Experimental Design & Statistics

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431 domain-specific abstractions whose origin domain is Experimental Design & Statistics. They span 339 subdomains — sort by that column to group them, or click any subdomain to filter to it.

Abstraction	Subdomain	Description
68–95–99.7 rule	—	The normal-distribution rule that about 68%, 95%, and 99.7% of probability lies within one, two, and three standard deviations of the mean.
Admissible Decision Rule	Statistical Decision Theory	In statistical decision theory, an admissible decision rule is a rule for making a decision such that there is no other rule that is always "better" than it (or at least sometimes better and never worse), in the precise sense of "better" defined below.
Analytic and enumerative statistical studies	Statistical Quality Improvement	Deming’s distinction between studies estimating a defined finite population and studies learning how a continuing process will behave under future conditions.
Ancestral graph	Graphical Models	A mixed graph using directed, bidirected and undirected edges to encode conditional independences left by latent-variable marginalization and selection conditioning in a DAG.
Anchor test	PsychometricsTest Equating	In psychometrics, an anchor test is a common set of test items administered in combination with two or more alternative forms of the test with the aim of establishing the equivalence of the test scores on the alternative forms.
Anderson–Darling test	Goodness of Fit Testing	Test a sample’s agreement with a specified continuous distribution by integrating squared empirical-CDF deviations with extra weight in the tails.
Antecedent variable	Causal Analysis and Social Statistics	A variable temporally or causally prior to an explanatory and outcome variable that can account for some or all of their observed association.
Approximate Bayesian Computation	Bayesian ComputationLikelihood Free Inference	A family of likelihood-free Bayesian methods that simulates data under proposed parameters and approximates a posterior from closeness to observed summaries.
Arbia's law of geography	Spatial Statistics	The geographic proposition that observations aggregated at coarser spatial resolution tend to appear more mutually related than observations at finer resolution.
Area chart	Statistical Graphics and Data Visualization	A quantitative graphic that plots a line against an ordered axis and fills the region to a baseline, optionally stacking multiple series to show composition over time or another continuum.
Asymptotic theory (statistics)	Large Sample Theory	The large-sample framework that studies limiting distributions, consistency and efficiency of estimators and tests as sample size tends to infinity.
Atomistic Fallacy	Multilevel Inference and Research Validity	The inferential error of reading a within-individual relationship directly onto a group or population, ignoring the contextual variance operating only at the group level — the mirror image of the ecological fallacy.
Attenuation Bias	Regression and Measurement Error	The systematic shrinkage of an OLS regression coefficient toward zero caused by classical random noise in the regressor — the estimate equals the true slope times the reliability ratio, a known-sign distortion invertible by dividing out that ratio or instrumenting.
Augmented Dickey–Fuller Test	Time Series AnalysisUnit Root Testing	A regression-based time-series hypothesis test whose null is a unit root, augmenting the Dickey–Fuller equation with lagged differences to absorb serial correlation under a declared deterministic specification and lag order.
Autoregressive Integrated Moving Average	Time Series Analysis	A time-series model family that combines differencing with autoregressive dependence and dependence on current and past innovations.
Balanced repeated replication	Survey Sampling and Variance Estimation	A replicate-weight variance estimator for complex surveys that repeatedly selects one primary sampling unit from each paired stratum according to a balanced sign matrix.
Bar chart	Statistical GraphicsData Visualization	A bar chart or bar graph is a chart or graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that they represent.
Barnardisation	Official StatisticsStatistical Disclosure Control	A statistical-disclosure-control method that pseudo-randomly perturbs nonzero interior table counts by plus one, zero or minus one according to a fixed probability rule before recomputing totals.
Bayes classifier	Statistical LearningClassification Theory	The decision rule that assigns each feature vector to the class with greatest posterior probability, minimizing expected classification loss when the true class distributions and loss function are known.
Bayesian Interpretation of Kernel Regularization	Statistical Machine LearningConnections Between RKHS Regularization and Gaussian Process Regression	The parameter-matched correspondence in which RKHS-norm-regularized least squares and Gaussian-process regression share a kernel matrix and yield the same point predictor, while retaining different inferential commitments.
Bayesian linear regression	Bayesian Statistics	A linear conditional model that combines a likelihood for outcomes with prior distributions over coefficients and noise parameters to obtain posterior inference and prediction.
Bayesian model reduction	Bayesian Statistics	A method deriving evidence and posterior parameters for models with altered priors from a previously fitted full Bayesian model.
Bayesian Optimal Mechanism	Bayesian Mechanism DesignOptimal Mechanisms Under Incomplete Information	A designer chooses an incentive-compatible mechanism that maximizes a declared expected objective under a common prior over agents' private types.
Benford's Law	Descriptive Statistics	Score a dataset's honesty by checking whether its leading digits follow the fixed logarithmic curve log₁₀((d+1)/d) — about 30% start with 1, only 5% with 9 — that scale-spanning multiplicative data must obey.
Benjamini–Hochberg Procedure	Multiple Testing	A step-up rule that sorts m p-values and rejects through the largest rank k where p(k) ≤ (k/m)·α, bounding the false discovery rate — the expected proportion of false rejections among discoveries — rather than the probability of any false positive.
Best linear unbiased prediction	Linear Mixed Models	The minimum-mean-square-error predictor among estimators linear in observations and unbiased for a target random effect under a specified linear mixed model.
Bhattacharyya distance	Statistical Distance	The negative logarithm of the Bhattacharyya coefficient, quantifying overlap between two probability distributions.
Big O in probability notation	Asymptotic StatisticsProbability Theory	The order in probability notation is used in probability theory and statistical theory in direct parallel to the big O notation that is standard in mathematics.
Binary classification	Statistical LearningSupervised Classification	Assign observations to exactly two declared classes through a learned or specified decision rule, keeping scores, thresholds, reference labels, asymmetric errors, prevalence, and evaluation population distinct.
Binomial Proportion Confidence Interval	Interval EstimationCategorical Data	Bound a common binary-trial success probability from a success count using a stated interval rule and repeated-sampling coverage.
Binomial Proportion Estimation	Statistical Estimation	Estimate an unknown binary-event probability from a success count under a declared binomial model, purpose and sampling-uncertainty account.
Binomial regression	Generalized Linear Models	Model a binomial response by linking each observation's success probability to predictors, keeping trial denominators, link choice, variance assumptions, and overdispersion diagnostics explicit.
Binomial test	Hypothesis TestingExact Tests	Binomial test is an exact test of the statistical significance of deviations from a theoretically expected distribution of observations into two categories using sample data.
Biplot	Multivariate Statistics and Visualization	A joint low-dimensional display of observations and variables from a data matrix, typically overlaying row scores with column loadings derived from a matrix factorization.
Biweight midcorrelation	Robust Statistics	A robust correlation measure that centers each variable at its median and downweights observations far from the median using a redescending biweight.
Bonferroni Correction	Multiple Testing	Control the family-wise probability of any false rejection across m tests by comparing each p-value with alpha/m, or equivalently multiplying each p-value by m, without requiring independence.
Bootstrapping populations	Algorithmic InferenceResampling Methods	A parametric algorithmic-inference method that generates parameter replicas compatible with an observed sample and plugs them into a model family to form candidate populations.
Box–Muller Transform	Computational StatisticsNormal Random Variate Generation	Convert two independent uniform variates into two independent standard-normal variates by assigning an exponential radial law and a uniform angle, then projecting the resulting point onto Cartesian axes.
Brown–Forsythe test	—	A robust test of equality of group variances obtained by applying one-way ANOVA to absolute deviations from group medians.
Bubble Chart	Statistical GraphicsMultivariate Quantitative Visualization	A trivariate scatterplot in which each observation's horizontal and vertical variables determine a circular mark's center while a third quantitative variable determines the mark's area under a disclosed size scale.
C-chart	Attribute Control Charts	Monitor the count of nonconformities in constant-size inspection units against Poisson-based center and control limits.
Canberra Distance	Multivariate AnalysisDissimilarity Measures	A coordinatewise distance between real vectors defined by summing |p_i−q_i|/(|p_i|+|q_i|), with a zero contribution when both coordinates are zero, thereby emphasizing relative differences near zero.
Canonical correlation	Multivariate Analysis	In statistics, canonical-correlation analysis (CCA), also called canonical variates analysis, is a way of inferring information from cross-covariance matrices.
Carryover Effect	—	The validity threat in crossover and within-subject designs where residual influence from an earlier treatment persists into a later measurement window, biasing the contrast — its magnitude set by the unit's relaxation time against the inter-treatment gap.
Categorical Variable	Descriptive StatisticsData Modeling	A variable that assigns observation units to declared category levels whose labels do not themselves measure arithmetic distance.
Causal Inference	Causal Inference	Infer the effect of changing X on Y from data by fixing a causal estimand and defending an identification design or assumption that separates that effect from noncausal association, then quantify its uncertainty and scope.
Chartjunk	Data VisualizationStatistical GraphicsVisualization Critique	Unnecessary or distorting visual material in a data graphic that impedes comprehension of the encoded information.
Chauvenet's criterion	Classical Outlier Rejection	Flag a single extreme observation when, under a fitted normal-error model, the expected number of sample observations at least as far from the mean is below one half.
Chinese restaurant process	Bayesian Nonparametrics	An exchangeable partition process in which each arriving item joins an existing block in proportion to its size or starts a new block with parameter-controlled probability.
Classical XY model	Statistical Mechanics	A lattice spin model whose sites carry planar unit vectors coupled by orientation-dependent interaction energy.
Coefficient of variation	—	A dimensionless relative-dispersion statistic equal to standard deviation divided by mean, interpreted only where the measurement scale and nonzero mean make the ratio meaningful.
Cohort Effect	Age Period Cohort Analysis	An observed outcome difference associated with membership in groups defined by a shared birth or entry interval, kept distinct from aging, period shocks, and any unproven causal account of the cohort contrast.
