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** Item Response Theory **
Ch. 1: Background
I. Classical Test Theory (CTT)
A. Model
1. Xip = Tip +Eip
An observed score for test i and person p is a composite of true test score
of test I and person p and error score of test I and person p.
2. The model is a tautology, which cannot be proved or disproved.
3. The model, however, has serious practical problems.
B. Shortcomings of CTT
1. Test-dependent true score: An examinee’s true score depends on the
difficulty level of a test.
2. Sample-dependent item parameters: The item parameter scores depend on
the ability of examinees.
3. The parallel test assumption is hard to meet in practice.
4. CTT provides no basis for an examinee’s performance estimates for an
item since it is a test-oriented model.
II. Hope for an ideal test model
A. Test-independent true score (ability or proficiency).
B. Sample-independent item parameters.
C. Free from the parallel test assumption.
D. Handling an examinee’s performance for each item.
III. Historical Perspective (Handout)
IV. Hambleton’s paper.
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