# [Rasch] What is the relationship between number of items and the number of participants needed?

Agustin Tristan ici_kalt at yahoo.com
Thu Jun 20 04:33:02 EST 2013

```Hi!
In the Institute we don't use thumb rules but we consider the following crteria:

a) The number of items is defined by: (1) the design error we accept for measurement and (2) the conditions imposed by the administration or the authorities who buy our tests concerning available time for the test (1 hour, 2 hours, 30 minutes). Depending on the standard time to solve an item (standard time may be obtained for each item or as a mean of the set of items) and the time indicated by the authorities we get the number of items and then we can get an estimation of the theoretical error of the test. If the theoretical error is less than say 5% or 0.25 logits we may accept the number of items otherwise we shall increase the number of items and ask the authorities to approve a longer test. This has implications in the number of items in the item bank and some economical aspects.

b) The number of persons needed for calibration is defined by: (1) the sample size needed to be representative of a focal group, (2) the number of persons needed to analyze a contingency table 2x2 in reference to CTT. For (1) the sample size, we are not related to Rasch analysis, but for representativeness, including age, gender, region, etc. this sample size may requiere 300, 500 or other figures. For (2) it is possible to calculate that we need 20 persons for an item close to 0 logits, 50 persons if our items are between -1.5 to 1-5 and 100 persons if our items are between -2 to +2 logits.

Hope this help.

regards
Agustin Tristan

INSTITUTO DE EVALUACION E INGENIERIA AVANZADA.
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Página Web (en español): http://www.ieia.com.mx/
Web page (in English): http://www.ieesa-kalt.com/English/Frames_sp_pro.html

From: Matthew Enos <matthewenos at mac.com>
To: rasch at acer.edu.au
Cc: Marci Enos <mizmarce at aol.com>
Sent: Wednesday, June 19, 2013 12:45 PM
Subject: Re: [Rasch] What is the relationship between number of items and the number of participants needed?

Mike,

Even though I am not actively engaged in measurement issues these days, I still glance at the Rasch exchanges -- and read the Mike L. posts with some care -- messages like this last one you sent capture my interest in science in general and measurement in particular. There is a wealth of thought in the exchanges on this line.

Discussions like the one below are especially interesting to me because they raise larger issues of measurement and science (and therefore of TRUTH). As a consummate educator, you always suggest, "...now, let's look into the subject a bit more deeply...." That's real teaching (and learning).

Marci and I miss the intellectual adventure in which you and Ben led us. At this point, we are not much involved, and have almost completely lost touch with Ben. Apparently, he is still in Chicago, but why is beyond me. The house is gone, but he continues in a Chicago hospital, right? Why is beyond me.

We hope all is well with you and Maureen. The news from Down Under is alternately beguiling and frightening. A wonderful continent, but with way too many things that bite or sting.

Take care of yourselves!

Matt

Matthew Enos
320 Crescent Drive
Glenview, IL 60025
Home: 847-983-0746

On Jun 18, 2013, at 6:13 PM, Mike Linacre wrote:

Michael:
>
>You asked: "What is the relationship between number of items and the
>number of participants needed?"
>
>Here are a few guidelines to launch our discussion:
>1) at least 30 observations of each item and of each person, if possible.
>2) at least 10 observations of each score-level on each rating scale.
>3) since we are usually more concerned about item fit than person fit,
>there must be more persons than items.
>
>
>Mike L.
>_______________________________________________
>Rasch mailing list
>Rasch at acer.edu.au
>Unsubscribe: https://mailinglist.acer.edu.au/mailman/options/rasch/matthewenos%40mac.com
>

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