>> 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)
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.
> 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.htm shows
> 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.
