Statistics — Page 5
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Multi-group EFA
Multi-group exploratory factor analysis estimates the latent factor structure of a set of items separately within each of two or more groups and then examines whether the discovered structures are consistent across groups. It is used to exp...
Multi-group Generalizability Theory
Multi-group generalizability theory (MG G-theory) extends classical generalizability theory to estimate and compare variance components — attributable to persons, items, raters, occasions, and their interactions — simultaneously across two...
Multi-group McDonald's omega
Multi-group McDonald's omega estimates and compares the reliability of a scale across two or more distinct groups. Rooted in confirmatory factor analysis, it uses the factor loadings and unique variances from each group's measurement model...
Multi-group Rasch model
The multi-group Rasch model fits the one-parameter logistic item response model simultaneously across two or more distinct groups, testing whether item difficulty parameters are invariant across groups. It is the primary psychometric tool f...
Multi-group Reliability Analysis
Multi-group reliability analysis estimates internal consistency or stability coefficients separately within each group and then formally compares them to determine whether a scale functions with equal precision across populations. It is a f...
Multi-group confirmatory factor analysis
Multi-group confirmatory factor analysis tests whether a measurement model holds equivalently across two or more groups — such as cultures, genders, or time points. By imposing increasingly stringent equality constraints and comparing model...
Multi-group content validity
Multi-group content validity extends the standard content validity index (CVI) procedure by computing and comparing item- and scale-level validity indices across two or more distinct expert panels or subgroups. It ensures that a scale's ite...
Multi-group convergent validity
Multi-group convergent validity examines whether items purported to measure the same latent construct relate strongly to that construct consistently across distinct subgroups such as demographic categories, cultures, or experimental conditi...
Multi-group discriminant validity
Multi-group discriminant validity assessment tests whether constructs measured by a scale are empirically distinct not just in one sample but consistently across two or more groups (e.g., cultures, genders, age cohorts). It extends standard...
Multi-group item analysis
Multi-group item analysis computes classical item statistics — difficulty, discrimination, and corrected item-total correlations — separately for each subgroup in a sample and then compares those statistics across groups. It is a standard d...
Multi-group item response theory
Multi-group item response theory fits IRT models simultaneously across two or more defined groups — such as males and females, or different cultural samples — to determine whether item parameters are invariant across those groups. It is the...
Multi-group measurement invariance
Multi-group measurement invariance testing examines whether a latent construct is measured in the same way across two or more distinct groups — such as cultures, genders, or age cohorts. It is a prerequisite for meaningful group comparisons...
Multi-group scale development
Multi-group scale development constructs and validates a measurement scale simultaneously across two or more distinct populations or groups. The approach integrates standard item generation and factor-analytic procedures with a systematic h...
Multi-group test-retest reliability
Multi-group test-retest reliability evaluates whether a measure produces stable scores across time separately for two or more defined groups — such as different genders, age cohorts, or clinical populations — and determines whether the degr...
Multilevel CFA
Multilevel confirmatory factor analysis tests a pre-specified factor structure while simultaneously accounting for the non-independence of observations caused by clustered data. It decomposes item variance into within-group and between-grou...
Multilevel Content Validity
Multilevel content validity extends the classical content validity framework to settings where items, raters, or respondents are nested within hierarchical structures — such as students within schools, patients within clinics, or items rate...
Multilevel Convergent Validity
Multilevel convergent validity evaluates whether items or scales intended to measure the same construct show coherent, strong associations at each level of a nested data structure — within individuals, within groups, and between groups. It...
Multilevel Differential Item Functioning
Multilevel DIF analysis detects whether individual test or survey items function differently across groups when respondents are clustered within higher-level units — such as students nested in schools, employees in organizations, or patient...
Multilevel Discriminant Validity
Multilevel discriminant validity evaluates whether theoretically distinct constructs are empirically separable when data are nested within higher-level units such as teams, schools, or organizations. It extends single-level discriminant val...
Multilevel EFA
Multilevel exploratory factor analysis uncovers latent factor structures simultaneously at two or more levels of a data hierarchy — for example, both within individuals and between groups — without imposing a fixed structure in advance. It...
Multilevel Generalizability Theory
Multilevel generalizability theory extends classical G-theory to measurement designs where observations are nested within higher-level units — for example, items nested within raters, or students nested within classrooms. It decomposes scor...
Multilevel McDonald's omega
Multilevel McDonald's omega estimates reliability at two distinct levels — within groups and between groups — for scales administered to individuals nested in clusters such as classrooms, teams, or organizations. It accounts for the non-ind...
Multilevel Measurement Invariance
Multilevel measurement invariance testing evaluates whether a latent construct is measured equivalently both within clusters (e.g., individuals within teams) and between clusters (e.g., team-level aggregates). It extends standard measuremen...
Multilevel Rasch Model
The multilevel Rasch model extends the standard Rasch model to data with a nested structure — for example, students within classrooms within schools — by embedding person ability parameters inside a hierarchical linear model. It yields item...