Statistics — Page 5
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Polytomous Measurement Invariance
Polytomous measurement invariance testing evaluates whether a scale with ordered categorical (polytomous) response options — such as Likert-type items — measures the same latent construct in the same way across two or more groups. It extend...
Polytomous Rasch Model
The Polytomous Rasch Model extends the dichotomous Rasch framework to ordered response scales with three or more categories, such as Likert items or partial-credit tasks. It estimates person ability and item difficulty on the same interval-...
Polytomous Reliability Analysis
Polytomous reliability analysis estimates the internal consistency or precision of measurement for scales composed of items with more than two ordered response categories, such as Likert-type, rating, or partial-credit items. It corrects a...
Polytomous scale development
Polytomous scale development is the systematic construction and validation of measurement instruments whose items have three or more ordered response categories — such as Likert-type, rating, or partial-credit items. It applies polytomous i...
Process Tracing
Process Tracing is a qualitative research method developed by George and Bennett (2005) for studying causal mechanisms and causal chains within individual cases. It involves examining the sequence of events and decision-making processes wit...
Pupillometry
Pupillometry is the measurement of changes in pupil size in response to cognitive, emotional, or perceptual stimuli. The pupil automatically dilates (mydriasis) during mental effort, emotional arousal, or approach-related states, and constr...
Q-Methodology
Q-Methodology is a mixed-methods approach that combines quantitative factor analysis with qualitative interpretation to identify distinct perspectives, viewpoints, or 'factors' shared by groups of people. Introduced by William Stephenson in...
Racial Resentment Scale
The Racial Resentment Scale, developed by Donald Kinder and Lynn Sanders in Divided by Color (1996), measures a modern, symbolic form of racial prejudice in which anti-Black affect is fused with the traditional American value of individuali...
Rasch Model
The Rasch model, introduced by Georg Rasch in 1960, is the simplest member of the Item Response Theory (IRT) family. It assigns a single difficulty parameter to each test item and places both item difficulties and person abilities on the sa...
Redundancy Analysis
Redundancy Analysis (RDA) is a multivariate technique developed by van den Wollenberg (1977) that combines multiple regression and principal component analysis. RDA finds linear combinations of predictor variables that best predict variatio...
Regulatory Focus Questionnaire
The Regulatory Focus Questionnaire (RFQ), developed by Higgins and colleagues in 2001, measures two independent motivational orientations derived from regulatory focus theory: a promotion focus concerned with growth, ideals, gains, and eage...
Repertory Grid
The Repertory Grid is a qualitative-quantitative method derived from Personal Construct Theory that elicits how individuals construe (interpret and evaluate) a domain of interest—people, concepts, events, or objects—through their own idiosy...
Rescorla-Wagner Model
The Rescorla-Wagner Model is a quantitative theory of associative learning that predicts how organisms learn associations between stimuli (e.g., tone and shock in fear conditioning). The model proposes that learning is driven by prediction...
Robust Content Validity
Robust content validity assessment applies outlier-resistant statistical methods to the aggregation of expert panel ratings in content validation studies. By detecting and down-weighting idiosyncratic or extreme rater judgements, it yields...
Robust Differential Item Functioning
Robust differential item functioning analysis detects items that behave differently across demographic groups after matching respondents on the underlying trait, while protecting the procedure against distortion by outliers, model misfit, o...
Robust Discriminant Validity
Robust discriminant validity assessment determines whether distinct latent constructs in a measurement model are sufficiently different from one another. Unlike traditional AVE-based approaches, robust methods such as the Heterotrait-Monotr...
Robust Item Analysis
Robust item analysis applies outlier-resistant statistical methods to the evaluation of individual test or scale items. Instead of classical means and Pearson correlations — both sensitive to extreme scores — it uses trimmed means, Winsoriz...
Robust McDonald's Omega
Robust McDonald's omega estimates the internal consistency reliability of a composite scale using factor-analytic loadings obtained through robust estimation methods (such as MLR or DWLS). Unlike standard omega or Cronbach's alpha, it remai...
Robust Measurement Invariance
Robust measurement invariance testing evaluates whether a psychometric instrument measures the same latent construct in the same way across groups when observed data violate multivariate normality. It adapts standard multi-group CFA sequenc...
Robust Nomological Validity
Robust nomological validity evaluates whether a psychological construct relates to theoretically expected variables in the predicted directions, using statistically robust estimation methods that remain trustworthy when distributional assum...
Rule Space Methodology
Rule Space Methodology (RSM) is a diagnostic classification approach developed by Tatsuoka (1983) that uses Item Response Theory and geometric methods to classify examinees into knowledge states based on their response patterns. Unlike clas...
SCAD Penalized Regression
SCAD (Smoothly Clipped Absolute Deviation) is a variable selection and regularization method developed by Fan and Li (2001) that addresses limitations of L1 penalization (lasso). SCAD uses a non-concave penalty that automatically performs v...
SIBTEST
SIBTEST (Simultaneous Item Bias Test) is a non-parametric method for detecting differential item functioning (DIF) and differential test functioning (DTF) developed by Shealy and Stout (1993). Unlike parametric approaches, SIBTEST does not...
Scale development
Scale development is a structured, multi-step process for creating psychometrically sound measurement instruments that capture latent psychological constructs. It encompasses construct definition, item generation, expert review, exploratory...