# [Rasch] A basic question about variance calculations

Mike Linacre mike at winsteps.com
Tue Aug 20 14:09:44 EST 2013

```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...?
>

-------------- next part --------------
An HTML attachment was scrubbed...
URL: https://mailinglist.acer.edu.au/pipermail/rasch/attachments/20130819/93cc35cf/attachment.html
```