Cokurtosis	Multivariate StatisticsHigher Order Comoments	Measure fourth-order joint variation by taking standardized expectations of products containing four centered random-variable factors, retaining how extreme deviations co-occur beyond covariance and coskewness.
Collider (Causal Graph)	Causal InferenceCausal Directed Acyclic Graphs	A path-relative node where arrowheads converge, blocking that graph path until conditioning on the node or one of its descendants can activate the path and induce dependence.
Collinearity Inflation	Statistics and Regression Inference	The pathological ballooning of individual regression-coefficient variance when predictors carry overlapping information — a near-singular predictor cross-product matrix that degrades per-predictor attribution while leaving joint prediction untouched, unfixable by more data.
Combinatorial Meta-Analysis	Meta Analysis	Combinatorial meta-analysis (CMA) is the study of the behaviour of statistical properties of combinations of studies from a meta-analytic dataset (typically in social science research).
Completely randomized design	Design of Experiments	In the design of experiments, completely randomized designs are for studying the effects of one primary factor without the need to take other nuisance variables into account.
Complex Wishart distribution	Matrix ProbabilityMultivariate Statistics	In statistics, the complex Wishart distribution is a complex version of the Wishart distribution.
Computerized adaptive testing	PsychometricsAdaptive Assessment	Computer-administered assessment that updates an examinee ability estimate after each response and selects subsequent items to maximize information subject to content, exposure and stopping constraints.
Concentration parameter	Distribution Shape Parameters	A distribution-family parameter controlling how tightly probability mass clusters around a direction, center or base distribution without necessarily changing that center.
Concordance correlation coefficient	Measurement Agreement	An agreement coefficient combining Pearson correlation with penalties for differences in mean and scale between two measurements.
Conditionality principle	Foundations of Statistical Inference	The most well-known conditionality principle is the principle of statistical inference that Allan Birnbaum formally defined and studied in an article in the Journal of the American Statistical Association, .
Confirmatory factor analysis	PsychometricsFactor Analysis	In statistics, confirmatory factor analysis (CFA) is a special form of factor analysis, most commonly used in social science research.
Congruence coefficient	Multivariate StatisticsFactor Analysis	In multivariate statistics, the congruence coefficient is an index of the similarity between factors that have been derived in a factor analysis.
Consistency (statistics)	Statistical Asymptotics	An asymptotic property in which a statistical estimator, test, interval, or other procedure approaches the correct target or decision as sample information grows.
Content validity	Psychometrics	The extent to which a measure's items adequately represent every relevant facet of its intended construct or content domain.
Continuous variable	Variable TypesMeasurement Scales	A quantitative variable able to take every real value between any two attainable values within the interval under consideration.
Control chart	Statistical Process ControlQuality Control	Shewhart, or process-behavior charts) are graphical plots used in statistical process control (SPC) to determine whether a manufacturing or business process is in a state of statistical control.
Control variates	Computational Statistics	A Monte Carlo variance-reduction method that adjusts an estimator using correlated quantities whose expectations are known.
Controlling for a variable	Causal Inference and Statistics	A design or analysis operation that compares or models observations at fixed or adjusted values of a variable to block a specified noncausal association, with validity determined by the causal structure.
Convenience Sampling	Survey MethodologyNonprobability Sampling	A nonprobability recruitment method in which ease of reaching eligible units, rather than a target-population probability design, primarily determines who enters a study.
Cophenetic correlation	BiostatisticsCluster Analysis	In statistics, and especially in biostatistics, cophenetic correlation (more precisely, the cophenetic correlation coefficient) is a measure of how faithfully a dendrogram preserves the pairwise distances between the original unmodeled data points.
Correct sampling	Sampling TheoryParticulate Material Sampling	In Gy's sampling theory, a material-sampling condition in which every particle in the target population has the same nonzero probability of inclusion in the sample.
Correlation ratio	—	An effect-size measure equal to the square root of between-category variance divided by total variance, detecting nonlinear mean association.
Correspondence analysis	Multivariate Statistics	A dimension-reduction and visualization method for contingency tables using chi-square geometry to jointly map row and column profiles.
Counternull	Hypothesis TestingEffect Size Reporting	A nonnull effect value or set that matches a designated null's p-value under a specified test of the observed data.
Covariance operator	Functional Probability and Statistics	The linear operator encoding second-order variation of a random element by mapping a direction to its expected covariance-weighted displacement.
Covariate	Regression Analysis	Depending on the context, an independent variable is sometimes called a "predictor variable", "regressor", "covariate", "manipulated variable", "explanatory variable", "exposure variable" (see reliability theory), "risk factor" (see medical statistics), "feature" (in machine learning and pattern recognition) or "input variable".
Cramér–Rao Estimator Efficiency	Estimation TheoryParametric Inference	Compare an unbiased scalar estimator's variance with its regular-model Cramér–Rao information bound, under explicit conditions.
CUSUM	Statistical Process ControlSequential Analysis	A sequential change-detection method that accumulates signed deviations from a reference value, resets or branches according to a declared rule, and signals when the cumulative evidence crosses a decision threshold.
Cuzick–Edwards Test	Spatial StatisticsSpatial Epidemiology	A case-control nearest-neighbor significance test for detecting spatial clustering of cases within an already nonuniform background population represented by control locations.
D'Agostino's K-squared test	Normality TestingHypothesis Testing	An omnibus sample-normality test that transforms sample skewness and kurtosis into approximately standard-normal components and sums their squares, testing an i.i.d. Gaussian null specifically against skewness and tail/peakedness departures.
Data Augmentation	Bayesian ComputationMissing Data	Data augmentation is a statistical technique which allows maximum likelihood estimation from incomplete data.
Data editing	Survey MethodologyOfficial Statistics	Data editing is defined as the process involving the review and adjustment of collected survey data.
Davis distribution	Statistical DistributionsIncome Size Models	A three-parameter continuous income distribution on x>μ with a Planck-like exponential denominator and Pareto upper tail, introduced by Harold T. Davis in 1941.
Dendrogram	Cluster AnalysisHierarchical Clustering	A dendrogram is a tree diagram that represents nested grouping or branching relations, especially the sequence of cluster merges or splits in hierarchical clustering.
Detection limit	Measurement Science	The smallest signal or corresponding quantity distinguishable from background under a declared decision rule and error criterion.
Determining the number of clusters in a data set	Cluster Analysis and Unsupervised Learning	The model-selection problem of choosing a clustering resolution or number k that balances within-cluster fit, separation, stability, complexity, domain meaning, and intended use.
Deviance (statistics)	Statistical Modeling and Generalized Linear Models	A likelihood-based goodness-of-fit quantity comparing a fitted statistical model with a saturated model, conventionally twice their maximized log-likelihood difference.
Deviance Information Criterion	Bayesian Model Comparison	Compare Bayesian hierarchical models by adding posterior mean deviance to an effective-complexity penalty derived from posterior deviance, using quantities readily estimated from MCMC draws.
DFFITS	Regression DiagnosticsInfluence Analysis	A regression influence diagnostic measuring the studentized change in an observation's fitted value when that observation is omitted from model estimation.
Dichotomous Statistical Thinking	Interpretation of Statistical EvidenceNull Hypothesis Significance Testing	The interpretive error of treating a continuous or uncertain statistical result as if a threshold created a sharp evidential divide, so nearly identical values receive categorically different scientific conclusions.
Difference-in-Differences	Causal Inference	Estimate a causal effect from observational data by subtracting the control group's before-after change from the treatment group's, netting out time-invariant unit confounders and common time trends — valid only if parallel trends holds.
Differential effects	Causal InferenceObservational Treatment Comparison	In observational causal comparison, the outcome contrast produced by applying one treatment rather than another, distinguished from differential assignment bias that can mimic that contrast.
Differential item functioning	PsychometricsMeasurement Invariance	A psychometric condition in which people from different groups with the same level of the measured trait have different probabilities of an item response.
Dilution assay	Bioassay StatisticsDose Response Analysis	The term dilution assay is generally used to designate a special type of bioassay in which one or more preparations (e.g. a drug) are administered to experimental units at different dose levels inducing a measurable biological response.
Directional symmetry (time series)	Forecast EvaluationDirectional Accuracy	A forecast-accuracy statistic equal to the percentage of successive periods in which predicted and observed changes have the same sign.
Dirichlet negative multinomial distribution	Multivariate Count DistributionsCompound Distributions	A multivariate count law formed by Dirichlet-mixing negative-multinomial category probabilities.
Discrepancy function	Structural Equation Modeling	A scalar covariance-mismatch objective minimized when fitting a structural equation model.
Distribution-free control chart	Statistical Process Control	A statistical process-monitoring chart whose in-control performance does not depend on a specified underlying process distribution.
Donsker classes	Empirical Process Theory	Classes of measurable functions for which the centered empirical process converges weakly in a uniform-function space to a tight Gaussian limit.
Ecological Correlation	Aggregation and Inference Fallacies	A correlation computed on aggregated group-level units that need not equal — and can reverse the sign of — the individual-level correlation, so it warrants no claim about the individuals inside the groups.
Ecological Inference Problem	Aggregation and Inference Fallacies	Recover individual-level joint distributions from group-level marginal totals, a many-to-one inverse problem where the data alone only pin the answer to the Duncan-Davis bounds and any tighter estimate rests on an explicit, contestable identifying assumption.
Ecological regression	Quantitative Social Science	Regression on aggregate units used to estimate relationships or subgroup behavior from group-level totals.
Eigenstate Thermalization Hypothesis	Quantum Statistical MechanicsThermalization in Isolated Many Body Systems	A quantum-statistical ansatz in which few-body observable matrix elements become smooth thermal functions on the energy diagonal and entropy-suppressed fluctuations off it, allowing individual eigenstates of generic isolated many-body systems to reproduce equilibrium predictions.
