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An absence of measurement bias against distinct groups is a prerequisite for the use of a given psychological instrument in scientific research or high-stakes assessment. Factor analysis is the framework explicitly adopted for the identification of such bias when the instrument consists of a multi-test battery, whereas item response theory is employed when the focus narrows to a single test composed of discrete items. Item response theory can be treated as a mild nonlinearization of the standard factor model, and thus the essential unity of bias detection at the two levels merits greater recognition. Here we illustrate the benefits of a unified approach with a real-data example, which comes from a statewide test of mathematics achievement where examinees diagnosed with dyscalculia were accommodated with calculators. We found that items that can be solved by explicit arithmetical computation became easier for the accommodated examinees, but the quantitative magnitude of this differential item functioning (measurement bias) was small.

the quantitative methods for psychology

A unified factor-analytic approach to the detection of item and test bias: Illustration with the effect of providing calculators to students with dyscalculia