Statistics — Page 2
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
DINO Model
The DINO Model (Deterministic Inputs, Noisy Outputs—Disjunctive) is a cognitive diagnostic model that relaxes DINA's conjunctive (AND) skill requirement logic. DINO assumes an examinee only needs to master one of multiple possible skill pat...
Differential Distractor Functioning
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 distrac...
Differential Item Functioning
Differential item functioning identifies test or survey items that behave differently for examinees from different groups — such as gender, ethnicity, or language background — after controlling for the underlying ability or trait being meas...
Differential Item Functioning in Educational Testing
Differential item functioning (DIF) analysis is the central statistical tool for evaluating the fairness of test items in education. An item shows DIF when examinees of equal ability but different group membership — for example by gender, r...
Discriminant Validity
Discriminant validity is evidence that a latent construct is empirically distinct from other constructs it should differ from. Originating in Campbell and Fiske's multitrait-multimethod framework (1959), it is a core component of construct...
Fuzzy-Set Qualitative Comparative Analysis
Fuzzy-Set Qualitative Comparative Analysis (fsQCA) is a set-theoretic method developed by Charles Ragin in the early 2000s that combines the configurational logic of qualitative case studies with the mathematical rigor of fuzzy sets. It bri...
G-Theory
Generalizability Theory, developed by Lee J. Cronbach and colleagues in the 1960s and formalised by Brennan (2001), is an ANOVA-based framework that extends Classical Test Theory by decomposing observed score variance into multiple, separat...
Generalizability Theory
Generalizability Theory is a psychometric framework that decomposes observed score variance into multiple sources — persons, items, raters, occasions, and their interactions — using analysis of variance. It replaces the single reliability c...
Item Analysis
Item analysis is the foundational psychometric procedure for evaluating the quality of individual test or scale items within the Classical Test Theory (CTT) framework, as systematised by Allen and Yen (1979) and Crocker and Algina (1986). I...
Item Response Theory
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 guessi...
Longitudinal Construct Validity
Longitudinal construct validity evaluates whether a psychological scale measures the same latent construct in the same way across multiple time points. It is tested by progressively constraining a confirmatory factor model across waves and...
Longitudinal DIF
Longitudinal differential item functioning detects whether individual test or scale items behave differently across measurement occasions for the same respondents. It extends standard DIF methodology to repeated-measures designs, ensuring t...
Longitudinal Discriminant Validity
Longitudinal discriminant validity tests whether a psychological construct measured at two or more time points is empirically distinct across occasions — ensuring that the same construct does not collapse into a single undifferentiated mass...
Longitudinal Generalizability Theory
Longitudinal generalizability theory extends classical G-theory to repeated-measures and longitudinal designs, decomposing score variance across persons, measurement occasions, raters, and items simultaneously. It quantifies how reliably sc...
Longitudinal IRT
Longitudinal IRT extends classical item response theory to data collected at multiple time points, allowing researchers to model both the initial latent trait level and its change over time. It is used in educational assessment, clinical tr...
Longitudinal McDonald's omega
Longitudinal McDonald's omega estimates scale reliability separately at each measurement occasion in a panel or repeated-measures study. By fitting a confirmatory factor model at each wave, it tracks how consistently a set of items measures...
Longitudinal Measurement Invariance
Longitudinal measurement invariance testing determines whether a psychological scale measures the same construct in the same way across two or more time points. It is a prerequisite for interpreting mean-level change scores in panel and rep...
Longitudinal Nomological Validity
Longitudinal nomological validity evaluates whether a construct's theoretically predicted relationships with other constructs hold consistently across multiple measurement occasions. It extends the nomological network framework of Cronbach...
Longitudinal Reliability Analysis
Longitudinal reliability analysis evaluates the consistency and stability of measurement instruments across two or more time points. It extends classical reliability concepts — internal consistency, test-retest stability, and measurement pr...
Longitudinal Test-Retest Reliability
Longitudinal test-retest reliability quantifies how consistently a scale or measure performs across two or more time points in a longitudinal study. It extends the classic test-retest paradigm by accounting for planned, often substantive, t...
Longitudinal content validity
Longitudinal content validity evaluates whether the items of a measure adequately and consistently represent the intended content domain not only at a single point in time but across repeated administrations. It ensures that the conceptual...
Longitudinal convergent validity
Longitudinal convergent validity evaluates whether a scale's indicators correlate with theoretically related constructs not just at a single time point but consistently across repeated measurement occasions. It extends standard convergent v...
Longitudinal scale development
Longitudinal scale development is the systematic process of constructing and validating a measurement instrument using data collected at multiple time points. It extends classical scale development by additionally testing whether the scale...
MCP Penalized Regression
MCP (Minimax Concave Penalty) is a variable selection method developed by Zhang (2010) that uses a concave penalty function for automated feature selection. Like SCAD, MCP addresses bias in lasso by avoiding shrinkage of large coefficients,...