An item response theory-based statistical procedure for detecting concurrent internal bias in ability tests
Shealy, Robin Todd
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https://hdl.handle.net/2142/23174
Description
Title
An item response theory-based statistical procedure for detecting concurrent internal bias in ability tests
Author(s)
Shealy, Robin Todd
Issue Date
1989
Doctoral Committee Chair(s)
Stout, William F.
Department of Study
Statistics
Discipline
Statistics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Statistics
Psychology, Psychometrics
Language
eng
Abstract
A statistical procedure is developed with the purpose of detecting internal bias occurring concurrently in several items in an ability test. Concurrent internal bias (CIB) is considered in a nonparametric multidimensional item response theory (IRT) model which models both an ability intended to be measured by the test (target ability) and nuisance determinant abilities. If the nuisance ability distributions conditional on a fixed target ability are different across group, and contamination of several items with these nuisance abilities is present in their item response functions, then bias occurs concurrently in these items.
Using test responses based on the above IRT model, a statistical test is developed to detect CIB in the items suspected to be biased (the Suspect Subtest). The necessity of the existence of a subtest measuring only target ability (a Valid Subtest) to test for CIB is established. The procedure is intended to test the IRT-based hypothesis of no CIB in the Suspect Subtest conditional on target ability, but since target ability is unknown, it is developed to test the corresponding empirical hypothesis of no difference in Suspect Subtest response distributions across group, conditional on the Valid Subtest score. However, if target ability difference between the two groups is present, the test statistic exhibits an inflated Type I error when testing the IRT hypothesis. Two solutions are offered to this phenomenon: (1) the test statistic is shown to be asymptotically normal as the number of examinees from both groups and the number of items on the Valid Subtest increases to infinity at a prescribed rate, and (2) more importantly, an adjustment to the test statistic in order to extract the contribution of target ability difference to it is developed. An important feature of the resultant statistical procedure is that it tests for bias in more than one item simultaneously without the need for an iterative procedure or simultaneous statistical inference.
A moderate sized simulation study is performed to test the CIB test statistic both alone and alongside the commonly-used Mantel-Haenszel statistic adapted for test responses by Holland & Thayer (1988).
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