Statistics — Page 11
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Characteristics Approach to Population Aging
The characteristics approach reconceptualizes what it means to be 'old' by measuring age through people's characteristics rather than the number of years since birth. Developed by Warren Sanderson and Sergei Scherbov and set out comprehensi...
Chi-Square Power Analysis
Chi-square power analysis is a prospective calculation that determines the minimum sample size required — or the statistical power achievable with a given sample — for chi-square independence tests or goodness-of-fit tests. It rests on Cohe...
Chi-square goodness-of-fit test
The chi-square test of independence is a nonparametric hypothesis test that determines whether two categorical variables are statistically associated or independent of one another. Introduced by Karl Pearson in 1900, it remains the standard...
Chi-square test
The chi-square test of independence is a nonparametric hypothesis test that examines whether two categorical variables are associated by comparing observed and expected frequencies in a cross-tabulation. It rests on the chi-square criterion...
Chow Test
The Chow test, introduced by Gregory Chow in 1960, checks whether the coefficients of a linear regression are the same across two subsamples — that is, whether a structural break occurs at a known point such as a policy change, crisis, or r...
Circular Migration Measurement
Circular migration measurement provides a quantitative grammar for distinguishing migrants who move back and forth across a border from those who settle permanently or return for good. Constant and Zimmermann's 2011 study proposed measuring...
Clark Density Model
The Clark density model is the classic empirical description of how urban population density falls with distance from the city centre, formulated by the economist Colin Clark in 1951. It states that density declines exponentially outward fr...
Cluster Analysis
Cluster analysis is a family of unsupervised multivariate techniques that partition a set of objects or observations into internally homogeneous, mutually distinct groups — clusters — based on measured characteristics, without any prior kno...
Cluster-Robust Standard Errors
Cluster-robust standard errors correct the variance of regression coefficients when observations are correlated within clusters such as schools, hospitals, or regions. The clustered sandwich estimator grew out of Liang & Zeger's (1986) gene...
Co-kriging
Co-kriging is a geostatistical interpolation technique that predicts the spatial distribution of a primary variable by leveraging its spatial cross-correlation with one or more secondary (co-) variables. It extends ordinary kriging to multi...
Coale-Demeny Model Life Tables
The Coale-Demeny regional model life tables are a system of standard age patterns of mortality, distilled from hundreds of empirical life tables into four regional families — North, South, East, and West — each indexed by a mortality level....
Coale-McNeil Marriage Model
The Coale-McNeil model is a parametric description of how first marriages are distributed by age. Ansley Coale and Donald McNeil showed in 1972 that the age pattern of first marriage in widely different populations has a common shape, captu...
Coale-Trussell Model
The Coale-Trussell model is a two-parameter parametric description of the age pattern of marital fertility, introduced by Ansley Coale and James Trussell in 1974. It expresses observed age-specific marital fertility as a standard natural-fe...
Cochran Q Test
Cochran's Q test is a nonparametric hypothesis test introduced by William G. Cochran in 1950 for comparing proportions across three or more related binary measurements. It extends McNemar's test to the multiple-condition case and is the met...
Cohen's Kappa
Cohen's kappa (κ) is a statistical measure of inter-rater reliability for categorical classifications, introduced by Jacob Cohen in 1960. Unlike simple percent agreement, kappa corrects for the level of agreement that would be expected pure...
Cointegration Test
The cointegration test examines whether non-stationary time series that each contain a unit root share a stable long-run equilibrium relationship. The single-equation residual approach was introduced by Engle and Granger (1987) and the syst...
Cokriging
Cokriging extends kriging to use one or more correlated secondary variables to improve prediction of a primary variable. When the variable of interest is sparsely sampled but a related, cheaper-to-measure variable is densely sampled, cokrig...
Competing Risks Analysis
Competing risks analysis, formalized by Fine and Gray in 1999, is a survival analysis framework for settings where a subject can experience one of several mutually exclusive event types. The key quantity is the cumulative incidence function...
Component GARCH
Component GARCH decomposes conditional variance into transitory (short-term) and permanent (long-term) components with different dynamics, allowing flexibility in capturing volatility behavior at multiple frequencies. Introduced by Engle an...
Compositional Data Analysis
Compositional Data Analysis (CoDA) is a branch of multivariate statistics designed for data that represent parts of a whole — proportions, percentages, or concentrations that sum to a constant. Introduced by John Aitchison in his landmark 1...
Condition Index
The Condition Index, introduced by Belsley, Kuh, and Welsch (1980), is a scalar measure derived from singular value decomposition of the scaled regressor matrix. It quantifies the degree of near-linear dependence among predictors in ordinar...
Conditional Geostatistical Simulation
Conditional Geostatistical Simulation — most commonly implemented as Sequential Gaussian Simulation (SGS) — generates multiple stochastic realizations of a spatial random field that are each consistent with observed sample data and with a f...
Conditional Logit
The Conditional Logit Model, introduced by Daniel McFadden in 1974, is a discrete-choice econometric model designed to explain an individual's selection among a finite set of mutually exclusive alternatives. Unlike multinomial logit, it use...
Conditional Value-at-Risk
Conditional Value-at-Risk (CVaR), also called Expected Shortfall, is a coherent tail-risk measure that quantifies the conditional expectation of losses beyond the Value-at-Risk threshold. It was introduced for optimization by Rockafellar an...