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...
Actor-Partner Interdependence Model
The Actor-Partner Interdependence Model (APIM), formalized by Kenny, Kashy, and Cook, is the standard framework for analyzing dyadic data in which two people's outcomes depend on both their own and their partner's characteristics. For each...
Anti-Immigrant Prejudice Scale
The Anti-Immigrant Prejudice Scale, developed by Thomas Pettigrew and Roel Meertens in 1995, measures prejudice toward immigrants along two dimensions: blatant prejudice, which is hot, close, and direct, expressing open rejection and percei...
BIS/BAS Scales
The BIS/BAS Scales, developed by Carver and White in 1994, are self-report measures of two fundamental motivational systems proposed by Gray's reinforcement sensitivity theory. The Behavioral Inhibition System (BIS) governs sensitivity to p...
Bayesian Confirmatory Factor Analysis
Bayesian confirmatory factor analysis tests a pre-specified factor structure using Bayesian inference. Instead of point estimates with p-values, it produces full posterior distributions for loadings, factor correlations, and residual varian...
Bayesian Construct Validity
Bayesian construct validity assessment uses Bayesian confirmatory factor analysis and related Bayesian structural equation models to evaluate whether a scale or test measures the intended latent construct. It yields full posterior distribut...
Bayesian Convergent Validity
Bayesian convergent validity applies Bayesian statistical inference to assess whether different measures of the same construct converge as theory predicts. Rather than a single-point correlation estimate, it yields a full posterior distribu...
Bayesian Cronbach's alpha
Bayesian Cronbach's alpha applies Bayesian inference to estimate the classical internal-consistency coefficient, yielding a full posterior distribution over alpha rather than a single point estimate. This allows researchers to quantify unce...
Bayesian Differential Item Functioning
Bayesian differential item functioning analysis detects whether a test item behaves differently across demographic or cultural groups — such as males vs. females — after accounting for the underlying ability or trait being measured. It appl...
Bayesian Discriminant Validity
Bayesian discriminant validity assessment evaluates whether two theoretically distinct latent constructs are empirically separable, using posterior distributions and credible intervals rather than single-point null-hypothesis tests. It is a...
Bayesian EFA
Bayesian exploratory factor analysis applies a full probabilistic framework to the common factor model. By placing prior distributions over factor loadings and unique variances, it yields posterior distributions rather than point estimates,...
Bayesian Item Analysis
Bayesian item analysis applies Bayesian inference to estimate item-level statistics — difficulty, discrimination, and distractor effectiveness — by combining observed response data with prior knowledge. It produces full posterior distributi...
Bayesian McDonald's omega
Bayesian McDonald's omega applies Bayesian statistical estimation to the omega reliability coefficient, yielding a full posterior distribution over omega rather than a single point estimate. This provides credible intervals and probabilisti...
Bayesian Measurement Invariance
Bayesian measurement invariance testing evaluates whether a scale's factor loadings and item intercepts are equivalent across groups, using a Bayesian framework that allows parameters to deviate from strict equality by a small, probabilisti...
Bayesian Scale Development
Bayesian scale development applies Bayesian statistical inference to the construction and evaluation of psychometric scales. Rather than relying on single point estimates of item and person parameters, it produces full posterior distributio...
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...
Blatant Dehumanization Scale
The Blatant Dehumanization Scale, also called the Ascent of Man measure, captures the willingness to overtly deny full humanity to an out-group. Developed by Nour Kteily, Emile Bruneau, Adam Waytz, and Sarah Cotterill in 2015, it uses the i...
CAT Cronbach's Alpha
Cronbach's alpha applied to computerized adaptive test (CAT) data estimates internal consistency reliability under the special condition that different examinees receive different subsets of items. Because the classic formula assumes every...
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 Test-Retest Reliability
Computerized adaptive test (CAT) test-retest reliability quantifies the consistency of ability estimates obtained when the same examinees complete a CAT on two separate occasions. Because adaptive algorithms tailor each examinee's item set...
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'...