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1Copyright© 2004, Graduate Management Admission Council®. All Rights Reserved.
Expected Classification Accuracy
Lawrence M. RudnerGraduate Management Admission
Council®
LRudner@gmac.com
2Copyright© 2004, Graduate Management Admission Council®. All Rights Reserved.
I will discuss
Classification Accuracy with IRT
False Positives – False Negatives
Repeat opportunities
Lower operational cut scores
2-categories / n-categories
Easy estimate
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Classification table
classified mastertrue master
classified non-mastertrue master
classified mastertrue non-master
classified non-mastertrue non-master
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Example
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False Positive
P c i( | )
is the area to the right of
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Illustration 1• Dataset
– 50 items: [a,b,c]=[1.43, 0.00, 0.20]– N(0,1): mean see= .393, r= .92– θc = -.25; 40th %ile
Table 2: Expected and true examinee classifications
Expected Classification
Master Non-Master
TrueMaster 53.9 5.0
Non-Master 6.5 34.6
Accuracy = 88.5%
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Application 1• add 10 items with parameters
a=2.0, b=-.25 and c=0
:
Expected and true examinee classifications adding 10 optimal items Expected Classification
Master Non-Master
TrueMaster 55.4 3.6
Non-Master 4.8 36.3
Accuracy = 91.7%
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Application 2
Expected and true examinee classifications using an adjusted operational cut score Expected Classification
Master( c'>-.40)
Non-Master( c'<-.40)
True
Master( c>-.25) 56.2 2.7
Non-Master( c< -.25) 9.8 31.3
Accuracy = 87.5%
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Multiple categories
P ro b ( | ) ( ( ) ) ( ( ) )a b bse
ase
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Simplified estimate
sea
b ase se seb a a( )
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Simplified Estimate
• 81.7% calculated correct classification
• 78.0% estimated correct classification
10-item 2001 Maryland State Performance Assessment Program Grade 8 Reading Test, Form A.
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