[Rasch] analysing CTT construct using IRT

Mike Linacre (RMT) rmt at rasch.org
Tue Oct 27 22:41:14 EST 2009


Thank you for the clarification, Kate.

The Test Information Function (TIF) is equivalent to the computation of a 
standard error (precision) for every raw-score and every person measure on 
the test. This is much more than CTT, which gives us an average standard 
error across all the raw scores on a test (expressed as a reliability index).

The TIF reports on precision, not on fit. Chi-squares report on fit, not on 
precision.

Here are three test design philosophies:
1. We want roughly equal measurement precision across a wide range of 
person measures. For this, the more uniform the distribution of items on 
the latent variable the better .
or
2. We want higher precision (certainty) on person measures near cut-points 
(pass-fail points). For this, we need the items to pile up around the 
cut-points.
or
3. We want the precision of this test to be the same as the precision of 
another test for all scores/measures. For this, we select items which 
produce matching TIFs.

OK?

Does anyone else have input into this topic?

Mike Linacre

At 10/27/2009, you wrote:
>Dear Mike,
>
>Thank you very much for your reply. My question was about Test Information 
>Function.  Is it necessary to evaluate the precision of the measures? I 
>was reading a book Data Analysis Multivariate Social Science Data and 
>found that many examples of IRT it uses for analysing Likert scale data 
>have not even been given any information about the Test Information but 
>fit index such as Chi-Square. I understood that the Test Information is 
>supposed to be one of the advantages of the IRT compared to CTT, but is it 
>used much in practice for purposes other than designing a ability test?
>
>Thanks!
>
>Kate

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