Statistics — Page 37
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Mixture Design
Mixture experiment design is a class of constrained experimental design in which the factors are the proportions of components in a blend, subject to the constraint that all proportions sum to one. The framework was formalised by Henry Sche...
Mixture Modeling
Mixture modeling assumes that a population is composed of K unobserved subpopulations, each described by its own probability distribution. The observed data are treated as draws from a weighted combination of these component distributions....
Model Confidence Set
The Model Confidence Set (MCS) is a sequential hypothesis-testing procedure introduced by Hansen, Lunde, and Nason (2011) that identifies the smallest collection of forecasting or predictive models statistically indistinguishable from the b...
Moderated Mediation
Moderated mediation tests whether the indirect effect of an independent variable on an outcome — transmitted through a mediator — differs in strength depending on the level of a moderator variable. It answers the question: for whom, or unde...
Moderation Analysis
Moderation analysis tests whether the effect of a predictor X on an outcome Y changes with the level of a third variable W, the moderator. It is estimated within a regression framework through an interaction term X×W, popularised by Aiken &...
Monte Carlo Simulation with Missing Data
Monte Carlo simulation with missing data combines stochastic simulation — drawing random values from probability distributions — with principled missing-data strategies such as multiple imputation. Instead of discarding incomplete records o...
Mood's Median Test
Mood's median test is a nonparametric procedure that compares the medians of k independent groups by counting how many observations in each group fall above and below the pooled (grand) median, then applying a chi-square test to the resulti...
Moralizing Gods Database Analysis
Moralizing gods database analysis is a cross-cultural quantitative method that codes the presence of moralizing or 'big' supernatural enforcers and measures of social complexity across many historical polities over time, then models their r...
Moran's I
Moran's I is the standard global statistic for detecting spatial autocorrelation: whether nearby locations tend to share similar values. The index ranges from approximately −1 (perfect dispersion) through 0 (spatial randomness) to +1 (perfe...
Moran's I
Moran's I is a global statistic, introduced by Patrick Moran in 1950, that measures whether and how a continuous variable is spatially autocorrelated across mapped units. A positive value signals clustering of similar values, a negative val...
Motivation Scale for Sport Consumption
The Motivation Scale for Sport Consumption (MSSC) is a multidimensional self-report instrument that measures why people consume spectator sport, developed by Galen Trail and Jeffrey James in 2001. Rather than treating sport interest as a si...
Moving Average Model
The Moving Average model of order q — written MA(q) — expresses the current value of a time series as a linear combination of the current and past random shocks (innovations). Unlike the AR model which uses lagged values of the series itsel...
Multi-Armed Bandit
The multi-armed bandit (MAB) is an adaptive experimental framework that allocates trials sequentially across competing arms to minimise cumulative regret while simultaneously learning which arm performs best. Formalised by Robbins in 1952 a...
Multi-State Model
The multi-state model is a generalised survival framework, formalised in the work of Andersen and Keiding and brought to wide biostatistical practice by Putter, Fiocco and Geskus (2007), that models individuals moving through multiple disti...
Multi-group Cronbach's alpha
Multi-group Cronbach's alpha estimates and compares the internal consistency reliability of a scale separately within each of two or more defined subgroups. It is used in cross-cultural, demographic, and comparative psychometric research to...
Multi-group Differential Item Functioning
Multi-group differential item functioning examines whether test or scale items function equivalently across three or more distinct groups — such as gender, ethnicity, or country — after matching respondents on the underlying trait being mea...
Multi-group EFA
Multi-group exploratory factor analysis estimates the latent factor structure of a set of items separately within each of two or more groups and then examines whether the discovered structures are consistent across groups. It is used to exp...
Multi-group Generalizability Theory
Multi-group generalizability theory (MG G-theory) extends classical generalizability theory to estimate and compare variance components — attributable to persons, items, raters, occasions, and their interactions — simultaneously across two...
Multi-group McDonald's omega
Multi-group McDonald's omega estimates and compares the reliability of a scale across two or more distinct groups. Rooted in confirmatory factor analysis, it uses the factor loadings and unique variances from each group's measurement model...
Multi-group Rasch model
The multi-group Rasch model fits the one-parameter logistic item response model simultaneously across two or more distinct groups, testing whether item difficulty parameters are invariant across groups. It is the primary psychometric tool f...
Multi-group Reliability Analysis
Multi-group reliability analysis estimates internal consistency or stability coefficients separately within each group and then formally compares them to determine whether a scale functions with equal precision across populations. It is a f...
Multi-group confirmatory factor analysis
Multi-group confirmatory factor analysis tests whether a measurement model holds equivalently across two or more groups — such as cultures, genders, or time points. By imposing increasingly stringent equality constraints and comparing model...
Multi-group content validity
Multi-group content validity extends the standard content validity index (CVI) procedure by computing and comparing item- and scale-level validity indices across two or more distinct expert panels or subgroups. It ensures that a scale's ite...
Multi-group convergent validity
Multi-group convergent validity examines whether items purported to measure the same latent construct relate strongly to that construct consistently across distinct subgroups such as demographic categories, cultures, or experimental conditi...