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	Testowanie niezmienniczości pomiaru porządkowego	Teoria odpowiedzi na pozycje (IRT)
Dziedzina	Psychometria	Psychometria
Rodzina	Latent structure	Latent structure
Rok powstania	1984–2011	1952–1968
Twórca	Roger Millsap; Bengt Muthén	Frederic M. Lord (and Allan Birnbaum for the 2PL/3PL models)
Typ	Multi-group model comparison	Probabilistic measurement model
Źródło pierwotne	Millsap, R. E. (2011). Statistical Approaches to Measurement Invariance. Routledge. ISBN: 978-1848728936	Lord, F. M. & Novick, M. R. (1968). Statistical Theories of Mental Test Scores. Addison-Wesley.
Inne nazwy	ordinal MI, measurement invariance for ordinal data, ordinal CFA invariance, categorical measurement invariance	IRT, latent trait theory, item characteristic curve theory, modern test theory
Pokrewne	6	5
Podsumowanie	Ordinal measurement invariance testing evaluates whether a multi-group confirmatory factor model holds equivalent measurement properties across groups when scale items are ordinal — such as Likert-type response scales. It uses polychoric correlations and categorical estimators (WLSMV/DWLS) rather than Pearson-based methods, correcting the systematic bias that arises when ordinal data are treated as continuous.	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.