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	Testowanie niezmienniczości pomiaru	Analiza zróżnicowanego funkcjonowania pozycji testowej (DIF)	Modelowanie równań strukturalnych (SEM)
Dziedzina	Psychometria	Psychometria	Statystyka
Rodzina	Latent structure	Latent structure	Latent structure
Rok powstania	2000	1988	1970
Twórca	Vandenberg & Lance	Paul W. Holland & Dorothy T. Thayer (Mantel-Haenszel approach, 1988)	Karl Jöreskog (LISREL framework, 1970s)
Typ	Multi-group confirmatory factor analysis procedure	Item-level fairness / measurement equivalence analysis	Latent variable / causal modeling
Źródło pierwotne	Vandenberg, R. J., & Lance, C. E. (2000). A review and synthesis of the measurement invariance literature. Organizational Research Methods, 3(1), 4–70.	Holland, P. W. & Thayer, D. T. (1988). Differential Item Performance and the Mantel-Haenszel Procedure. ETS Research Report Series.	Hair, J. F., Black, W. C., Babin, B. J. & Anderson, R. E. (2019). Multivariate Data Analysis (8th ed.). Cengage Learning. ISBN: 978-1473756540
Inne nazwy	Factorial Invariance, Measurement Equivalence, Configural-Metric-Scalar Testing, Ölçüm Değişmezliği	Madde Yanlılık Analizi (DIF — Differential Item Functioning), item bias analysis, Mantel-Haenszel DIF, Lord chi-square DIF	Yapısal Eşitlik Modellemesi (SEM), structural equation modelling, covariance structure analysis, latent variable modeling
Pokrewne	3	4	5
Podsumowanie	Measurement invariance testing is a sequence of nested confirmatory factor analysis (CFA) models that examines whether a psychological scale measures the same latent construct in the same way across distinct groups or time points. Systematized and popularized by Vandenberg and Lance (2000), the procedure tests a hierarchy of constraints — from identical factor patterns to identical item intercepts — so that researchers can justify meaningful group comparisons on latent means.	Differential Item Functioning analysis examines whether examinees from different groups — such as gender, ethnicity, or language background — who have the same underlying ability respond differently to a test item. First formalised by Holland and Thayer in 1988 via the Mantel-Haenszel procedure, it is the principal tool in modern test development for detecting and removing item bias.	Structural equation modeling is a multivariate statistical framework that simultaneously estimates a measurement model — relating observed indicators to latent constructs — and a structural model specifying directional or reciprocal relationships among those constructs. Rooted in the LISREL tradition developed by Karl Jöreskog in the 1970s, SEM is the standard tool for testing complex theoretical models in the social, behavioural, and management sciences.