Statistics — Page 3
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Ordinal CFA
Ordinal confirmatory factor analysis (Ordinal CFA) tests a pre-specified factor structure when the observed indicators are ordinal — typically Likert-type survey items. By using polychoric correlations and robust estimators such as WLSMV, i...
Ordinal Cronbach's Alpha
Ordinal Cronbach's alpha is a reliability coefficient computed from polychoric or polyserial correlations rather than Pearson correlations, making it appropriate for Likert-type and other ordinal item response data. It corrects the systemat...
Ordinal EFA
Ordinal exploratory factor analysis discovers latent factors underlying a set of ordinal items — typically Likert scales — by computing polychoric correlations among the items and then applying a weighted least squares estimator. It avoids...
Partial Least Squares Structural Equation Modeling
PLS-SEM is a variance-based approach to structural equation modeling developed by Herman Wold (1985) that estimates latent variable models by maximizing the variance explained in dependent variables. Unlike covariance-based SEM, PLS-SEM is...
Polytomous Confirmatory Factor Analysis
Polytomous confirmatory factor analysis (CFA) tests a pre-specified factor structure when items have three or more ordered response categories (e.g., Likert scales). By working with polychoric correlations and robust estimators such as WLSM...
Polytomous EFA
Polytomous exploratory factor analysis extends standard EFA to ordered categorical (Likert-type) response data by replacing the Pearson correlation matrix with a polychoric correlation matrix. It recovers the latent continuous variable that...
Robust Cronbach's Alpha
Robust Cronbach's alpha adapts the classical internal consistency coefficient to data that violate the assumption of multivariate normality or contain influential outliers. By replacing the conventional sample covariance matrix with a robus...
Robust Exploratory Factor Analysis
Robust exploratory factor analysis discovers the latent factor structure of a set of items using estimation methods that are resistant to outliers and violations of multivariate normality. It applies the same measurement model as standard E...
Robust Test-Retest Reliability
Robust test-retest reliability quantifies how consistently a measure ranks or scores the same individuals across two occasions while protecting the estimate from distortion by outliers and non-normal score distributions. It replaces or supp...
School Effectiveness Modeling
School effectiveness modeling estimates how much, and in what ways, individual schools contribute to student outcomes once differences in what students bring with them are taken into account. Using multilevel (hierarchical) models, it adjus...
Short-Form CFA
Short-form confirmatory factor analysis applies CFA to a reduced subset of items drawn from a longer validated scale, testing whether the abbreviated version preserves the original factor structure with acceptable model fit and reliability....
Short-form Cronbach's alpha
Short-form Cronbach's alpha quantifies the internal consistency reliability of an abbreviated version of a psychological scale. It applies Cronbach's alpha formula to a reduced item set, verifying that the shortened instrument retains suffi...
Student Growth Percentiles
Student growth percentiles (SGPs) describe how much a student grew academically relative to peers with similar score histories. Introduced by Damian Betebenner in 2009, the method fits a series of conditional quantile regressions of a curre...
Test-Retest Reliability
Test-retest reliability quantifies the temporal consistency of a measure by correlating scores obtained from the same participants on two separate occasions. It is a cornerstone of psychometric validation, directly indicating whether a scal...
Value-Added Teacher Evaluation
Value-added teacher evaluation uses longitudinal student test scores to estimate how much individual teachers contribute to their students' achievement growth, net of what students brought into the classroom. Statistically it applies value-...