[Rasch] analysing CTT construct using IRT

Man Xu man.xu at education.ox.ac.uk
Wed Oct 28 02:58:51 EST 2009

Dear Mike,

Thank you for your help. I am definately not looking for a cutting off point here. I guess it is very nice when the instrument (set of items to measure the trait) is equally precise on the latent trait continuum. But I found this is unlikely to be true for the instruments developed under CTT because the items were simply created without taking "difficulties" into account. So there is always a peak somewhere for such data. If my purpose if not to get a precise cut off point but to evaluate say a particular model in educatioal psychology for all students where the path coefficients are my interests, would the precision still be a concern for me, apart from the fit indeces?


From: rasch-bounces at acer.edu.au [rasch-bounces at acer.edu.au] On Behalf Of Mike Linacre (RMT) [rmt at rasch.org]
Sent: 27 October 2009 11:41
To: Rasch at acer.edu.au
Subject: RE: [Rasch] analysing CTT construct using IRT

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 .
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.
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.


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?



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