"mat" <mats_trash at hotmail.com> wrote in message
news:43525ce3.0207190255.4ebf0ab1 at posting.google.com...
> > 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
> >
>> It is quite amusing how you spount this anti-"everything other than
> me" dogma, citing test results, when you yourself are apparently akin
> to two short planks.
>> Your math suggests that I am CERTAIN to get one answer correct if I
> guess on four multiple choice questions (probability of 1). Can you
> not see that this is illogical just on the basis of common sense?
> thats like saying if I throw a dice six times I'm sure to throw a six,
> which of course is totally dumb
>
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
answer correct".
Obviously you were never taught probabilities and statistics. This is the
most basic principle possible. No, it doesn't happen that way EVERY time,
but over a long series of questions and answers, it will eventually end up
this way.
>>> > >
> > > 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.
>> You still have yet to address the conclusion that if 100% answer
> correctly no-one guessed and if 0% answer correctly then something
> very strange happens as the population taking the test suddenly
> increases by a third but their papers are somehow lost. As you might
> see from working with the latter case, your analysis does not hold.
It's not clear what you're saying, but the last part of your statement means
that it's obviously wrong--and it's ceretainly not consistent with the
original statement. Consider the two extremes:
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
the answer correct, and the rest of the answers are spread evenly over the
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, and you don't have to
worry that "something very strange happens as the population taking the test
suddenly increases by a third but their papers are somehow lost".
Did that address your point?
John Knight