Empirical Bayes method	Hierarchical and Compound Decision Methods	Estimate a shared prior distribution or its hyperparameters from the same ensemble of observations and then perform Bayesian-style shrinkage or posterior inference conditional on that estimate.
Empirical likelihood	—	A nonparametric likelihood method that assigns probabilities to observed sample points and maximizes their product subject to estimating-equation constraints.
Empirical probability	—	An event-probability estimate given by its observed relative frequency in a finite sample of trials.
Endogeneity	Causal Inference and Econometrics	The condition in which a regressor is correlated with a model's error term — through confounding, simultaneity, or measurement error — so OLS coefficients are biased and inconsistent for the causal effect, collapsing the coefficient's causal reading while leaving its predictive one intact.
Energy distance	Mathematical Statistics	A metric between probability distributions built from expected pairwise Euclidean distances within and across independent samples.
Estimation of Covariance Matrices	Multivariate Statistical InferenceCovariance Estimation	Inferring a population covariance matrix from multivariate samples using an estimator whose assumptions, conditioning, and error criterion are made explicit.
Estimator	Estimation Theory	In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished.
EWMA chart	Statistical Quality ControlStatistical Process Monitoring	Monitor a time-ordered process by plotting a recursively updated exponentially weighted statistic against model-based control limits, retaining geometrically decreasing memory to improve sensitivity to sustained small shifts.
Exact test	Statistical Inference	A hypothesis test whose null distribution and resulting type-I error control are derived without an asymptotic approximation under the stated sampling model.
Exchangeable random variables	Probability and Bayesian Statistics	A finite or infinite sequence whose joint probability law is invariant under every finite permutation of its indices.
Expectation–Maximization Algorithm	Maximum LikelihoodIncomplete Data	An iterative likelihood-fitting method that alternates conditional expectation over hidden data with maximization of the resulting complete-data objective.
Exploratory data analysis	Exploratory Analysis	Exploratory data analysis denotes approach of analyzing data sets in statistics within statistics.
Exponentiated Weibull distribution	Probability Distributions	A positive continuous distribution formed by raising the Weibull cumulative distribution function to an additional positive shape parameter.
External Validity	Research Design and Validity Theory	The warrant by which an effect estimated in one study setting can be expected to hold in a target setting outside it — holding conditional on every effect-modifying feature that differs between the two being matched or adjusted.
Extreme value theory	Extreme Value Analysis	A branch of statistics modeling the limiting behavior and tail risk of unusually large or small observations, especially block maxima and threshold exceedances.
F-test of equality of variances	Statistical Testing	A parametric hypothesis test that compares two independent normal-population variances using the ratio of their sample variances.
Factor Analysis	—	A latent-variable statistical model explains covariance among observed variables through fewer common factors, variable-specific loadings, and residual variation while making rotational and identification choices explicit.
Factor Regression Model	Latent Variable ModelsFactor Analysis	A multivariate latent-factor model that represents each observation as the sum of loadings on unobserved factors, regression effects from observed design variables, an intercept, and residual error.
False confidence theorem	Uncertainty Quantification and Inferential Validity	Show that a continuous data-dependent additive probability distribution can, for some false assertion, assign arbitrarily high belief with high sampling probability, motivating assertion-wise validity checks.
False coverage rate	Multiple ComparisonsSelective Inference	The expected proportion of selected confidence intervals that fail to contain their corresponding true parameters, controlled to address selective reporting in multiple-parameter inference.
False Discovery Rate	Multiple Testing	The expected proportion of false rejections among all rejected hypotheses, conventionally V/max(R,1), used as an at-scale error criterion that accepts a controlled fraction of false discoveries in exchange for power.
False Positive Rate	Binary ClassificationDiagnostic Testing	The fraction of actual negatives incorrectly called positive by a fixed binary decision rule: FP divided by FP plus TN, when that denominator is nonzero.
Family-Wise Error Rate	Multiple Hypothesis Testing	The probability that a declared family of simultaneous hypothesis tests contains at least one false rejection, with weak or strong control determined by which configurations of true nulls are covered.
Field Experiment	Experimental Design	Field experiments are experiments carried out outside of laboratory settings.
File Drawer Problem	Meta Research and Publication	Recognize that studies with null results disproportionately go unpublished while significant ones enter the literature, so any synthesis treating the published record as the full population of conducted research systematically overestimates effect sizes toward the filter.
First-Hitting-Time Model	Survival Analysis	A model that represents an event time as the first instant a latent stochastic process reaches or crosses a specified boundary, translating path dynamics into a distribution of survival and failure times.
Fisher Consistency	Estimation Theory	A population-level calibration property requiring an estimator or decision rule, viewed as a functional, to recover the target parameter or Bayes-optimal action when applied to the true data-generating distribution.
Fisher information	Mathematical Statistics and Information Geometry	The expected squared score, or negative expected log-likelihood curvature under regularity conditions, measuring local sensitivity of a probability model to its parameter.
Five-number summary	Descriptive StatisticsRobust Summaries	Compress a univariate ordered dataset into minimum, first quartile, median, third quartile, and maximum, exposing center, spread, skew, and extremes while remaining dependent on the chosen quartile convention.
Floor Effect	—	An instrument or scale compresses distinct low-end target states at its minimum, erasing downward discrimination and attenuating observed differences or change.
Focused Information Criterion	Statistical Model Selection	Select a candidate statistical model by the estimated risk of its estimator for a declared focus parameter, allowing the preferred model to change when the inferential target changes.
Folded-t and half-t distributions	Folded Distributions	Nonnegative distributions obtained by taking the absolute value of a Student-t variate, with the half-t arising from a centered symmetric t distribution restricted or folded at zero.
Forecast bias	ForecastingForecast Evaluation	A forecast bias occurs when there are consistent differences between actual outcomes and previously generated forecasts of those quantities; that is: forecasts may have a general tendency to be too high or too low.
Formation Matrix	—	The inverse expected or observed likelihood-information matrix expresses local parameter dispersion for covariance bounds, standard errors, and likelihood asymptotics.
Fowlkes–Mallows Index	Cluster Analysis	Compare two partitions by the geometric mean of pairwise co-membership precision and recall, rewarding pairs clustered together by both while excluding true-negative pairs from the score.
Fraction of variance unexplained	Regression Goodness of Fit	A regression-fit statistic equal to the proportion of dependent-variable variance left unexplained by the model's predictions.
Fractional factorial design	Design of Experiments	An experimental design using a structured subset of full-factor combinations to estimate selected effects with fewer runs at the cost of aliasing.
Frequency (statistics)	Descriptive Statistics	The absolute count of observations in a declared category or event within a bounded data set; relative frequency divides that count by the total, and cumulative frequency aggregates ordered categories up to a threshold.
Functional correlation	Functional Data AnalysisDependence Analysis	A family of dependence measures for paired random functions that reduces infinite-dimensional covariance structure to interpretable associations between curves or functional components.
Functional principal component analysis	Functional Data Analysis	A dimension-reduction method representing random curves or functions in the eigenbasis of their covariance operator.
Funnel Plot Asymmetry	Meta Analysis and Publication Bias Diagnostics	Plot each study's effect against its precision and read a departure from the symmetric inverted-funnel expected under unbiased sampling — a gap where small null studies should be — as the visual fingerprint of a publication filter, licensing scrutiny against a fixed set of causes rather than a verdict.
Gamma-minimax inference	Robust Bayesian Decision Theory	A robust statistical decision rule that minimizes worst-case risk over a specified class Gamma of plausible prior distributions rather than committing to one prior.
Gaussian process emulator	Uncertainty Quantification	A probabilistic surrogate that uses a Gaussian process fitted to selected simulator runs to predict an expensive model's output and quantify interpolation uncertainty.
Geary's C	Spatial StatisticsGlobal Spatial Autocorrelation	Measure global spatial autocorrelation by comparing weighted squared differences between neighboring observations with overall variance.
Gelman–Rubin Statistic	Bayesian ComputationMarkov Chain Monte Carlo	Compare between-chain with within-chain spread to flag incomplete mixing of iterative simulations.
Generalized Additive Model for Location, Scale, and Shape	Distributional RegressionRegression Modeling	The generalized additive model for location, scale and shape (GAMLSS) is a distributional regression model in which a parametric statistical distribution is assumed for the response (target) variable but the parameters of this distribution can vary according to explanatory variables.
Generalized hydrodynamics	Statistical Mechanics	A hydrodynamic theory for integrable many-body systems that evolves local quasiparticle distributions under infinitely many conservation laws.
Generalized least squares	Regression and Econometrics	A linear-model estimator that minimizes residuals in the inverse-covariance metric when errors have known nonconstant variance or correlation.
Generalized p-value	Statistical Inference	A nuisance-parameter-controlled tail probability derived from a generalized pivotal quantity for testing hypotheses lacking a conventional exact pivot.
Generalized Randomized Block Design	Design of Experiments	A randomized block experiment with within-block replication of every treatment, enabling treatment-by-block interaction to be separated from experimental error.
Geometric standard deviation	—	A dimensionless multiplicative spread factor obtained by exponentiating the standard deviation of logarithms.
Gold-Standard Erosion	Validation and Evaluation	Recognize that a model scored against a mutable reference label can show stable metrics while its real validity silently degrades, because the answer key — not the model — has drifted away from the construct it once operationalized.
Gower's Distance	Multivariate Analysis	Compare mixed-type records by converting each available feature to a bounded type-appropriate similarity or dissimilarity, then taking a weighted pairwise average with missingness and binary-presence rules in the denominator.
Grand Potential	Statistical MechanicsEquilibrium Statistical Mechanics	The thermodynamic state function obtained by replacing entropy and particle numbers with reservoir controls, whose value generates grand-canonical equilibrium and response at fixed temperature, volume, and chemical potentials.
