[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 

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 
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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