[Rasch] Let us say that one has 10 items that have been Rasch scaled. They look like they are equally spaced. How does one test that hypothesis?

Agustin Tristan ici_kalt at yahoo.com
Thu Sep 9 05:09:55 EST 2010

The uniform distribution may be tested using a chi2 test but the problem is that chi2 sign is always positive and then it produces wrong decisions because it is not sensitive to other forms of distributions. We used this fact to demonstrate that the Ferguson's delta does not work, unfortunately, the paper has not been accepted because (1) few people knows about Ferguson´s delta or even less use it - it seems more used in health questionnaires and (2) because a paper presenting negative results are not well received in the journals - as has been reported in many meta-analysis documents. The paper is under procedure to be accepted in ERIC in the following months.
A more practical solution: It is possible to do a construction to test the uniform distribution using the test design line (TDL), I cannot attach the file here, please please look in http://www.eric.ed.gov/PDFS/ED501232.pdf
Trtistan, L.A. & Vidal, U.R. (2007) Linear model to assess the scale's validity of a test. AERA meeting. Chicago. 
The model compares the observed difficulties or measures to a uniform distribution, you may adapt this model to other considerations. It is not useful to do a hypothesis test due to the problem of sign and also because it will become sensitive to the number of items, while the TDL is able to compare to any number of items and give you information about the sign if your wish (the sign will indicate if a test is harder or easier than expected), and the mean absolute distance indicates how close you are to the TDL.
Hope this helps.
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--- On Mon, 9/6/10, Michael Lamport Commons <commons at tiac.net> wrote:

From: Michael Lamport Commons <commons at tiac.net>
Subject: [Rasch] Let us say that one has 10 items that have been Rasch scaled. They look like they are equally spaced. How does one test that hypothesis?
To: Rasch at acer.edu.au
Date: Monday, September 6, 2010, 7:16 PM

Let us say that one has 10 items that have been Rasch scaled.  They look like they are equally spaced.  How does one test that hypothesis?  Now replace those items with a tightly packed group around each of the 10 items.  Any way to test whether the means of each are equally spaced?
My Best,

Michael Lamport Commons, Ph.D.
Assistant Clinical Professor

Department of Psychiatry
Harvard Medical School
Beth Israel Deaconess Medical Center
234 Huron Avenue
Cambridge, MA 02138-1328

Telephone (617) 497-5270
Facsimile (617) 491-5270
Cellular	(617) 320–0896
Commons at tiac.net

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