Statistics — Page 43
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
STAR Model
The Smooth Transition Autoregressive (STAR) model is a nonlinear time-series model, developed in Teräsvirta's 1994 framework, that lets the dynamics move smoothly rather than abruptly between two regimes. The logistic variant (LSTAR) captur...
STIRPAT Model
The STIRPAT model, short for Stochastic Impacts by Regression on Population, Affluence, and Technology, is a statistical reformulation of the IPAT identity that allows the drivers of environmental impact to be estimated and tested rather th...
SVAR
Structural Vector Autoregression (SVAR) is a multivariate time-series model, developed by Christopher Sims (1980), that extends the reduced-form VAR by imposing economically motivated identifying restrictions on contemporaneous relationship...
Scanner Panel Analysis
Scanner panel analysis models individual households' brand choices using the purchase histories captured by UPC scanner panels, in which the same households are tracked occasion by occasion with the brand chosen and the prices and promotion...
Scheffé Test
The Scheffé test is a post-hoc multiple comparison procedure that controls the family-wise error rate simultaneously for all possible linear contrasts among group means following a significant ANOVA. Introduced by Henry Scheffé in his landm...
School Effectiveness Modeling
School effectiveness modeling estimates how much, and in what ways, individual schools contribute to student outcomes once differences in what students bring with them are taken into account. Using multilevel (hierarchical) models, it adjus...
Seemingly Unrelated Regression
Seemingly Unrelated Regressions, introduced by Arnold Zellner in 1962, is a system regression method that estimates several linear equations jointly when their error terms are correlated across equations. By exploiting that cross-equation c...
Sequential Analysis
Sequential analysis is a framework for conducting hypothesis tests with pre-planned interim looks at accumulating data, allowing a study to stop early for efficacy or futility while controlling the overall Type I error rate. The group seque...
Sequential Monte Carlo
Sequential Monte Carlo (SMC) is a family of simulation-based algorithms that approximate evolving probability distributions by propagating and reweighting a cloud of weighted random draws called particles. It handles nonlinear, non-Gaussian...
Sequential Monte Carlo with Measurement Error
Sequential Monte Carlo (SMC) with measurement error is a particle-based Bayesian filtering method for tracking hidden states in dynamical systems when observations are corrupted by noise. It propagates a weighted cloud of particles through...
Sequential Monte Carlo with Missing Data
Sequential Monte Carlo (SMC) with missing data extends the standard particle filter to state-space models in which some observations are absent. When an observation is missing at a given time step the update step is simply skipped: particle...
Shapiro-Wilk test
The Shapiro-Wilk test is a hypothesis test that checks whether a continuous variable was drawn from a normal distribution. It was introduced by Samuel Shapiro and Martin Wilk in 1965 and is regarded as one of the most powerful normality tes...
Short-Form CFA
Short-form confirmatory factor analysis applies CFA to a reduced subset of items drawn from a longer validated scale, testing whether the abbreviated version preserves the original factor structure with acceptable model fit and reliability....
Short-form Cronbach's alpha
Short-form Cronbach's alpha quantifies the internal consistency reliability of an abbreviated version of a psychological scale. It applies Cronbach's alpha formula to a reduced item set, verifying that the shortened instrument retains suffi...
Siegel-Tukey test
The Siegel-Tukey test is a nonparametric hypothesis test that detects differences in variability (spread) between two independent groups whose central tendencies are equal or have been equalised. Introduced by Sidney Siegel and John W. Tuke...
Sign Test
The sign test is the simplest nonparametric hypothesis test for deciding whether the median of paired differences — or of a single sample — differs significantly from a hypothesised value. Formalised by W. J. Dixon and A. M. Mood in 1946, i...
Siler Mortality Model
The Siler model is a parametric description of the entire age pattern of mortality, from birth to extreme old age, built as the sum of three competing hazards: a high but rapidly declining risk in early life, a roughly constant background r...
Simple Linear Regression
Simple linear regression is the foundational parametric method for modelling a straight-line relationship between one continuous predictor and one continuous outcome, estimating the slope and intercept by ordinary least squares (OLS). The l...
Simulation-Based Power Analysis
Simulation-based power analysis estimates the statistical power and required sample size of a study by repeating a full analysis pipeline thousands of times on artificially generated data. Because it relies on Monte Carlo simulation rather...
Slice Sampling
Slice sampling is a Markov chain Monte Carlo (MCMC) algorithm introduced by Radford M. Neal in his 2003 Annals of Statistics paper. It generates samples from a target distribution by drawing uniformly from the region under the density curve...
Slope Index of Inequality
The slope index of inequality (SII) is a regression-based summary measure that expresses the absolute difference in a health outcome between the bottom and the top of the socioeconomic hierarchy. Rather than comparing only the most extreme...
Slutsky Equation
The Slutsky equation, derived by Russian economist Eugen Slutsky in 1915, is a fundamental identity in microeconomics that decomposes the total change in demand for a good into two effects: the substitution effect and the income effect. For...
Small-Area Health Estimation
Small-area estimation produces reliable health indicators for places where the survey sample is too thin to support a trustworthy direct estimate. A national health survey may interview only a handful of people in a given county or census t...
Sn and Qn Scale Estimators
Sn and Qn are robust estimators of scale (spread) proposed by Rousseeuw and Croux (1993) as alternatives to the median absolute deviation (MAD). Both attain a 50% breakdown point while delivering higher statistical efficiency than MAD, so t...