[Rasch] Explained variance

Mike Linacre (RMT) rmt at rasch.org
Wed Oct 22 18:16:38 EST 2008


Theo, thank you for your question about explained variance.

If we know our testing situation, we can predict the variance explained 
using the nomogram at www.rasch.org/rmt/rmt221j.htm

For instance,
Item measure S.D. is 1 logit. Person S.D. is 1 logit. Targeting is 1 logit. 
The nomogram predicts: 25% explained variance
Item measure S.D. is 2 logit. Person S.D. is 2 logit. Targeting is 1 logit. 
The nomogram predicts: 50% explained variance
Item measure S.D. is 4 logit. Person S.D. is 4 logit. Targeting is 1 logit. 
The nomogram predicts: 75% explained variance

The first factor in the residuals is unlikely to be guessing unless the 
guessing correlates across several items. It is more likely to be a shared 
sub-dimension, such as word-problems in arithmetic.

Mike L.

At 10/20/2008, you wrote:
>Are there any established standards for the percentage of variance we
>would like to see explained by the Rasch measure? Our cognitive
>developmental assessments run 70%-80%, but for conventional tests we
>have worked with the value is often lower than 30%.
>
>Also, for multiple choice tests, would it be typical for the first
>factor from the residuals to have something to do with guessing?
>
>Theo

Mike Linacre
Editor, Rasch Measurement Transactions
rmt at rasch.org www.rasch.org/rmt/ Latest RMT:  22:1 Summer 2008
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