Here is an attempt to explain how a correction factor works...
The first point to realize is that the obtained number of correct
answers is a mixture of cases, C (correct answers due to
knowledge) and L (correct answers due to lucky guessing).
The second point is the amount of correct answers that are
cases of L depends on the number of questions answered (A). In
the case of a pure guesser with 5 items per question, then L =
1/5*A.
Imagine 3 people with equivalent states of knowledge who employ
different guessing strategies on a 100-item test.
Person 1 answers 30 questions(A), knows the answers to 20 (C)
and guesses on 10. These are pure guesses, so L = 1/5 * 10 and
this person ends up with a Raw Score of 22.
Persons 2 and 3 have equivalent amounts of knowledge (C) but are
more likely to guess.
Person A C Guess L Raw Score
1 30 20 10 2 22
2 50 20 30 6 26
3 80 20 60 12 32
At this point, you can see there is an advantage to guessing.
The question is how to "correct" this score so there is no
advantage. There are lots of calculation techniques that will
accomplish this, and all center around an estimate of the number
of cases in the raw score that are L cases.
Here is one method...
For Person 1, we know a raw score of 22 is due to the mixture of
C + L. The number of wrong answers was 8. Wrong answers
represents the case where the testtaker was unlucky. There are
4 ways to be wrong on a 5-item question. (This is the
source of using a correction value of .25) We can calaculate the
chance of choosing a *wrong* item to estimate the number items
guessed at and then subtract that estimate of guesses from the
raw score.
Person Raw Score Wrong * (1/4) = Guesses Corrected
1 22 8 2 20
2 26 24 6 20
3 32 48 12 20
The actual value of the correction factor will depend upon your
calculation technique (are you estimating how a score will be
inflated by guessing or are you estimating how inflated is this
obtained score).
The more general point is that if ETS is using a technique for
correction that assumes guessing is truly blind then you improve
your chances by choosing answers when you have some knowledge.
Ken
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Kenneth M. Steele [EMAIL PROTECTED]
Dept. of Psychology
Appalachian State University
Boone, NC 28608
USA
