Statistical Methods and Data Analysis
Research articles on statistical methods and data analysis.
- Item Response Theory: How Modern Tests Work
Standardized tests — IQ assessments, college entrance exams, professional certifications — rely on statistical models that most test-takers never learn about.
- Bridging Psychology and Psychometrics
In 2024, Psychometrika ran an unusual exchange. Three senior psychometricians — Klaas Sijtsma, Jules Ellis, and Denny Borsboom — published a focus article arguing that...
- Differential Item Functioning and Response Process
A test item that scores differently for two groups of equally able examinees is called a differential item functioning (DIF) item, and identifying these items is now a...
- Integrating SDT and IRT Models for Mixed-Format Exams
Lawrence T. DeCarlo’s recent article introduces a psychological framework for mixed-format exams, combining signal detection theory (SDT) for multiple-choice items and...
- Rotation Local Solutions in Multidimensional IRT
Multidimensional item response theory (MIRT) extends one-dimensional models like the 2PL or 3PL to test items that load on more than one latent trait.
- Group-Theoretic Symmetries in Item Response Theory
Item response theory (IRT) parameters are not unique. Different parameterizations of the same model fit the data identically, and the choice between them is settled by...
- Bayesian Hierarchical 2PLM with ADVI
Calibrating a two-parameter logistic (2PL) item response theory model on a small or sparse dataset is a recurring practical problem. Maximum-likelihood estimators give...
- Coefficient Alpha and Alternatives in Non-Normal Data
Cronbach’s coefficient alpha is the most-reported reliability statistic in psychology and educational measurement. It is also one of the most-misunderstood.
- Attenuation-Corrected Reliability Estimators
Most psychometrics textbooks teach the classical “correction for attenuation” — Spearman’s century-old technique for estimating what the correlation between two...
- Bayesian SEM Prior Sensitivity
The standard confirmatory factor analysis (CFA) machinery requires the analyst to commit, in advance, to which cross-loadings are exactly zero.
- Missing Data Methods in Educational Testing
Missing data is the rule, not the exception, in educational testing. Examinees skip items they don’t know, run out of time on long tests, encounter technical glitches...
- Item Distributions and Cronbach’s Alpha
Cronbach’s coefficient alpha is the most widely reported reliability statistic in psychology, education, and most other social sciences.
- Factor Retention in Exploratory Factor Analysis
Choosing the number of factors to retain in an exploratory factor analysis is the methodological decision that most determines what the analysis reports.
- Rasch vs Classical Equating in Small Samples
Equating is the procedure that lets two different forms of the same test produce comparable scores. A candidate who scores 70 on Form A should be regarded as having the...
- Estimation Methods and SEM Fit Indices
Structural equation modeling (SEM) reports its goodness of fit through a small set of indices that have, by convention, hardened into thresholds.
- JCCES and GAMA: Multidimensional Scaling Analysis
Cognitive batteries that combine verbal and nonverbal subtests routinely report a single composite score, but the underlying structure — how the subtests relate to each...
- JCCES and GAMA: Cognitive Factor Analysis
Whether the Jouve Cerebrals Crystallized Educational Scale (JCCES) and the General Ability Measure for Adults (GAMA, Naglieri & Bardos, 1997) measure distinct cognitive...
- JCCES and ACT: A Factor Analysis
The American College Test (ACT) is one of the two dominant college-admission examinations in the United States, alongside the SAT. Its four sections — English,...
- Item Parameter Estimation for GGUM
Most item response models are cumulative: the probability that a respondent endorses a higher response category increases monotonically with the latent trait.
- Dimensional Structure of JCCES Math Items
Mathematical problem-solving is not a single cognitive ability — it draws on numerical reasoning, algorithmic computation, applied analytic thinking, spatial...
- JCCES and RIAS Verbal Scale: PCA Analysis
Crystallized intelligence and verbal ability are conceptually overlapping but operationally distinct constructs. The Cattell-Horn theory (Cattell, 1963; Horn & Cattell,...
- JCCES General Knowledge Item Structure Analysis
The General Knowledge (GK) subtest of the Jouve Cerebrals Crystallized Educational Scale (JCCES) measures factual breadth — the accumulated stock of information about...
- Validity and Reliability of the CCAT
The Cerebrals Cognitive Abilities Test (CCAT) is the original three-subtest crystallized-intelligence battery developed in the Cogn-IQ research program.