# [Rasch] Explaining diferences in scores and measures

Stephen Humphry shumphry at cyllene.uwa.edu.au
Sat Mar 8 14:36:27 EST 2008

```Andres, I think I misunderstood something. I think you are saying the
expected score (raw score corresonding with the cut-score location) is
21, with a maximum of 24. If they are all dichotomous, the 23rd item
is the second highest. Is that correct?

If so, the principle applies to your second case, but in the opposite
direction -- the student more opportunities to respond incorrectly to
easy items (below location) than response correctly to difficult items
(above cut-score location) if I understand you correctly.

If you specified exactly the same ability location as the cut-score
and added a number of items near and above that location, the expected
score would increase.

The non-linear relationship between the raw score and ability estimate
is also very relevant at the extremes of the range of
scores/abilities. Again, if you add items near and above the
cut-score, the curve would become steeper in the region of the cut
score.

Regards,

Steve

Quoting Burga León  Andrés  Alberto <21781 at upch.edu.pe>:

> Hello to everybody on the list:
>
> I hope you could helop me explaining the situation I have aboput the
>  diferences in measures and scores.
>
> I'm working with two diferent test (math and reading), made of 24
> items. The objective is to use the mesure in order to calsify each
> student into a proficiency level. We have two cut-point for each
> test ( so tree proficiency levels). If a student have a greater than
>  0.62 probability of giving a correct answer to the cut-point item,
> he is classified into that proficciency level.
>
> I have this same situation in both test. For example, the first cut
> score is on the 11th item. A student with a 0.62 propability of
> answering that items must have 13 correct items on the test. The
> second cut score is on the 23th item. A student with a 0.62
> propability of answering that items must have 21 correct items on
> the test.
>
> Why for the first cur score a sudent need more correct answer (13)
> than the cut score (11th item) and for the second cut score he need
> less correct answer (21) than the cut scores (23th item)? I found
> this dificult to explain.
>
> Kindly
>
> Andres
>
>
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>

```