Statistics
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
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...
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 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...
CFA — Scale Validation
Confirmatory factor analysis is a measurement modelling technique that tests whether a hypothesised factor structure — typically derived from theory or an earlier exploratory analysis — fits observed data from a new sample. Developed by Kar...
Confirmatory factor analysis
Confirmatory factor analysis tests a researcher-specified factor structure against observed data. Unlike exploratory approaches, the researcher decides in advance which indicators load on which latent factor, and the model is evaluated by h...
Cross-Classified Multilevel Models in Education
Cross-classified multilevel models extend hierarchical linear modeling to situations where units belong to two or more groupings that do not nest neatly inside one another. In education, students are often classified by both school and neig...
DIF Analysis
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 Holla...
EFA for Scale Development
Exploratory Factor Analysis for Scale Development is the psychometric application of EFA in which an item pool is administered and the resulting response data are analysed to discover the latent factor structure underlying the items. Origin...
Educational Growth Curve Modeling
Educational growth curve modeling is a longitudinal multilevel technique for describing and explaining how individual students change over time on an outcome such as reading or mathematics achievement. Building on the hierarchical linear mo...
Educational Hierarchical Linear Modeling
Educational hierarchical linear modeling (HLM) is a multilevel regression framework for data in which students are nested within classrooms and classrooms within schools. Formalized for education by Raudenbush and Bryk, it lets the intercep...
Educational Production Function
The educational production function is the economist's framework for relating the inputs of schooling — class size, teacher quality, expenditure, family background — to an output, usually measured achievement. Borrowing the production-funct...
Exploratory Structural Equation Modeling
Exploratory Structural Equation Modeling (ESEM) is a hybrid approach that combines exploratory factor analysis (EFA) with confirmatory factor analysis (CFA) and path modeling, developed by Asparouhov and Muthén (2009). ESEM relaxes restrict...
Fuzzy ANOVA
Fuzzy ANOVA extends classical analysis of variance to fuzzy data where observations and group memberships are imprecise or uncertain. Developed by Viertl and others, Fuzzy ANOVA tests whether fuzzy-valued groups differ significantly while a...
Interrater Reliability
Interrater reliability quantifies the degree to which two or more independent raters produce consistent scores when evaluating the same individuals or products. The family encompasses Cohen's kappa, introduced in 1960 for categorical judgme...