# [Rasch] Testing uni-dimensionality: need references

Steven L. Kramer skramer1958 at verizon.net
Fri Dec 14 03:11:06 EST 2007

```In my previous email ("Rasch applied rashly") I asked, in essence,  "What is to be done?"

Reflectioning on this question, it might be useful as a first step to test my claim that there is socially-constructed--and in fact curriclum-constructed--"unidimensionality" in mathematics ability.  Specifically, I can see whether two different high school curricula construct two different (but each internally consistent) uni-dimensional versions of "math ability".

Fortunately, I have a data set that might be used to address this question.  Unfortunately, I need help figuring out how to do the analysis.

For my dissertation, I tested four cohorts of students at a single high school.  The earlier cohort used a tradional curriculum; the later cohorts used an integrated math curriculum called "IMP".  In eleventh grade, students took a test with items that favored IMP-style teaching, and a test with items that favored traditional-style teaching.  In twelfth grade, many of these same students took released NAEP items.

I have data from over 500 students, split roughly evenly between the two curricula.

Research questions might be:
1. Within each curriculum group, is the full set of test questions "uni-dimensional"?  If not, what dimensions are there?

2. Are there demonstrable differences between the dimensions and ordering of item difficulties within the dimensions, depending on curriculum?

3. If we assume unidimensionality, do we get very different item ordering and difficulties, depending on the curriculum?

4. If I simulate adaptive testing (i.e. pretend each student takes only part of the test, even though I have complete data for most students), do students from curriculum A systematically get placed as lower ability when using item difficulties developed under the curriculum B than they do when using item difficulties developed under curriculum A?  Do the results differ depending on whether students start with the "easy" vs. the "difficult" items in the simulated adaptive test?

But I don't know how to use Rasch methods to analyze dimensionality, or to rigorously test it.  I have used ConQuest to develop Rasch scores, but not to analyze something like this.  Can anyone lead me to references that might help me do this study?

Alternatively:  I'm short on free time, so I could provide someone else the data set, if they wanted to analyze it.  Any takers?

Steve Kramer
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