Mathematics and statistics

Cluster sampling

Cluster sampling, or a cluster sample, is a probability sampling method in which the population is divided into groups called clusters, and units within selected clusters are surveyed.

Coadjoint orbit

A coadjoint orbit is the orbit of a Lie group in the dual of its Lie algebra, carrying a canonical symplectic structure central to Kirillov's orbit method.

Coalgebra

Coalgebra is a mathematical structure dual to an algebra, using comultiplication instead of multiplication, and foundational to Hopf algebras and state-based systems in computer science.

Coarse geometry, also called large-scale geometry, is the branch of mathematics that studies metric spaces viewed from a great distance, where spaces that look alike from far away count as equivalent.

Coastline paradox

The coastline paradox, or coastal paradox, is the observation that a coastline's measured length grows as the measuring unit shrinks, so no single length exists.

Cobordism

Cobordism, also called bordism, is a relation between closed manifolds: two n-dimensional manifolds are cobordant if together they form the boundary of an (n+1)-dimensional manifold, a central idea of algebraic topology.

Cochran–Armitage test

The Cochran–Armitage test, proposed by William Cochran in 1954 and Peter Armitage in 1955, tests whether binomial proportions increase or decrease across ordered levels of an explanatory variable.

Cochran–Mantel–Haenszel test

The Cochran–Mantel–Haenszel (CMH) test is a statistical test of whether two categorical variables are associated after controlling for stratification variables, developed from 1954 and 1959 papers.

Cochran's Q test

Cochran's Q test is a statistical test that checks whether proportions are equal across multiple paired groups, and, in meta-analysis, whether study effect estimates vary more than sampling error alone would explain.

Coding theory

Coding theory, also called code theory, is the branch of mathematics and engineering that designs error-correcting codes; its methods appear in 5G, QR codes, and deep space communication.

Coefficient

A coefficient, or multiplicative factor, is the number multiplying a variable in an algebraic term, such as the 3 in 3x or the leading term of a polynomial.

Coefficient of determination

The coefficient of determination, or R-squared, is a statistic in regression analysis measuring the proportion of variation in a response variable explained by a model's predictors.

Coefficient of variation

The coefficient of variation, or relative standard deviation, is a statistical measure of dispersion, computed as the standard deviation divided by the mean and often expressed as a percentage.

Cofinality

Cofinality, written cf(α), is a set theory concept measuring how hard an ordinal is to approach from below: the least order type of a cofinal subset of it.

Cograph

A cograph, short for complement-reducible graph, is a graph with no induced path on four vertices, introduced by Corneil, Lerchs, and Stewart Burlingham in 1981.

Cohen structure theorem

The Cohen structure theorem is a 1946 result in commutative algebra describing every complete local ring as a quotient of a formal power series ring.

Cohen–Macaulay ring

A Cohen–Macaulay ring, also called a Macaulay ring, is a Noetherian commutative ring in which depth equals Krull dimension locally, a standard measure of how well behaved a ring is.

Cohen's d

Cohen's d is a standardized effect size for the difference between two means, introduced by psychologist Jacob Cohen and the most widely reported standardized mean difference.

Cohen's kappa

Cohen's kappa, also called the kappa coefficient, is a chance-corrected statistic for agreement between exactly two raters classifying subjects into nominal categories; Jacob Cohen introduced it in 1960.

Coherent risk measure

A coherent risk measure assigns a capital-like number to a financial position while satisfying four axioms, including subadditivity, so diversification is never penalized; introduced by Artzner, Delbaen, Eber, and Heath in 1999.

Coherent sheaf

A coherent sheaf is a sheaf of modules over a ringed space that is locally finitely generated with finitely generated relations, introduced by Cartan in 1944 and Serre in 1955.

Coherent sheaf cohomology

Coherent sheaf cohomology, or coherent cohomology, studies coherent sheaves on schemes via the right derived functors of the global-section functor; it was founded in Jean-Pierre Serre's 1955 paper FAC.

Cohort (statistics)

In statistics and epidemiology, a cohort is a group of people with a common experience or exposure, followed over time for new diseases or events.

Coin flipping

Coin flipping, also called coin tossing or heads or tails, is throwing a coin to choose between two alternatives, treated as a random event with even odds.

Coinduction

Coinduction is a proof and definition principle for greatest fixed points, dual to induction, used to reason about infinite and circular objects like streams and concurrent processes.

Cointegration test

A cointegration test is a statistical procedure for determining whether nonstationary time series share a long-run equilibrium relationship, introduced by Engle and Granger in their 1987 Econometrica paper.

Cokernel

The cokernel of a homomorphism f: M → N between modules is the quotient N/im(f), the dual of the kernel, and is zero exactly when f is surjective.

Colimit (category theory)

A colimit in category theory is a universal construction producing, from a diagram, a new object receiving maps from every object in the most economical way; it is the dual of a limit.

Colin de Verdière graph invariant

The Colin de Verdière graph invariant, also called the Colin de Verdière number, is a spectral graph parameter introduced by Yves Colin de Verdière in 1990.