact that a certain proportion scored
> very highly while others knew very little. Collating all the scores
> into one figure is just plain stupid.
The standard deviations show this not to be the case, or at least that it
can't affect the curve by that much. And what is it that would cause such
lumps in the curve? Even if you compare each sex by race, there's a
distinct separation between the curves.
However, your last sentence says much: about your knowledge, but not about
the scores, nor the test.
John Knight
