Thank you soo much! I figured out what I was doing wrong... I was using the values from auxiliary table 3 all the time which depends on a=1 so that is why my values were different.. Now I'm ready for the exam :D thx!
Hey guys, I have a question regarding Q12 from the 2014 exam. It says the following (roughly translated from the dutch exam:
Three math tests each consist of 3 items and comply with the Rasch model. However, the tests differ with regard to the item parameters.
Test I has an item with a = 1 and b = -1, an item with a = 1 and b = 0, and an item with a = 1 and b = +1.
Test II has three items with each a = 1, and b = 0.
Test III has three items, each with a = 0.50 and b =1.
Question: which test provides the most information of math ability θ of people that actually have an θ value of 1? (nB: exp (O) = 1, exp (0.5): 1.65, exp (1) = 2.72, exp (2) = I .39) .
Apparently the answer is B (Test II), but I have no clue how to compute this. I thought that the correct answer would be Test III, as this one has the most items with a difficulty of 1, which matches the θ of 1.
Anyone know how to get to this answer? Thank you in advance!
You have to compute the test information. The test information is the sum of all the item information. It depends on the difficulty level of the items (b) and their discrimination ability (a). A lower a means a worse discrimination ability. Thus, some people end up passing or failing that item by pure chance; it doesn't measure skill that reliably. Now to the computational part. Refer to page 41 of the course manual.
For test 2 we have a=1 and b=0. Calculating the probability of success on that item with the table, we get P=0.73. Plugging it in into the test information formula, we get a^2 P(1-P) = 1 * 0.73 * 0.27 = 0.1971. 0.1971*3 = 0.5913. Your test information is thus 0.59 for test 2.
For test 3 we have a=0.5 and b=1 . That yields you a P=0.5 (because theta equals difficulty).
For the item information formula we get 0.5^2 *0.5^2 = 0.5^4 = 0.0625.
Test information is thus 3*0.0625=0.1875.
-> Test 2 yields more information