Statistical Methods in Psychology: A Researcher’s Guide

Modern psychological research relies on sophisticated statistical methods to measure latent constructs, validate assessments, and draw reliable conclusions from data. From item response theory to structural equation modeling, these techniques form the backbone of psychometric science. This hub indexes our technical articles, accessible to researchers learning new methods and to practitioners who want to understand the tools behind the tests.

For the tests these methods evaluate, see the companion hub on IQ testing and psychological measurement. For the cognitive constructs being measured, see cognitive abilities and intelligence research.

Item response theory: foundations and extensions

Item response theory provides a rigorous probabilistic framework for modeling how examinees respond to test items. These articles cover the core models and their generalizations.

Item response theory: how modern tests work — an accessible introduction to the IRT framework.
Group-theoretic symmetries in item response theory — algebraic structure underlying IRT model invariance.
Rotation local solutions in multidimensional IRT — identifying optimal factor rotations.
Integrating SDT and IRT models for mixed-format exams — combining signal detection and IRT for free-response items.
Item parameter estimation for GGUM — the generalized graded unfolding model.

Computerized adaptive testing and item monitoring

Adaptive testing delivers items tailored to each examinee’s estimated ability, dramatically improving measurement efficiency.

Computerized adaptive testing explained — how modern tests adapt difficulty in real time.
Advanced computerized adaptive testing techniques — item selection, exposure control, and stopping rules.
Sequential GLR tests for online item monitoring — detecting compromised items in operational testing.
Missing data methods in educational testing — principled handling of unanswered items.

Differential item functioning and test equating

Group invariance and cross-form comparability are essential for fair, defensible cognitive assessment.

Differential item functioning and response process — what DIF detects and what it cannot.
Rasch vs. classical equating in small samples — method comparison for low-N test equating.
Continuous norming for cognitive tests — smooth norm development across age or ability.

Reliability theory and coefficient alpha

Reliability is the foundation of measurement. These articles cover the assumptions, alternatives, and corrections of classical reliability coefficients.

Coefficient alpha and alternatives in non-normal data — when alpha breaks and what to use instead.
Item distributions and Cronbach’s alpha — the assumptions underlying alpha.
Attenuation-corrected reliability estimators — correcting validity coefficients for measurement error.
Tellegen-Briggs formula 4 for composite scores — computing reliability of composite measures.
Nonmemory-based performance validity tests — detecting suboptimal effort.

Factor analysis and SEM

Factor-analytic and structural-equation methods recover the latent structure of cognitive measures.

Factor retention in exploratory factor analysis — how many factors to extract.
Estimation methods and SEM fit indices — ML, robust ML, WLSMV, and the fit-index landscape.
JCCES and GAMA: cognitive factor analysis — applied factor analysis on the JCCES.
JCCES and ACT: a factor analysis — relating cognitive measures across instruments.
JCCES Crystallized Index and academic measures — convergent validity of crystallized assessment.

Bayesian methods in psychometrics

Bayesian estimation handles small samples, hierarchical structures, and prior information in ways frequentist methods cannot.

Bayesian hierarchical 2PLM with ADVI — variational inference for the two-parameter logistic model.
Bayesian SEM prior sensitivity — how prior choice influences structural conclusions.
Simulated IRT datasets for psychometric research — tools for method development and testing.

Norming, scaling, and missing data

Practical decisions about test scaling, norms, and incomplete data shape what scores actually mean.

JCCES and GAMA: multidimensional scaling analysis — non-metric scaling of cognitive measures.
Dimensional structure of JCCES math items — scaling analysis of mathematical reasoning items.
JCCES and RIAS verbal scale: PCA analysis — principal component analysis of verbal measures.
JCCES general knowledge item structure — item-level analysis of crystallized knowledge.

Applied psychometric studies

These applications connect statistical method to substantive cognitive research.

JCTI: validity and reliability — psychometric properties of the Jouve-Cerebrals Test of Induction.
Age-based reliability of the JCTI — precision profiles across the lifespan.
JCCES: reliability of the Crystallized Educational Scale — reliability of crystallized ability assessment.
JCFS: assessing nonverbal intelligence — psychometric evaluation of figural sequences.
JCWS: a verbal abilities test — word-similarities measure of crystallized verbal ability.
IAW: assessing verbal intelligence — analogies-based verbal reasoning instrument.
Validity and reliability of the CCAT — psychometric evaluation of the Cerebrals Cognitive Abilities Test, the original three-subtest crystallized battery later revised into the JCCES.
SAT scores and general cognitive ability — factor-analytic decomposition of the SAT.
GALAMM models of cognitive and brain development — latent-variable modeling of longitudinal change.
Eye movement models of decision making — computational modeling of decision processes.

Effect sizes, validity, and meta-science

Beyond specific methods, these articles cover overarching issues in interpreting psychological research.

Effect size vs. p-value explained — why magnitude matters more than significance.
Psychometrics: the science of psychological measurement — the foundational discipline.
Bridging psychology and psychometrics — aligning theory of construct with theory of measurement.
Resistance to online misinformation — cognitive reflection and information evaluation.