Graphical perception	Graphical Methods	Human visual decoding of quantities and patterns encoded in graphs, shaped by the marks, layout, and comparison task.
Hannan–Quinn information criterion	Model SelectionTime Series Analysis	In statistics, the Hannan–Quinn information criterion (HQC) is a criterion for model selection.
HARKing (Hypothesizing After the Results are Known)	Research Integrity and Questionable Research Practices	The research practice of building a hypothesis by inspecting already-collected data and then presenting it as if it had been specified in advance, silently inflating the reported false-positive rate because the test's independence assumption is violated.
Hat matrix	Regression AnalysisRegression Diagnostics	The diagonal elements of the projection matrix are the leverages, which describe the influence each response value has on the fitted value for that same observation.
Hellinger Distance	Statistical Distance	A metric between probability laws given, in the normalized convention, by one over square root two times the L2 distance between their square-root densities.
Hidden Markov model	Statistical ModelingLatent State Sequence Models	Model an observed sequence as emissions from an unobserved Markov state process, separating state transition dynamics from state-conditioned observation distributions.
Hierarchical Dirichlet process	Bayesian StatisticsNonparametric Mixture Models	A Bayesian nonparametric prior for grouped data in which group-specific discrete distributions share a global random set of mixture components while retaining different group weights.
Hierarchical generalized linear model	Multilevel and Generalized Linear Modeling	An extension of generalized linear modeling that represents clustered or multilevel responses through random effects and linked conditional distributions that can be nonnormal.
Higher-order statistics	—	Statistics based on third- or higher-order moments, cumulants or spectra that characterize distributional shape and nonlinear dependence beyond mean and covariance.
Hodges' Estimator	Asymptotic StatisticsEfficiency and Nonregular Estimation	Modify a regular root-n estimator by snapping estimates in a shrinking, wider-than-root-n neighborhood to a designated parameter value, gaining pointwise superefficiency there while paying with nonregular and potentially unbounded local risk.
Homoscedasticity and heteroscedasticity	Regression Variance Structure	Distinguish statistical models whose disturbance variance is constant across the conditioning space from models whose variance changes with predictors, fitted values, time, or another declared index.
Inferential Error	Statistical Inference	An inferential error is a conclusion, evidential interpretation, or uncertainty statement that is not warranted because the analysis misstates the target, unit, dependence structure, model, probability meaning, comparison, identification assumptions, multiplicity, or scope connecting observations to claims.
Information field theory	Bayesian Inference	A Bayesian statistical field theory for reconstructing continuous fields from incomplete noisy data using field priors and methods adapted from quantum field theory.
Innovation (signal processing)	Time Series AnalysisStatistical Signal Processing	The new-information residual in a sequential model, obtained by subtracting the optimal prediction based on prior information from the current observation.
Instrumental variable	Causal Inference	Recover the causal effect of a confounded treatment by finding a quantity Z that moves the treatment, reaches the outcome only through it, and is independent of the confounders — then reading the effect off the ratio of Z's reduced-form to first-stage effects, importing randomization the analyst never performed.
Inter-Annotator Agreement	Qualitative and Coding Methods	Measure whether independent raters applying the same coding scheme to the same items converge, using a statistic that subtracts the agreement expected by chance from the marginal label distribution.
Interaction (statistics)	Statistical Modeling	A model relation in which the association or effect of one predictor on an outcome changes with the level of another predictor.
Internal validity	Research Design	The property of an empirical study that warrants its causal claim within its own sample and setting — whether the observed intervention-outcome association is genuinely produced by the intervention rather than by confounders, selection, or bias — established by ruling out a closed catalog of named threats.
Interval Predictor Model	Regression AnalysisUncertainty Quantification	A regression model that predicts input-dependent lower and upper envelopes from an admissible set of functions or parameters, with explicit coverage or violation guarantees rather than a full response distribution.
Invariant estimator	Statistical Decision Theory	An estimator whose output transforms compatibly with a group action applied to both data and parameter space.
Inverse probability weighting	Weighted Estimation	An estimation method that weights observed units by the inverse probability of their observed sampling, treatment or response status to reconstruct a target population or intervention distribution.
Ising model	Statistical MechanicsLattice Spin Models	A statistical-mechanical model of binary spins on a graph whose energy rewards or penalizes neighboring alignment and external-field orientation, exhibiting collective order and phase transitions.
Item analysis	PsychometricsTest Item Evaluation	A psychometric evaluation and selection process that examines candidate questions for difficulty, discrimination, redundancy, model fit, fairness and construct coverage before assembling or revising a test.
Item response theory	Psychometrics	A psychometric framework modeling the probability of an item response as a function of a latent trait and item parameters.
Item-total correlation	Psychometrics	The correlation between one scored assessment item and a total or rest score, used to evaluate whether the item aligns with the construct measured by the scale.
Jeffreys prior	Bayesian StatisticsObjective Priors	A Bayesian prior measure proportional to the square root of the Fisher-information determinant, constructed to remain invariant under smooth reparameterization.
Jeffreys-Lindley Paradox	Statistical Inference and Bayesian Methods	The result that a frequentist significance test and a Bayesian posterior-odds comparison of the same data against the same point null can reach opposite verdicts, with the disagreement growing without bound as sample size increases — because the two answer different questions.
Johnson's SU-distribution	Probability Distributions	An unbounded four-parameter distribution obtained by applying an inverse-hyperbolic-sine transformation to a standard normal variable.
Join Count Statistic	Spatial StatisticsCategorical Spatial Analysis	A categorical spatial summary that tallies neighboring unit pairs by their label combination under a declared adjacency convention.
K-statistic	Mathematical Statistics	A symmetric unbiased estimator of a population cumulant constructed from sample power sums.
Kaniadakis Distribution	Statistical MechanicsKappa Statistics	A family of probability laws built from the kappa-deformed exponential, retaining the ordinary exponential limit while producing power-law tails.
Kaniadakis logistic distribution	Probability DistributionsKappa Deformed Statistics	A four-parameter continuous distribution on nonnegative values that replaces ordinary exponentials in a generalized logistic form with the κ-exponential, recovering the classical limit as κ approaches zero.
Kaplan–Meier estimator	Survival and Event History Analysis	A nonparametric product-limit estimator of a survival function from observed event times in the presence of right-censoring.
Kendall rank correlation coefficient	Nonparametric Statistics	A rank-association statistic based on the excess of concordant over discordant observation pairs.
Kendall tau distance	Rank Distance MetricsRank Correlation	The Kendall tau distance or Kendall tau rank distance is a metric (distance function) that counts the number of pairwise disagreements between two ranking lists.
Kernel smoother	—	A nonparametric estimator that predicts a function by distance-weighted averaging of nearby observations.
Kriging	GeostatisticsSpatial Prediction	A best-linear-unbiased spatial prediction method whose weights derive from a modeled covariance or variogram under stated mean assumptions.
Kruskal–Wallis Test	Nonparametric InferenceHypothesis Testing	A rank-based omnibus test for whether two or more independent groups have the same response distribution, with a location or median interpretation only when group distributions have comparable shape and spread.
KTHNY theory	Statistical Mechanics	A theory of two-dimensional melting through two continuous transitions driven first by dislocation and then disclination unbinding, with an intermediate hexatic phase.
L-estimator	Robust Statistics	An estimator formed as a linear combination of sample order statistics.
Lack-of-Fit Sum of Squares	Regression Analysis	Decompose regression residual variation at replicated predictor settings into irreducible within-setting pure error and systematic discrepancy between fitted values and setting means.
Latent growth modeling	Longitudinal StatisticsStructural Equation Models	A longitudinal structural-equation framework that represents individual repeated measures through latent intercept and slope factors, estimating average trajectories and between-person variation.
Learnable Function Class	Statistical Learning TheoryLearnability Theory	A hypothesis class for which some learner can attain a uniform finite-sample population-risk guarantee under a declared statistical learning model.
Least absolute deviations	Robust Regression	Fit a model by minimizing the sum of absolute residuals, yielding median-centered robustness to large response outliers while retaining leverage and identifiability boundaries.
Least Trimmed Squares	Robust Regression	A robust regression estimator that minimizes the sum of the h smallest squared residuals, reselecting the retained cases for each trial fit.
Lexis ratio	Historical Statistics	A dispersion ratio comparing observed variation in grouped binomial proportions with the variation expected under one common success probability.
Likelihood principle	Statistical Foundations	The proposition that, for a fixed statistical model, all sample evidence about its parameters is contained in the observed-data likelihood up to proportionality.
Linear belief function	Evidential Statistics	A Dempster–Shafer belief-function representation for continuous variables in which evidence is encoded by linear equations with normal residual uncertainty.
Linear Discriminant Analysis	Multivariate Analysis	A supervised linear projection and classifier that separates labeled classes relative to their within-class covariance.
Linear separability	Statistical Learning Theory	The property that two labeled point sets lie on opposite sides of at least one affine hyperplane.
Linear-on-the-Fly Testing	PsychometricsTest Form Assembly	A testing method that assembles a candidate-specific nonadaptive exam form from an item bank under shared content and difficulty requirements.
Ljung–Box Test	Time Series DiagnosticsTime Series Analysis	A portmanteau hypothesis test that combines sample autocorrelations through a chosen lag to assess whether a time series or fitted-model residuals retain serial correlation across that lag set.
Location parameter	—	A distribution parameter whose change translates the probability law along its sample space without changing its shape.
Location test	Hypothesis Testing	A location test is a statistical hypothesis test that compares the location parameter of a statistical population to a given constant, or that compares the location parameters of two statistical populations to each other.
Log-Linear Analysis	Categorical Data AnalysisContingency Tables	Fit and compare expected-count models for categorical contingency tables by using log-scale interaction terms to express joint and conditional associations.
