[Rasch] How many anchor items do I need

RISA KRAMER skramer1958 at verizon.net
Tue Jul 10 22:02:48 EST 2007

Dear Rasch colleagues,

I'm trying to determine how many anchor items one needs to equate two subject-matter tests.  I estimated 20, or 25% of total test, whichever is greater, based on a rule-of-thumb they used at ETS and on one article that found on Florida's FCAT that 15 or 20 anchor items worked as well as 30.

(Note: I'm thinking here about how one would create a pool of items for the U.S. NCLB to form a de-facto standard of "what should be taught," with the pool of items forming a portion (25%) of each state's test.  I realize the equating won't be perfect, but the goal is a good rough measure. Here is what I'm saying about the idea currently:
It should also be noted that it is impossible to precisley equate two tests designed to different standards.  Strictly speaking, two students' scores can  be directly compared only if they are being tested on the same thing.  If State A emphasizes statistics in eighth grade math and 
State B emphasizes geometry, it is not precisely possible to compare the math knowledge of students from the two states. Who is the more "knowledgeable" student: the one good at statistics or the one good at geometry?  Thus,equated  math (or reading) scores of State A and State B will be a rough reflection of how much math (reading) students know.  If in a particular state students who get a lot of state test items correct also tend to get a lot of the more difficult "common core" items correct, then high scores on the state test will equate to very high scores on the common scale.  If in a particular state many students tend to get many state test items correct while missing most of the"common core" items, then high scores on the state test will equate to somewhat lower scores on the common scale.)

So:  I know the equating will be imperfect.  
But am I correct that 20 items are sufficient for this imperfect equating?

Steve Kramer
Math Science Partnership of Greater Philadelphia
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