Ch. 8: Differential Item Functioning (DIF)
I. Introduction
A. Definition 1:
An item shows DIF if two groups are different in their mean performance on the
item (p-value in CTT). Does not consider a real difference between the two
groups.
B. Definition 2:
An item shows DIF if individuals with the same ability in different groups have
different probability of getting the item correct (P( ) in IRT). An item shows
DIF if the item response functions across different sub-groups are not identical
over the same ability range.
II. DIF in IRT
A. Item parameter comparison
1. Testing Ho: b1 = b2, Ho: a1 = a2, Ho: c1 = c2.
2. If item parameters are identical, ICCs should be identical over all points of
ability scale for two different groups. No DIF.
3. If Ho’s are rejected, DIF is present for the item.
4. Test statistics (
2
)
2
= (ad bd cd)’
1
(ad bd cd)
where
ad = a2 – a1,
bd = b2 – b1,
cd = c2 – c1.
= covariance matrix of ad, bd, and cd.
ad bd cd
=
2
2
2
ccbca
bcbba
acaba
,
1
= inverse of .
5. Test statistic is asymptotically
2
-distribution with df = p
(p= # of parameters).
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