# [Rasch] Explaining diferences in scores and measures

Stephen Humphry shumphry at cyllene.uwa.edu.au
Sat Mar 8 13:57:45 EST 2008

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Hi Andres. I gather you scaled the items with the Rasch model,
determined a cut score by looking at the items in order, and defined
the cut-off in terms of the person location at which there is Pr=0.62
of a correct response to a specific item. I also assume you have
dichotomous items. Is that right?

If not, let me know.

> 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.

You say "less than the cut scores (23rd item)". The 23rd item is not
itself a score or cut-score, its difficulty estimate can be defined as
such (I assume that's your definition).

Can you obtain the expected score for a person at the location of your
cut-score, either from a Test Characteristic Curve or by interpolating
from a table of correspondences between raw scores and expected scores?

The expected score for any ability depends upon the distribution of
items. Response patterns do not generally follow a Guttman pattern;
ie. Xn = 0,0,0,0,....,0,1,1,1....,1. Consequently, respondents answer
some items above their location correctly and some below their
location incorrectly. If the item distribution is denser above the
person location than below, in the relevant region of the scale, there
will tend to be an asyemmetric pattern, in the sense that the number
Na of questions above the person answered correctly will be greater
than the number Nb of questions below the person answered incorrectly.
This is simply because the person has more opportunities to attept
difficult items (above person location) than easy items (below) if the
item distribution is denser above the location.

I think the expected score should be greater than the number of items
counted in order, particularly if the person estimates are unbiased;
e.g. WLE estimates in RUMM. I could be wrong -- it's a while since I
was looking at this, but whatever the case I think it will be helpful
to look at the expected score for an ability estimate at your cut-score.

Regards,

Steve Humphry

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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>
>

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