Look-Elsewhere Effect	High Energy Physics	Discount an exciting best-of-many find by the size of the search that produced it — converting a local p-value at one scanned peak into a global p-value asking whether any peak this extreme would occur anywhere, via the trials factor.
Lord's Paradox	Causal Inference	Show that two arithmetically correct analyses of the same pre-post data — raw change scores versus baseline adjustment — can reach opposite verdicts about an effect, because adjustment is a causal-modeling choice and the two answer different questions depending on whether baseline is itself caused by group membership.
M-Estimator	Robust StatisticsEstimation Theory	An extremum estimator obtained by optimizing a sample-average criterion—or more generally solving an estimating equation—encompassing maximum likelihood, nonlinear least squares, and many but not inherently robust procedures.
MAGIC criteria	Statistical Argumentation	A five-part framework for evaluating whether a statistical argument is compelling through magnitude, articulation, generality, interestingness and credibility.
Main effect	—	The marginal effect of one factor on a response averaged over the levels or distribution of the other factors in a factorial model.
Mann–Whitney U test	Nonparametric Statistics	The Mann–Whitney U test (also called the Mann–Whitney–Wilcoxon (MWW/MWU), Wilcoxon rank-sum test, or Wilcoxon–Mann–Whitney test) is a nonparametric statistical test of the null hypothesis that randomly selected values X and Y from two populations have the same distribution.
MAP estimator	Bayesian InferenceEstimation Theory	A Bayesian point estimator that selects the parameter value maximizing posterior density, combining the data likelihood with a prior and reducing to maximum likelihood only when the prior is constant over the relevant domain.
Marginal likelihood	Bayesian Statistics	The probability density of observed data under a Bayesian model after integrating the likelihood over the prior distribution of its parameters.
Matrix t-distribution	Matrix Variate Statistics	A heavy-tailed probability distribution for random matrices that generalizes the multivariate t distribution with separate row and column scale structure.
Matrix variate Dirichlet distribution	Matrix Probability	A probability law on several positive-definite matrices whose sum remains below the identity, generalizing scalar Dirichlet and matrix beta distributions.
Maximal information coefficient	Exploratory Statistics	A normalized statistic searching over bounded grid partitions to measure potentially nonlinear association between two variables.
Maximum entropy thermodynamics	Statistical Mechanics	An inference-centered formulation of equilibrium thermodynamics that selects the probability distribution of greatest entropy subject to known macroscopic constraints.
Maximum likelihood estimation	—	Parameter estimation by selecting the model value that makes the observed data most likely under a specified statistical family.
Maxwell–Boltzmann distribution	Statistical MechanicsClassical Kinetic Theory	Give the equilibrium probability density of speeds for classical, nonrelativistic, noninteracting particles in an isotropic ideal gas, with scale fixed by mass and temperature.
Mean absolute error	Statistical Evaluation	The arithmetic mean of absolute differences between paired predictions or estimates and corresponding observed or reference values.
Mean absolute scaled error	Forecasting	A scale-free forecast-accuracy measure dividing mean absolute forecast error by the in-sample mean absolute error of a specified naive benchmark.
Mean integrated squared error	Nonparametric Statistics	The expected integrated squared difference between a functional estimator and its unknown target, commonly used as global density-estimation risk.
Measurement Invariance	Psychometrics	Establish that an instrument relates latent construct values to observed responses by the same measurement rule across specified groups, occasions, or conditions before interpreting their score differences.
Medcouple	Robust Statistics	A robust median-based statistic of univariate skewness formed from paired observations on opposite sides of the sample median.
Median Absolute Deviation	Robust Statistics	A robust measure of univariate dispersion defined as the median of the absolute distances from the sample median, resistant to a minority of extreme observations.
Method of Moments	Point Estimation	A parameter-estimation procedure that equates selected model moments to empirical moments and solves the resulting identifying equations.
Midhinge	Robust Location Summaries	Summarize distributional location by averaging the first and third quartiles, placing the center halfway between the hinges while keeping the interquartile spread analytically separate.
Misuse of p-values	Hypothesis TestingStatistical Inference	Inferential errors that treat a p-value as evidence about hypothesis probability, causation, effect magnitude, practical importance, replicability, or categorical truth beyond its model-conditional tail-probability meaning.
Modifiable temporal unit problem	Temporal Aggregation BiasSpatiotemporal Analysis	In addition, the Modifiable Temporal Unit Problem can also arise when the time units are irregular or when the data is missing for some periods.
Modified Kumaraswamy distribution	Probability Distributions	A positive continuous two-parameter probability distribution obtained by a Kumaraswamy-type transformation, with an explicit density, distribution function and quantile representation.
Molecular Dynamics	Computational Statistical MechanicsParticle Simulation	A molecular-simulation method that repeatedly evaluates forces and numerically advances particle positions and momenta to generate trajectories from which dynamical and ensemble observables are estimated.
Monotone Likelihood Ratio Property	Mathematical StatisticsStatistical Decision Theory	Order a parametric family so every higher-parameter to lower-parameter likelihood ratio is nondecreasing in one statistic, making larger statistics monotonically stronger evidence for the higher parameter.
Monte Carlo method in statistical mechanics	Statistical Mechanics	The use of stochastic sampling, commonly Markov-chain transitions, to estimate equilibrium or path-ensemble observables from high-dimensional statistical-mechanical distributions.
Monty Hall problem	Probability Puzzles	A worked three-door puzzle in which switching wins 2/3 of the time because the host's reveal was constrained by what he knew — drilling the move of updating on the protocol that produced an observation, not on its bare surface.
Moran's I	Spatial Statistics	A weighted statistic measuring global spatial autocorrelation by comparing cross-products among neighboring observations with overall variance.
Mosaic plot	Categorical Data Visualization	An area-proportional display of a contingency table that recursively partitions a rectangle by categorical frequencies so each tile represents one combination of levels.
Multilevel regression with poststratification	Survey Statistics	An estimation method fitting a hierarchical outcome model to sample data and averaging cell predictions using known target-population cell counts.
Multistage sampling	Survey Sampling	A probability-sampling design that selects successively nested units—such as regions, households and people—using explicit probabilities at each stage.
Multivariate Gamma Function	Multivariate Statistical TheoryFunctions of Matrix Argument and Matrix Variate Distributions	A dimension-indexed special function that evaluates a gamma-type integral over the cone of real symmetric positive-definite matrices, factors into shifted ordinary gamma terms, and normalizes Wishart-family matrix distributions.
Multivariate Glyph	Data Visualization	A multivariate glyph encodes several attributes of one observation in distinct features of a single compact mark.
Multivariate t-distribution	Multivariate Statistics	An elliptically contoured heavy-tailed distribution for random vectors, parameterized by location, positive-definite scale matrix and degrees of freedom.
Natural Experiment	Causal Inference Methods	A design that borrows the RCT's identification logic from a real-world process — a policy, boundary, or lottery — judged plausibly as-good-as-random, where the as-if-random assumption must be substantively defended rather than guaranteed by protocol.
Nearest neighbour distribution	Spatial Point Processes	The probability distribution of distance from a typical point of a point process to its nearest other point.
Nemenyi test	Nonparametric Statistics and Multiple Comparisons	A rank-based post-hoc multiple-comparison procedure that identifies pairs of treatments whose average ranks differ beyond a familywise-error-controlled critical distance after repeated-block comparison.
Neyman Construction	Frequentist Inference	A frequentist confidence-set method that assigns each hypothesized parameter value a coverage-calibrated data acceptance region and inverts those regions after observation.
Non-sampling error	Survey Methodology	Survey or estimation error arising from causes other than random selection of the sample.
Noncentral distribution	Mathematical Statistics	A distribution family for a statistic under a shifted alternative, indexed by a noncentrality parameter in addition to the central family parameters.
Nonhomogeneous Gaussian Regression	Probabilistic ForecastingEnsemble PostprocessingRegression Analysis	Non-homogeneous Gaussian regression (NGR) is a type of statistical regression analysis used in the atmospheric sciences as a way to convert ensemble forecasts into probabilistic forecasts.
Nonlinear Least Squares	Nonlinear Regression	Estimate parameters that enter a model nonlinearly by minimizing a residual sum of squares, usually through initialization-sensitive local iterations built from the residual Jacobian.
Nonparametric skew	Robust Statistics	A bounded skewness statistic comparing a distribution’s mean and median relative to its mean absolute deviation.
Normal probability plot	Distribution Diagnostics	A quantile plot comparing ordered observations with expected normal quantiles so approximate normality appears linear and systematic departures reveal skew, tails, mixtures or outliers.
Normal-exponential-gamma distribution	Shrinkage Distributions	A heavy-tailed continuous location-scale-shape distribution obtained through a normal variance mixture whose variance follows an exponential-gamma hierarchy.
Normal-inverse-gamma distribution	Bayesian Statistics	A four-parameter joint distribution in which a variance has an inverse-gamma law and a mean conditional on that variance is normal, conjugate for a normal model with unknown mean and variance.
Normality test	Statistical Inference	A statistical diagnostic or hypothesis test assessing whether observed data are compatible with a normal-distribution model.
Np-chart	Attribute Control Charts	Monitor a fixed-size sequence of samples by plotting each sample's count of nonconforming units against binomial center and control limits, separating common-cause fluctuation from special-cause signals.
Nuisance parameter	—	A model parameter not itself of inferential interest but necessary to account for when estimating or testing the target parameter.
Null distribution	Statistical Hypothesis Testing	Represent the sampling distribution of a declared test statistic under the null hypothesis and sampling scheme used to calibrate tail probabilities, critical values, and type-I error.
Null Ritual	Inference Practice	The institutionalised practice of mechanically executing a null hypothesis significance test — nil-null, p-value, p < .05 verdict — severed from the alternatives, priors, effect sizes, and decision context inference requires, yet retaining full editorial authority as if it had not been.
