Statistics — Page 4
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Ordinal Generalizability Theory
Ordinal generalizability theory extends classical G-theory to the analysis of reliability and measurement error when item responses are ordered categorical (e.g., Likert-type) rather than continuous. It partitions score variance into compon...
Ordinal Item Analysis
Ordinal item analysis evaluates each individual item in a rating-scale or Likert-type instrument using descriptive and correlational statistics suited to ordered categorical response formats. It guides item selection and refinement by flagg...
Ordinal McDonald's omega
Ordinal McDonald's omega is a reliability coefficient designed for Likert-type and other ordinal rating scales. Unlike Cronbach's alpha, it bases its calculation on polychoric correlations among items — capturing the true latent relationshi...
Ordinal Measurement Invariance
Ordinal measurement invariance testing evaluates whether a multi-group confirmatory factor model holds equivalent measurement properties across groups when scale items are ordinal — such as Likert-type response scales. It uses polychoric co...
Ordinal Nomological Validity
Ordinal nomological validity examines whether a construct measured with ordinal items (e.g., Likert-type scales) behaves in theoretically predicted ways within a nomological network — a web of expected relationships with other constructs an...
Ordinal Rasch Model
The ordinal Rasch model extends the dichotomous Rasch framework to items with ordered response categories such as Likert-type scales. It places both persons and items on a shared interval-level metric, enabling principled measurement from o...
Ordinal Reliability Analysis
Ordinal reliability analysis estimates the internal consistency of scales whose items are measured on ordered-category (Likert-type) response formats. By basing computations on polychoric correlations rather than Pearson correlations, it co...
Ordinal Scale Development
Ordinal scale development is the systematic construction and validation of multi-item measurement instruments whose response options form an ordered but not necessarily equal-interval sequence — most commonly Likert-type formats (e.g., 1 =...
Ordinal Test-Retest Reliability
Ordinal test-retest reliability quantifies how consistently an ordinal measurement instrument — such as a Likert-scale questionnaire or a rating tool — ranks or scores the same participants across two separate administrations separated by a...
PCM / GPCM
The Partial Credit Model is an extension of the Rasch measurement framework designed for ordered polytomous items — items whose responses fall into more than two ordered categories, such as partial-credit tasks in performance assessment or...
Polytomous Construct Validity
Polytomous construct validity refers to the evaluation of whether a scale composed of ordered, multi-category items (e.g., Likert or rating-scale items) genuinely measures the intended latent construct. It extends classical validity framewo...
Polytomous McDonald's omega
Polytomous McDonald's omega estimates the internal consistency reliability of a scale composed of ordinal (polytomous) items — such as Likert-type responses — by computing omega from a factor model fitted to the polychoric correlation matri...
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...
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...
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...