[Rasch] point-biserial reference - was: Negative pt-bis and fit of 1.0? How can this be?

Kulas, John T. jtkulas at stcloudstate.edu
Wed Mar 7 15:13:44 EST 2012


Forgive the non-Rasch question but given the recent flurry of activity I couldn’t resist:

I've been searching for a good reference/history/formula/definition of the terms "biserial correlation" and "point-biserial correlation" for quite a while. I am aware that the common item(binary)-total(continuous) Pearson's coefficient is often referred to as a point-biserial but I am more interested in a formal definition or historical reference to these terms (biserial and point-biserial). Does anyone have a suggestion for a seminal reference or good overview for these terms? 

Thanks much - John

-----Original Message-----
From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On Behalf Of David Andrich
Sent: Tuesday, March 06, 2012 7:34 PM
To: rasch at acer.edu.au
Subject: Re: [Rasch] Negative pt-bis and fit of 1.0? How can this be?

Yes, Mark has explained it. The usual tests of fit have very little power if there is no person separation and little item separation. In that case a correct and incorrect score are more or less equally likely and so there is no evidence of unlikely responses (misfit). The connection between a traditional test theory statistic and power of the test of fit is the simple traditional reliability index (coefficient alpha), or in the case of some missing data, the index based on Rasch model estimates (which I call person separation but can be called Rasch model reliability). I consider that no fit statistics should be reported without this statistic also being reported, and a comment as to whether it is large enough to have power in detecting misfit. The usual number of 0.75 and above seems mandatory. In the program RUMM for example, we interpret this number as evidence of the power of the test of fit, with a colour coding from Excellent, Good, Reasonable, Low, and Too Low. 
Hope this helps

David


David Andrich, BSc MEd W.Aust., PhD Chic, FASSA Chapple Professor david.andrich at uwa.edu.au
 
Graduate School of Education
The University of Western Australia
M428, 35 Stirling Highway,
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AUSTRALIA

Telephone: +61 8 6488 1085
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Pearson Psychometric Laboratory
http://www.education.uwa.edu.au/ppl/courses
http://www.education.uwa.edu.au/raschconference
www.matildabayclub.net 

-----Original Message-----
From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On Behalf Of Stuart Luppescu
Sent: Wednesday, 7 March 2012 5:53 AM
To: rasch at acer.edu.au
Subject: Re: [Rasch] Negative pt-bis and fit of 1.0? How can this be?

On Tue, 2012-03-06 at 15:36 -0600, Stuart Luppescu wrote:
> Are you saying that if I just generated 1's and 0's randomly and tried 
> to calibrate them they would all fit? Hmmm. I'm going to have to try 
> that....

Very interesting, indeed! Of course, you get 0 reliability and point-biserials near 0, but all the fit statistics are very close to 1.0! Mark Moulton gets a beer next time I see him for providing the instructional moment of the day.

-- 
Stuart Luppescu -=- slu .at. ccsr.uchicago.edu        
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