Observed information	Likelihood Inference	The negative Hessian of a sample log-likelihood evaluated at a specified parameter value, measuring local realized curvature.
Observer bias	Research MethodologyDetection BiasMeasurement Error	Observer bias is one of the types of detection bias and is defined as any kind of systematic divergence from accurate facts during observation and the recording of data and information in studies.
Omitted Variable Bias	Regression Inference	Correct for the distortion in a regression coefficient when a left-out variable both causes the outcome and correlates with an included regressor, so the estimate absorbs the omitted effect as the signable product of two relationships.
One- and Two-Tailed Tests	Frequentist Hypothesis Testing	Hypothesis-test designs that allocate rejection probability to one prespecified direction or to extreme departures in both directions according to the scientific alternative.
Optimality criterion	Model and Phylogenetic Tree Selection	An objective measure used to compare candidate statistical models for a hypothesis and designate the model with the best criterion value.
Orthogonality principle	Statistical Estimation	The condition that a minimum-mean-square estimation error is orthogonal to every admissible variation or estimator-measurable function.
Oversampling and undersampling in data analysis	Statistical Learning	Resampling strategies that alter class frequencies in a dataset by adding or repeating minority observations or removing majority observations.
P-chart	Statistical Process ControlAttribute Control Charts	A binomial Shewhart control chart that monitors the proportion of nonconforming units in successive samples using center and control limits adjusted for sample size.
Paired difference test	Statistical Inference	A statistical location test applied to within-pair differences when two measurements are linked by subject, unit, match, or repeated observation.
Pairwise comparison (psychology)	Psychometrics	A psychometric elicitation method that presents two stimuli at a time and records a preference, similarity, or relative-attribute judgment for later scale estimation.
Partial residual plot	Regression Diagnostics	A regression diagnostic plotting a predictor against residuals augmented by that predictor's fitted contribution to reveal its adjusted functional relationship with the response.
Particle Filter	Sequential Bayesian Filtering	Approximate a recursive hidden-state posterior with a weighted particle population that is propagated through a state model, corrected by observation likelihoods, and selectively resampled to control weight degeneracy.
Pearson correlation coefficient	—	The unitless covariance of two variables divided by the product of their standard deviations, measuring linear association from minus one to one.
Phi Coefficient	Categorical AssociationBinary Statistics	The signed Pearson correlation of two varying binary variables, computed from the normalized cross-product difference of their 2×2 table.
Pivotal quantity	Statistical Inference	A function of observed data and unknown model parameters whose sampling distribution is independent of every unknown parameter.
Plackett–Burman Design	Design of ExperimentsScreening Designs	Plackett–Burman designs are experimental designs presented in 1946 by Robin L.
Point-biserial correlation coefficient	—	The Pearson correlation between one continuous variable and a genuinely dichotomous variable, expressible through group means, proportions and overall standard deviation.
Polychoric correlation	Latent Variable Association	An estimate of the correlation between two latent normally distributed continuous variables inferred from their observed ordinal categories through threshold models.
Polykay	Mathematical StatisticsUnbiased Cumulant Estimation	Estimate a specified product of population cumulants without finite-sample bias by evaluating its partition-indexed symmetric polynomial on an i.i.d. sample.
Polynomial Chaos Expansion	Uncertainty QuantificationStochastic Spectral Methods	Represent a finite-variance model response in polynomials orthogonal to the probability law of declared random inputs, enabling coefficient-based uncertainty propagation and moments.
Portmanteau test	Model Diagnostics	An omnibus hypothesis test designed to detect a broad family of departures from a well-specified null model rather than optimize power for one narrowly specified alternative.
Posterior Predictive Distribution	Bayesian Statistics	In Bayesian statistics, the posterior predictive distribution is the distribution of possible unobserved values conditional on the observed values.
Posterior probability	Bayesian StatisticsBayesian Updating	The probability distribution for an uncertain hypothesis or parameter after combining a prior distribution with observed-data likelihood through Bayes' rule.
Potts model	Statistical Mechanics	A lattice model whose sites take one of q states and whose interaction energy rewards or penalizes neighboring sites that occupy the same state.
Predictive value of tests	Diagnostic StatisticsTest Interpretation	The probability that a target condition is present or absent given a test result, combining test performance with condition prevalence in the population of use.
PRESS Statistic	Regression Diagnostics and Cross Validation	The sum of squared leave-one-out prediction errors from a fitted regression model, computed by refitting without each case or through leverage-adjusted ordinary residuals.
Principle of marginality	Statistical Modeling	The modeling principle that an interaction term should ordinarily be accompanied by its constituent lower-order main effects, whose meanings are marginal across the interacting variable.
Principle of Maximum Entropy	Information TheoryStatistical Modeling	A constrained probability-assignment rule that selects the feasible distribution with greatest entropy relative to a declared reference.
Probability Bounds Analysis	Uncertainty QuantificationImprecise Probability	An imprecise-probability method that propagates lower and upper cumulative-distribution bounds through a model under declared dependence assumptions, enclosing all compatible output laws.
Probability box	Uncertainty QuantificationImprecise Probabilities	A pair of noncrossing lower and upper cumulative-distribution bounds representing a set of admissible probability distributions for an uncertain quantity.
Probability of direction	Bayesian StatisticsPosterior Effect Indices	Summarize a posterior effect's sign certainty as the larger of Pr(θ>0) and Pr(θ<0), ranging from one-half to one for continuous posteriors while deliberately not measuring magnitude or practical importance.
Probability Plot Correlation Coefficient Plot	Distribution Diagnostics	A PPCC plot compares probability-plot correlations across a distribution family's shape values to locate plausible shapes and show how strongly the data favor them.
Process capability index	Statistical Quality Control	A family of ratios comparing a statistically stable process’s natural variation and centering with engineering specification limits.
Process performance index	Statistical Quality and Process Capability	A ratio comparing the nearest specification limit to three estimated long-term standard deviations from the observed process mean, commonly denoted Ppk.
Propensity score matching	Causal InferenceObservational Adjustment	An observational causal-inference method that matches treated and untreated units with similar estimated probabilities of treatment given observed covariates.
Prosecutor's fallacy	Forensic StatisticsBayesian Reasoning	The prosecutor's fallacy confuses the probability of observed evidence given innocence with the probability of innocence given that evidence, typically neglecting base rates and alternative hypotheses.
Pseudoreplication	Experimental Design	An inferential error that treats nonindependent observations or subsamples as independent experimental replicates, misidentifying the unit of analysis and usually understating uncertainty or confounding treatment with unit effects.
Publication Bias	Meta Research and Publication	A scientific record becomes systematically unrepresentative when the probability that a study, result, or outcome becomes publicly available depends on its direction, magnitude, statistical significance, novelty, or sponsor-favoredness.
Quadrant Count Ratio	Descriptive Statistics and Statistics Education	Center paired quantitative observations at their sample means, score same-side pairs as concordant and opposite-side pairs as discordant, and normalize the signed count difference by sample size to obtain a coarse association statistic in [-1, 1].
Qualitative variation	Categorical Data Analysis	The dispersion of observations across nominal categories, measured by indices that compare concentration in one category with diversity or evenness across categories.
Quantile normalization	Cross Sample Distribution Alignment	Replace values by a shared rank-indexed reference so multiple samples have the same empirical marginal distribution while preserving within-sample rank order.
Quantile–Quantile Plot	—	Pair corresponding quantiles from two distributions so reference-line alignment and systematic departures diagnose location, scale, shape, and tail disagreement.
Quartile	Quantiles	One of the three cut points corresponding approximately to the 25th, 50th and 75th percentiles, dividing ordered data or a distribution into four equal-probability parts.
Random Digit Dialing	—	Build a probability-oriented telephone survey frame by generating numbers within eligible numbering blocks, screening reached numbers, and weighting the resulting sample for selection and response.
Randomized decision rule	Statistical Decision TheoryHypothesis Testing	A statistical test making use of a randomized decision rule is called a randomized test.
Randomized response	Survey Methodology	Randomised response is a research method used in structured survey interview.
Randomness Test	Goodness of Fit Testing	Challenge a sequence against a specified stochastic null using a pattern-sensitive statistic and calibrated rejection rule, while treating a pass only as failure to detect the tested departures.
Rank product	Nonparametric StatisticsBioinformatics	A nonparametric statistic that combines an item's within-replicate ranks by their geometric mean, often with permutation-based significance estimation to detect consistently high or low differential expression across experiments.
Rank-Size Distribution	Distributional Analysis	A decreasing ordering of item sizes indexed by ordinal rank, yielding a discrete reverse-quantile representation rather than a probability distribution.
Rayleigh mixture distribution	Probability DistributionsMixture Distributions	In probability theory and statistics a Rayleigh mixture distribution is a weighted mixture of multiple probability distributions where the weightings are equal to the weightings of a Rayleigh distribution.
Receiver Operating Characteristic	Signal Detection Theory	Sweep a binary classifier's decision threshold across its full score range to trace every achievable sensitivity-versus-false-positive-rate tradeoff at once, factoring detection into orthogonal discriminability (the curve's height) and criterion (where the threshold sits) coordinates.
Reciprocal distribution	Probability Distributions	A bounded positive distribution whose density is proportional to one over the variable, equivalently uniform after logarithmic transformation.
Regression analysis	Regression Models	A family of statistical methods for estimating conditional relationships between an outcome and one or more predictors, supporting explanation, adjustment and prediction under explicit model assumptions.
Regression control chart	Statistical Process Control	A statistical process-control chart monitoring deviations from an expected regression relation when the process mean legitimately varies with one or more covariates.
Regression diagnostic	Regression Analysis	A graphical, numerical or inferential check assessing whether a fitted regression model and its assumptions adequately represent the data.
