[Rasch] Noise in observations ...

David Andrich david.andrich at uwa.edu.au
Mon Nov 5 11:51:57 EST 2007

Regarding this point from Mike Linacre, I have attached a paper that follows
directly from the logic of the Rasch model - which is much more readily
understood with the Poisson distribution. That is, that as the unit of
analysis is reduced, then the precision is increased but the variance in the
smaller unit is also increased. I would be interested in any comments on the
paper. This is directly analogous to "the more randomness in minor details,
the stronger the sense of historical truth". We have more variance in the
smaller unit, but we have more precision in the estimate.  It seems a great
insight for Gerd Theissen to see this realtionship qualitatively in history.

David Andrich, BSc., MEd. (UWA), PhD (Chic), FASSA
Chapple Chair, Graduate School of Education 
The University of Western Australia
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Crawley  6009
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Email: david.andrich at uwa.edu.au
On line Rasch measurement course July - November 2007
3rd International Conference in Rasch measurement, Perth, Australia
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From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On Behalf
Of Mike Linacre (RMT)
Sent: Sunday, 4 November 2007 3:56 PM
To: rasch at acer.edu.au
Subject: [Rasch] Noise in observations ...

Paul remarks: "... can only be measured if their observations contain
sufficient noise ..."

Of course, as scientists, we endeavor to reduce irrelevant noise in the
observations in the same way as nuclear physicists do in their experiments
in Quantum Mechanics.  But we don't trust only one observation, or
observations that are too close in agreement (recognized as the "attenuation
paradox" in classical test theory or "wood-shedding" in the legal arena). 

We are in the same position as historians:
"When considering an accumulation of evidence, the more randomness in minor
details, the stronger the sense of historical truth."
Gerd Theissen, University of Heidelberg, 1994  (lecture given at the Luther
School of Theology, Chicago).

We are looking for locally-independent sources of information about our
latent variable, in the same way that historians look for
locally-independent accounts of historical events. 

Mike L.

Mike Linacre
Editor, Rasch Measurement Transactions
rmt at rasch.org  <http://www.rasch.org/rmt/> www.rasch.org/rmt/ Latest RMT:
21:1 Summer 2007 

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