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Background on Q3
Test specialists need to assign item parameters to each item and
an examinee parameter to each examinee so that they can
probabilistically predict the response of any examinee to any item,
even if similar examinees have never taken similar items before. For
such a purpose, Item Response Theory (IRT) has been developed
and has popularly used for item analysis, test construction, and test
equating. Most commonly used 3parameter logistic IRT model takes the
mathematical form:
where is the item discrimination parameter, is the item
difficulty parameter, is the guessing parameter, and
is the probability that an examinee with ability level
answers item i correctly.
When an IRT model is used to analyze the data, ignoring the violation
of these assumptions, the estimated values of item parameters and the
examinee parameter may not be accurate. Moreover, the major usage of
the most standardized achievement test is selection, prediction and
placement. When the use of a test results can affect the life chances
or educational opportunities of examinees, The analysis of test data
should be done carefully.
Therefore, Several methods for assessing local dependence in the test
data have been developed. Yen [49] proposed that Q3 index is
useful to detect local dependence. Q3 is the correlation of a pair of
items with the trait estimate partialled out. Yen illustrated that the
residual is calculated as
where is the score of the examinee on the
item.
can be estimated by equation
6.6. Then Q3 is the correlation of deviation scores across
all examinees and can be expressed as

(8) 
for item i and j, and it provides a pairwise index of item
dependence. If local independence is held between any pair of items,
expected value of Q3 is supposed to be close to
,
where is the number of items on the test [50].
In [12], Q3 index has successfully used to provide an
evidence of local dependence.
Next: Data Description
Up: Q3  Local Dependence
Previous: Q3  Local Dependence
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Bryan Carpenter
20040609