Regression Discontinuity Design	Quasi Experimental Causal Inference	Recover a causal effect from a threshold rule by comparing units just above and just below a sharp cutoff on a continuous running variable, where they are comparable in expectation, so any jump in the outcome at exactly the cutoff is attributable to the treatment rather than to selection.
Regularized canonical correlation analysis	Multivariate Statistics	A canonical-correlation method that stabilizes singular or ill-conditioned covariance estimates by adding penalties, commonly ridge terms, before solving for paired linear variates.
Reliability Paradox	Psychometrics and Experimental Psychology	Explain why tasks with robust group-level effects (Stroop, IAT) can be useless for ranking individuals: the design minimized within-subjects error for group power without guaranteeing the between-subjects variance that reliability, true-score over total variance, requires.
Representative sequences	Sequence AnalysisLife Course Methods	In social sciences and other domains, representative sequences are whole sequences that best characterize or summarize a set of sequences.
Residual Sum of Squares	Regression AnalysisLeast Squares	Sum squared observed-minus-fitted response differences to obtain a nonnegative, model-relative measure of in-sample discrepancy.
Rice Distribution	Probability Distributions	In probability theory, the Rice distribution or Rician distribution (or, less commonly, Ricean distribution) is the probability distribution of the magnitude of a circularly symmetric bivariate normal random variable, possibly with non-zero mean (noncentral).
Ridgeline Plot	Statistical Graphics and Data Visualization	A graphic that places multiple comparable profile curves on vertically offset baselines over a shared horizontal scale so their shapes and positions can be compared.
Risk Score	Predictive ModelingRisk Stratification	A rule-governed numerical or ordinal summary that maps declared predictors to an estimate or stratum of a specified adverse outcome for a stated population, horizon, and use.
Robust Regression	Robust StatisticsRegression Estimation and Diagnostics	A regression family that preserves useful fit under limited contamination or model departure by controlling observation influence, treating response and leverage outliers explicitly, and measuring the robustness–efficiency tradeoff.
Rodger's method	—	A post-hoc multiple-comparison framework selecting orthogonal contrasts while controlling the expected proportion of false rejection decisions.
Round-robin test	Measurement Science	An interlaboratory study in which multiple participants independently apply a method to common or comparable test items.
Run chart	Quality Improvement	A time-ordered line plot used to reveal shifts, trends, cycles, and unusual runs in a process measure.
Sampling error	—	The difference between a sample statistic and the corresponding population parameter caused by observing only a sample.
Sampling frame	Survey Sampling	The operational list or spatial representation from which members or units of a target population can actually be selected.
Scale parameter	Probability DistributionsParametric Families	In probability theory and statistics, a scale parameter is a special kind of numerical parameter of a parametric family of probability distributions.
Score (statistics)	Likelihood TheoryFisher Information	In statistics, the informant or score is the gradient of the log-likelihood function with respect to the parameter vector.
Score test	Statistical Inference	A likelihood-based hypothesis test using the score gradient and information matrix evaluated at the null-constrained parameter estimate.
Scoring Rule	Probabilistic Forecast Evaluation	Evaluate a probabilistic forecast after its outcome by mapping the report–outcome pair to a numeric loss or reward, with propriety governing whether truthful distributions are optimal in expectation.
Seasonal subseries plot	Exploratory Time Series Analysis	A time-series display that groups observations by seasonal position into separate chronological subseries so between-season levels and within-season changes can be inspected together.
Selection on Observables	Causal Inference Assumptions	Assume that, conditional on a named set of measured covariates, treatment assignment is independent of potential outcomes — so within each covariate stratum treated and untreated units are exchangeable and adjustment recovers the causal effect.
Semivariance	GeostatisticsVariography	Likewise, the term semivariance can be misleading, since the values shown in a variogram are entire variances of observations at a given spatial separation (lag).
Sequential analysis	Statistical Decision Theory	Statistical inference in which data are evaluated as they arrive and sampling stops according to a predeclared evidence rule rather than a fixed sample size.
Shapiro–Wilk Test	Normality TestsHypothesis Testing	A statistical normality test whose statistic measures how closely ordered sample values align with expected order statistics from a normal population.
Shewhart individuals control chart	Statistical Process ControlVariables Control Charts	A paired individuals and moving-range control chart for monitoring a process one observation at a time when rational subgroups are unavailable or inappropriate.
Siegel–Tukey Test	Nonparametric Statistics	The Siegel–Tukey test is a two-sample nonparametric rank procedure that detects relative dispersion by assigning ranks alternately from the pooled extremes toward the center.
Sign test	Nonparametric Hypothesis Testing	Test a paired-difference or one-sample median null by reducing non-tied observations to positive and negative signs and evaluating the positive count against its exact binomial distribution under a declared null probability, usually one half.
Significant figures	Measurement Science	Digits retained in a measured or calculated quantity to communicate precision under a stated measurement and rounding convention.
Simplicial depth	Data DepthNonparametric Multivariate Statistics	A multivariate centrality measure equal to the number or probability of sample-generated d-simplices whose convex hull contains a query point.
Slice Sampling	Markov Chain Monte CarloComputational Statistics	An MCMC method that adds a height beneath an unnormalized density and updates within its level-set slice using a transition that preserves the target distribution.
Small-Study Effects	Meta Analysis	The meta-analytic pattern in which smaller studies report systematically larger effects than larger ones, producing funnel-plot asymmetry that inflates the pooled estimate — a shared symptom of several biases, not a diagnosis of any one cause.
Smearing retransformation	Regression Analysis	A nonparametric regression correction that converts predictions from a log-transformed outcome back to the original scale by averaging exponentiated residuals.
Smoothing	Nonparametric Regression and Exploratory Data Analysis	A scale-setting operator suppresses local or high-frequency variation in observed data to estimate a smoother component, exchanging variance and roughness for bias, lost resolution, and boundary dependence.
Snowball Sampling	Research Methods and Sampling	Recruit an unenumerable population by seeding a few participants and having each nominate others along their social ties, substituting relational proximity for random selection and buying access at the cost of representativeness.
Spatial Analysis of Principal Components	Spatial Statistics	A multivariate ordination method that finds genetic or ecological components maximizing variance while weighting either positive or negative spatial autocorrelation.
Spatial distribution	Spatial Statistics	The arrangement, density and pattern of observations or phenomena across geographic space.
Spurious relationship	Causal Statistics	An observed association that does not represent the inferred causal link because coincidence, common cause, trend or selection generates the pattern.
Square-Root-Biased Sampling	Sampling Theory	Square root biased sampling is a sampling method proposed by William H.
Standard error	Statistical Inference	The standard deviation of a statistic's sampling distribution, quantifying how much the statistic would vary across repeated samples under the stated design and model.
Standard of Care	Clinical Research and Practice	Use the currently accepted reference practice as the single dynamic baseline against which both efficacy (is a treatment better than what we already do?) and accountability (did a clinician meet what a reasonable body of practitioners would have done?) are measured by deviation.
Standard score	—	A normalized value equal to an observation’s deviation from a reference mean divided by the reference standard deviation.
Standardized Rate	Population Rate ComparisonEpidemiology	A population event rate adjusted to a declared reference composition or reference rate schedule, so a known difference in population mix does not masquerade as an event-rate difference.
Statistic	Mathematical Statistics	A measurable function of the observed sample alone, with no dependence on unknown population parameters, used to summarize data or support estimation and testing.
Statistical Contrast	Experimental Design and Anova	Encode a comparison among statistical means or parameters as a zero-sum linear estimand, propagate its sampling variance, and—when design-weighted orthogonality holds—decompose uncorrelated directions under the declared design.
Statistical Dependence	Probability and StatisticsProbability Theory	Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.
Statistical Literacy	Statistics EducationCivic and Adult Statistical Literacy	The capacity to interpret, critically evaluate, and communicate about statistical messages by connecting numbers and displays to data production, context, variation, uncertainty, assumptions, and the conclusions they can support.
Statistical Model	Foundations of Statistical Inference	Represent possible observable data by a declared sample space and family of candidate probability laws—often indexed by parameters and assumptions—so estimation, testing, prediction, and uncertainty statements have an explicit conditional basis.
Statistical regularity	Probability TheoryFrequentist Probability	The long-run stabilization of frequencies or distributional summaries across many repetitions or sufficiently comparable random events.
Statistical Test	Hypothesis TestingStatistical Inference	A statistical test is a formally specified procedure that compares observed data or a derived statistic with a sampling distribution, randomization distribution, or model under a null hypothesis to quantify incompatibility and apply a declared decision rule or evidential interpretation.
Stein's Paradox	Estimation Theory	The result that estimating three or more means each by its own sample mean is inadmissible under total squared-error loss — a shrinkage estimator pulling each toward a common reference achieves strictly lower joint error for every true parameter vector, however unrelated the quantities.
Stein's Unbiased Risk Estimate	Gaussian Mean EstimationUnbiased Risk Estimation	Estimate a fixed Gaussian mean estimator's squared-error risk from its data discrepancy and a noise-sensitivity correction, with unbiasedness understood in expectation under stated regularity and known variance.
Stepwise regression	Variable Selection	An automated regression-model selection procedure that iteratively adds, removes or exchanges predictors according to a prespecified statistical criterion.
Stochastic Equicontinuity	Asymptotic Statistics	Stochastic equicontinuity makes large local oscillations of indexed random functions unlikely as their arguments become close.
Student's t-Test	Parametric Inference for Means	A family of mean-inference procedures that divides an observed mean or mean difference by its estimated standard error and evaluates the resulting statistic against a Student t distribution whose degrees of freedom account for estimating variance from the sample.
Studentization	—	Dividing a sample statistic by a sample-based estimate of its standard deviation.
Studentized Range	Analysis of Variance and Multiple Comparisons	The range across several normal quantities divided by an independent estimate of their common standard deviation, producing a q-distribution whose group-count and degrees-of-freedom quantiles support simultaneous pairwise mean comparisons.
