# [Rasch] Unidimensionality (A different follow up)

demott at aol.com demott at aol.com
Tue May 13 05:02:26 EST 2008

```This is a great discussion, both from a philosophical view and from a practical view.
Here is what I would say: Of course the Rasch Model is wrong, in that no data will ever fit it perfectly. So are other models. The point is, is?Rasch useful. Does it help us in our understanding. The answer is yes, it helps me!

Now here is an interesting paradox:
In objectives-referenced testing (or standards-referenced testing) we compute how students do on each standard. We may then make some decision on whether thy have "mastered" the skills described. We also look at the total test score, e.g. Mathematics. We report how well the students do on that score domain. We may then say that a student has or has not "passed" the test. For both these purposes we may use the Rasch model (or 3 param IRT, or Clasical Test Theory, or even some Decision Theory model).

We treat the total test score as something meaningful. We treat the score on each objective as something meaningful.
Clearly the score on objective 1 means something different from the score on objective 2 -- otherwise why would we report them separately? Yet the scores on objectives 1 thru n add up to the total test score -- which we also report! Recall that each subscore can be shown to measure a more or less independent skill. So we are adding apples, oranges, bananas, grapes, plums, pears, etc. to get a "fruit" score. We do so with aplomb (please excuse the pun).

I guess this is akin to the fact that we may measure the height, length, and width of an object to infer its density, given its mass. In this case, the unifying entity is the object itself. I suppose the underlying entity in the testing scenario is the person. It has been noted that score on one reading test closely predicts the score on most other reading tests, for a given individual. In fact, the score on a reading test even predicts?the score on a mathematics test rather well. Yet we don't really believe the skills underlying are all the same.

In spite of clear paradoxes, we proceed.

DM

David E. W. Mott, Ph.D.
Tests for Higher Standards &
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