Compare methods

	Differential Distractor Functioning	Item Response Theory
Field	Education	Psychometrics
Family	Latent structure	Latent structure
Year of origin	2008	1952–1968
Originator	Item-bias methodology (Green, Crone & Folk; Penfield)	Frederic M. Lord (and Allan Birnbaum for the 2PL/3PL models)
Type	Group-difference analysis of the incorrect options (distractors) of multiple-choice items	Probabilistic measurement model
Seminal source	Penfield, R. D. (2008). An odds ratio approach for assessing differential distractor functioning effects under the nominal response model. Journal of Educational Measurement, 45(3), 247–269.	Lord, F. M. & Novick, M. R. (1968). Statistical Theories of Mental Test Scores. Addison-Wesley.
Aliases	DDF, Distractor-Level DIF, Differential Option Functioning, Distractor Functioning Analysis	IRT, latent trait theory, item characteristic curve theory, modern test theory
Related	4	5
Summary	Differential distractor functioning (DDF) extends test-fairness analysis from the correct answer to the wrong ones. It asks whether examinees of equal ability but different group membership are differentially attracted to particular distractors (incorrect options) of a multiple-choice item. By analyzing option-level rather than just right/wrong responses, DDF can detect bias that ordinary differential item functioning misses and, crucially, help explain why an item functions differently — pointing to the specific wrong option luring one group. Penfield's odds-ratio approach under the nominal response model is a standard tool.	Item response theory models the probability that a respondent answers an item correctly (or endorses it) as a function of the respondent's latent trait level and the item's own statistical properties — difficulty, discrimination, and guessing. Unlike classical test theory, IRT places persons and items on the same scale, yielding measurement that is sample-independent for items and test-independent for persons.