[Rasch] Error in Rasch Digest, Vol 35, Issue 8?

Fraser Rew Fraser.Rew at nzqa.govt.nz
Tue Jun 17 12:20:55 EST 2008

I would just like to query Mike's maths . . given 45 items in a 5-point scale (I presume that this means either 1-5 or 0-4), there are 181 possible grades (45-225 or 0-180). The main point of the argument still stands, as there are still likely to be scores at the very high and very low end that are not attained by any candidate, though this would be to a slightly lesser extent than Mike suggests. 

I don't claim to be a Rasch expert so I could very well be missing something here.



Fraser Rew
Researcher/Data Analyst
Qualificiations Division
DDI: 04 463 4368
Extn: 4368


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Today's Topics:

   1. RE: development and validation of instrument (Hendrickson, Peter)


Message: 1
Date: Mon, 16 Jun 2008 08:10:41 -0700
From: "Hendrickson, Peter" <PHendrickson at everettsd.org>
Subject: RE: [Rasch] development and validation of instrument
To: "Mike Linacre (RMT)" <rmt at rasch.org>,	<rasch at acer.edu.au>
	<96B1345B0BE8AB49AD6A43D7355AD845093A4D22 at lfbes02.everett.k12.wa.us>
Content-Type: text/plain; charset="us-ascii"

Dear Nancy-

Do you think I could ask Mike to explain the two ways Lynette and Rich
were related and we could write it down for others?  Love,  //Peter//
(Have an 8:45 dental this morning.)



From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On
Behalf Of Mike Linacre (RMT)
Sent: Saturday, June 14, 2008 12:46 PM
To: rasch at acer.edu.au 
Subject: Re: [Rasch] development and validation of instrument


Thank you for more questions, Juanito.

You wrote:

We develop a 50-item instrument anchored on a theory with 4 constructs.
We piloted the instrument to 203 persons, then we subjected to Rasch
analysis.  After our Rasch analysis we found that the 50 items are
unidimentional and the 5-point likert scale categories are logically
functional, but while retaining the 4 constructs, five items misfit the
model.  Thus, we decided to remove the 5 items and come up with a 45
item instrument.  Our questions to Rasch expert are:
1. Shall we gather again another data (say n=200) to validate the

Reply: In your original analysis of the 50-item instrument, you
discovered that 5 items were defective or off-dimensional in some way.
So you want to omit them from the revised 45-item instrument. Fine!
Do you think that the responses to those 5 items have skewed the
responses of your 203 persons to the other 45 items in any way? For
instance, perhaps the 5 items were the first 5 items on the instrument
and so could have caused the sample to misunderstand how they were
supposed to respond to the remaining 45 items. If they would have
distorted the responses to the other 45 items, then you need to repeat
the data collection with a new sample on the 45 item instrument. If not,
then the current sample's data is valid for the 45 items. There is no
need to repeat the data collection.

You wrote:

2. How do Rasch validation is done? Do we just repeat the rasch

Reply: Yes, you would repeat the Rasch analysis but now with only the 45
items. But remember that you have already excluded the 5 worst items, so
the sensitivity of the Rasch analysis to problems in the remaining 45
items has increased. You will now find another group of "worst items".
Don't automatically reject them to make a 40-item instrument, but
examine the new set of worst items closely. Is their misfit really bad
enough to distort the person measures?

You wrote:

3. Is our sample big enough for Rasch analysis?

Reply: This depends on your purpose for this instrument, and how you are
modeling the items. You have 45 items and each has a 5-point Likert
scale. So the possible range of raw scores is 0 to 225 (or 45 to 270).
So there are more possible raw scores (226) than your sample size (203).
Consequently it is likely that you have few of your sample with very
high or very low scores. If your instrument is intended to probe the
full range of person performance, then you may need to collect data from
more high or low performers to verify the operational range of the
instrument. But if your sample of 203 persons matches the intended use
of the instrument in all important respects, then your sample size is
probably large enough, see http://www.rasch.org/rmt/rmt74m.htm - There
are additional concerns if you are using the "Partial Credit" model.


Mike L.

Mike Linacre
Editor, Rasch Measurement Transactions
rmt at rasch.org www.rasch.org/rmt/ Latest RMT:  21:4 Spring 2008

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