[Rasch] A basic question about variance calculations

Imogene Rothnie irothnie at usyd.edu.au
Mon Aug 26 08:20:47 EST 2013

```Thanks Mike, Very helpful.
Imogene

From: rasch-bounces at acer.edu.au [mailto:rasch-bounces at acer.edu.au] On Behalf Of Mike Linacre
Sent: Tuesday, August 20, 2013 2:10 PM
To: rasch at acer.edu.au
Subject: Re: [Rasch] A basic question about variance calculations

Thank you for your questions, Imogene.

In http://www.winsteps.com/facetman/index.htm?table5.htm

Explained variance % by facet 1 = (Explained variance %) * v1 /vsum

where
Explained variance % = Variance explained by Rasch measures of all facets  / Total variance in the data
= (Score Population S.D.^2 - Resid^2) / (Score Population S.D.^2)

v1/vsum = Rasch variance explained by facet 1 / Total Rasch variance explained by all facets
= (measure S.D. facet 1)^2 /  sum ( (measure S.D. facet 1)^2 + (measure S.D. facet 2)^2 + ... )

so that, "Explained variance % by facet 1 " is the % of the total variance in the data explained by facet 1.

OK?

Mike L.

On 8/19/2013 17:32 PM, Imogene Rothnie wrote:
Dear All
I've been calculating the variance explained after a Facets analysis using the information from table 5 and 7 output in Facets and the formulas provided in the Help menu. A basic question: when we calculate a % variance explained for a facet, say Judge, is the a % of the 'variance explained ' total ? Or is it variance explained /100% ? (ie 100% including the residual error). Hence 40% variance explained by Judges  when 50% variance explained by the measures would be 20% variance explained of total in the former...?

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