Statistics
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
2PL IRT
The two-parameter logistic item response model, formalised by Frederic Lord (1980), describes the probability that a respondent answers a binary test item correctly as a smooth S-shaped function of the respondent's latent ability. By estima...
3PL IRT
The three-parameter logistic (3PL) model, introduced by Allan Birnbaum in 1968, is an item response theory model that describes the probability of a correct response to a binary test item as a function of three item-level parameters — diffi...
Bifactor Model
The bifactor measurement model specifies that every indicator loads simultaneously on a single general factor and on one of several specific (group) factors. Formally introduced by Holzinger and Swineford in 1937 and brought into mainstream...
CAT Generalizability Theory
Generalizability theory (G-theory) applied to computerized adaptive testing (CAT) evaluates the dependability of adaptive test scores by decomposing score variance across measurement facets such as persons, items, and occasions. Unlike clas...
CAT McDonald's Omega
McDonald's omega adapted for computerized adaptive testing (CAT) quantifies the reliability of ability or trait estimates when different examinees answer different subsets of items. Unlike Cronbach's alpha, omega is grounded in a factor mod...
CAT Scale Development
Computerized adaptive test (CAT) scale development is the process of constructing, calibrating, and validating a large item bank such that the assessment algorithm can select items tailored to each examinee's estimated ability or trait leve...
CAT-DIF
CAT-DIF identifies items in a computerized adaptive test that behave differently across demographic or group subpopulations after controlling for overall ability. Because adaptive algorithms select items non-randomly based on each examinee'...
Case-Cohort Design
Case-cohort design is an epidemiological study design developed by Prentice (1986) that efficiently combines features of case-control and cohort studies. Researchers enroll an entire cohort, follow it for outcomes, then measure exposures on...
Cognitive Diagnosis Model
Cognitive Diagnosis Models (CDMs) are a family of latent variable models designed to classify examinees according to their mastery of a set of discrete cognitive attributes or skills. The Generalized DINA (G-DINA) framework, introduced by J...
Cognitive Diagnostic Computerized Adaptive Testing
Cognitive Diagnostic Computerized Adaptive Testing (CD-CAT) combines computerized adaptive testing (CAT) with cognitive diagnostic models (CDMs) to efficiently assess students' specific skill profiles. Rather than producing a single overall...
Cognitive Diagnostic Modeling
Cognitive diagnostic models (CDMs), also called diagnostic classification models, are restricted latent class models that report not a single ability score but a profile of which discrete skills or attributes a student has mastered. Each it...
Computerized Adaptive Test Content Validity
Content validity in computerized adaptive testing (CAT) ensures that an adaptively administered assessment adequately samples the intended content domain despite delivering only a subset of items to each examinee. It integrates classical co...
Computerized Adaptive Test Convergent Validity
Convergent validity assessment for computerized adaptive tests (CATs) examines whether the ability or trait estimates produced by an adaptive algorithm correlate substantially with scores from other measures of the same construct. Because e...
Computerized adaptive test Rasch model
Computerized adaptive testing with the Rasch model selects items in real time based on each examinee's evolving ability estimate, so that every person receives a test precisely calibrated to their proficiency level. The result is a shorter,...
Computerized adaptive test construct validity
Construct validity in computerized adaptive testing evaluates whether the latent trait estimates produced by a CAT instrument genuinely measure the intended psychological or educational construct. Because adaptive algorithms select items in...
Computerized adaptive test discriminant validity
Discriminant validity in computerized adaptive testing (CAT) is the evaluation process confirming that a CAT-administered scale measures its intended construct distinctly from related but conceptually different constructs. Despite the adapt...
Computerized adaptive test item response theory
Computerized adaptive testing based on item response theory is a sequential measurement procedure in which a computer algorithm selects successive test items tailored to each examinee's estimated ability level. Drawing on IRT to model item...
Computerized adaptive test measurement invariance
Computerized adaptive test measurement invariance evaluates whether a CAT instrument measures the same latent construct with the same psychometric properties across different groups (e.g., gender, language, clinical vs. community) or time p...
Computerized adaptive test reliability analysis
CAT reliability analysis quantifies measurement precision in computerized adaptive tests where each examinee receives a unique, individually tailored subset of items. Rather than a single classical coefficient, it uses item response theory...
Conditional Standard Error of Measurement
The conditional standard error of measurement (CSEM) describes how much measurement error a test score carries at each point along the score scale, rather than as a single average. A test typically measures more precisely in some score rang...
Construct Validity
Construct validity is the degree to which a test or scale actually measures the theoretical construct it is intended to measure. Introduced by Cronbach and Meehl in 1955, it is the central validity concern in psychological and educational m...
Content Validity
Content validity is evidence that a measurement instrument adequately samples the full domain of the construct it is intended to measure. It is established through systematic expert review and quantified with indices such as Lawshe's Conten...
Convergent Validity
Convergent validity is the degree to which multiple indicators that are theoretically expected to measure the same construct actually correlate with one another. It is one of the two complementary forms of construct validity identified by C...
DINA Model
The DINA Model (Deterministic Inputs, Noisy Outputs) is a cognitive diagnostic model developed by Junker and Sijtsma (2001) that classifies examinees into latent skill classes based on their item response patterns. DINA assumes a determinis...