Subgroup analysis	Clinical Trial AnalysisMultiple Comparisons	Subgroup analysis refers to repeating the analysis of a study within subgroups of subjects defined by a subgrouping variable.
Suppressor variable	Multiple Regression	A predictor whose inclusion improves another predictor's criterion-relevant signal by accounting for variance that is irrelevant, oppositely signed, or otherwise obscuring in the reduced model.
Surrogate Endpoint Problem	Clinical Trials	The failure that arises when a trial's biomarker surrogate diverges from the clinical endpoint it stands in for — because the intervention acts through off-pathway mechanisms the surrogate cannot see — so individual-level correlation does not license an intervention-level claim.
Survival Analysis	BiostatisticsTime to Event Analysis	Survival analysis is a branch of statistics for analyzing the expected duration of time until one event occurs, such as death in biological organisms and failure in mechanical systems.
Systematic sampling	Survey MethodologySampling Designs	A probability-sampling design that chooses a random start in an ordered frame and then selects units at a fixed interval, with variants for unequal probability and spatial grids.
T-statistic	Inferential Statistics	A standardized statistic equal to an estimate’s departure from a hypothesized value divided by its estimated standard error.
Tag SNP	Statistical GeneticsLinkage Disequilibrium Based Marker Selection	A tag SNP is a single-nucleotide polymorphism selected from a declared reference population and variant set because its linkage-disequilibrium correlation predicts one or more untyped variants above a chosen threshold, preserving common-variant association coverage while reducing genotyping burden.
Tampering (quality control)	Statistical Process Control	Adjustment of a stable process in response to ordinary common-cause variation, thereby increasing rather than reducing output variability.
Temporal Raster Plot	Data Visualization	A nested-time grid places observations by interval and position within that interval, encoding each cell's value to compare recurring temporal structure.
Testing hypotheses suggested by the data	Statistical Inference	The invalid reuse of the same observations both to select a hypothesis and to test it as though the test had been specified independently.
Think aloud protocol	Research Methods	A research method in which participants verbalize their moment-to-moment thoughts while performing a task, producing process data for transcription and analysis.
Thompson Sampling	Bayesian Sequential DesignMulti Armed Bandits	A Bayesian bandit policy that samples a plausible reward model from the current posterior and chooses the action optimal under that sample, thereby probability-matching exploration to uncertainty.
Thurstone scale	Psychometrics	An equal-appearing-interval attitude scale built by having judges locate statement favorability and selecting items with separated medians and low ambiguity.
Thurstonian model	PsychometricsComparative Judgment	A latent-variable model that explains discrete choices, rankings or ordered responses by comparing noisy continuous psychological values, commonly modeled as jointly normal.
Truncated Regression Model	Regression ModelsSample Selection	Infer a population response–covariate relation from records admitted only when the response falls inside a known region, by conditioning on that inclusion.
Tsallis Distribution Family	Nonextensive Statistical MechanicsMaximum Entropy Probability Models	Organize probability laws obtained from declared Tsallis-entropy constraints around a q-exponential kernel whose support, tails, moments, and classical limit depend on the deformation index and parameterization.
Tukey's Test of Additivity	Two Way AnovaInteraction Tests	Test a one-degree product-of-main-effects departure from additivity in a two-way response table, especially when each cell has one observation.
Two-Step M-Estimator	Estimation Theory	A target M-estimator whose sample criterion or equation plugs in a preliminary nuisance M-estimate rather than its known value.
Two-way analysis of variance	—	An analysis-of-variance model estimating two categorical factors’ main effects and their interaction on a continuous response.
Twyman's law	Data AnalysisData Quality	Twyman's law states that "Any figure that looks interesting or different is usually wrong", following the principle that "the more unusual or interesting the data, the more likely they are to have been the result of an error of one kind or another".
Type M Error	Estimation Under Selection	Quantify how much a significant effect's reported magnitude is exaggerated by the significance filter under low power, via the exaggeration ratio — the expected significant estimate divided by the true effect — computable from the design before any data exist.
Type S Error	Estimation Under Selection	Quantify the risk that a statistically significant estimate points the wrong way by computing, before data collection, the probability that a two-sided significance filter is cleared from the opposite tail when the true effect is near zero relative to noise.
U-chart	Statistical Quality Control	A statistical process-control chart for nonconformities per inspection unit when the number or size of units inspected can vary between samples.
U-statistic	Statistical Theory	A statistic formed by averaging a symmetric kernel over all fixed-size subsets of a sample, yielding an unbiased estimator of its corresponding population functional.
Uncertainty analysis	Uncertainty QuantificationMeasurement Uncertainty	The systematic identification, quantification, propagation, and communication of uncertainty in measurements, model inputs, assumptions, and outputs used for inference or decisions.
Underfitting	Model Capacity	The failure mode where a model's hypothesis class is too restrictive to capture the structure genuinely present in the data — high bias, with training and test error both elevated and close together — curable only by a richer functional form, not by more data or regularization.
Unevenly spaced time series	Irregular Longitudinal Data	A time series represented by observation-time and value pairs whose successive observation intervals are not constant.
Universal Hypothesis Testing	Goodness of Fit and Large Deviations	A goodness-of-fit testing problem that compares one fully specified null distribution with the unrestricted alternative of every other distribution, seeking level-controlled tests that remain consistent or error-exponent optimal without modeling a particular alternative.
Unmatched count	Survey Methodology	A privacy-preserving survey experiment estimating prevalence of a sensitive trait from differences in mean item counts between randomized lists.
Variance	Dispersion Measures	The expected squared deviation of a random variable from its mean, measuring dispersion in squared units and equaling its second central moment.
Variance function	Exponential Dispersion Models and Mean Variance Modeling	A smooth function expressing the conditional variance of a random quantity as a function of its mean.
Variance reduction	Monte Carlo Methods	A family of Monte Carlo design changes that lowers estimator variance for a fixed computational budget while preserving the target quantity under stated conditions.
Variance-based sensitivity analysis	Uncertainty QuantificationGlobal Sensitivity Analysis	A global sensitivity method decomposing model-output variance into first-order and interaction contributions from uncertain inputs, commonly summarized by Sobol' indices.
Variation ratio	Descriptive Statistics	A nominal-data dispersion measure equal to the proportion of observations outside the modal category.
Variational Bayesian Methods	Approximate Bayesian Inference	Bayesian inference methods that choose a tractable distribution from a declared family by optimizing an evidence bound or divergence to approximate an intractable posterior.
Variational Message Passing	Variational Inference in Probabilistic Graphical Models	Compile mean-field variational Bayes updates into local exchanges of moments and natural-parameter contributions on a probabilistic graph, iteratively increasing an evidence lower bound without claiming exact posterior recovery.
Variogram	—	A geostatistical lag function measuring expected squared differences between field values, used to model spatial dependence, anisotropy, nugget, range, and kriging weights.
Violin Plot	—	A statistical distribution graphic that mirrors a kernel-density estimate around an axis, usually combining shape with median, quartiles, box-plot summaries, or raw observations.
Wald test	Statistical Inference	A hypothesis test comparing an unrestricted parameter estimate with a constrained null value using its estimated covariance as a precision weight.
Wald–Wolfowitz runs test	Nonparametric Statistics	The Wald–Wolfowitz runs test (or simply runs test), named after statisticians Abraham Wald and Jacob Wolfowitz is a non-parametric statistical test that checks a randomness hypothesis for a two-valued data sequence.
Whitening transformation	Multivariate Statistics	A linear transformation that maps a centered random vector with nonsingular covariance to variables having identity covariance.
Widely applicable information criterion	Bayesian Statistics	A Bayesian predictive-fit criterion combining log pointwise posterior predictive density with a variance-based effective-complexity penalty.
Wiki survey	Survey MethodologyParticipatory Deliberation Platforms	An open, adaptive survey method in which participants both evaluate statements and contribute new ones while an aggregation system identifies broadly supported or bridging positions.
Will Rogers phenomenon	Statistical Paradox	The rise of both group averages when observations between the two original means are reclassified from the higher-mean group to the lower-mean group.
Winsorizing	Robust StatisticsData Preprocessing	Winsorizing limits observations beyond selected lower and upper cut points by replacing them with the boundary values, reducing extreme-value influence without deleting observations.
Wombling	Spatial Statistics	Spatial statistical detection and estimation of boundaries where a modeled field changes rapidly.
Working–Hotelling procedure	Regression AnalysisSimultaneous Confidence Bands	A simultaneous-inference procedure giving a confidence band for the entire mean-response line in linear regression rather than separate pointwise intervals.
X-bar and S Chart	Statistical Process ControlControl Charts	A paired variables-control-chart method that monitors subgroup means and standard deviations against control limits for process location and dispersion.
X-bar chart	Statistical Process Control	A variables control chart that plots successive subgroup means against a center line and statistically derived limits to monitor shifts in a process mean.
Youden's J Statistic	Diagnostic Test EvaluationBiostatistics	Youden's J statistic (also called Youden's index) is a single statistic that captures the performance of a dichotomous diagnostic test.
Yule–Simon Distribution	—	A one-parameter distribution on positive integers with beta-function probability mass and a power-law tail, associated with cumulative-advantage frequency models.
Z-test	Hypothesis Testing	A hypothesis test whose null statistic follows, exactly or approximately, a standard normal distribution after centering and scaling by a known or consistently estimated standard error.
Zero-truncated Poisson distribution	Probability DistributionsCount Data Models	In probability theory, the zero-truncated Poisson distribution (ZTP distribution) is a certain discrete probability distribution whose support is the set of positive integers.
Ziv–Zakai bound	Estimation Theory	A Bayesian lower bound on estimation error that integrates binary hypothesis-testing difficulty across parameter separations.