Statistics — Page 42
Explore statistical methods, their assumptions, interpretation and limitations.
Research field
Method family
Robust Wilcoxon signed-rank test
The robust Wilcoxon signed-rank test extends the classical Wilcoxon signed-rank test by incorporating outlier-resistant location measures or robust preprocessing steps, improving inference on paired data when extreme observations or heavy-t...
Robust Zero-Inflated Model
The robust zero-inflated model extends standard zero-inflated count regression — which handles excess zeros via a mixture of a point mass at zero and a count distribution — by replacing or supplementing classical maximum likelihood with rob...
Robust Zivot-Andrews test
The Robust Zivot-Andrews test extends the classic Zivot-Andrews (1992) unit root test to provide reliable inference when the error term may be heteroscedastic or non-normal. It tests whether a time series has a unit root while endogenously...
Robust chi-square test
The robust chi-square test extends the classic Pearson chi-square framework to remain reliable when standard assumptions — especially the minimum expected-cell-count rule — are violated. Using power divergence statistics (Cressie & Read, 19...
Robust frequency analysis
Robust frequency analysis applies outlier-resistant estimation and resampling or exact methods to the counting and tabulation of categorical data, reducing the distortion caused by extreme observations, sparse cells, or violations of large-...
Robust independent samples t-test
The robust independent samples t-test compares the central tendency of two independent groups using trimmed means and Winsorized variances, making it substantially less sensitive to outliers and non-normality than the classical Student or W...
Robust one-sample t-test
The robust one-sample t-test replaces the ordinary mean with a trimmed mean and the sample variance with a Winsorized variance to compare a population location against a hypothesized value. It retains the t-test decision framework while sha...
Robust one-way ANOVA
Robust one-way ANOVA compares the central tendency of three or more independent groups while resisting the distorting effects of outliers and heterogeneous variances. By replacing ordinary means with trimmed means and ordinary variances wit...
Robust paired samples t-test
The robust paired samples t-test replaces arithmetic means with trimmed means and Winsorized variance to compare two related measurements while resisting the distorting influence of outliers and non-normal distributions, producing reliable...
Robust power analysis
Robust power analysis computes the statistical power or required sample size for hypothesis tests that use robust estimators — such as trimmed means or Winsorized variances — instead of ordinary means and standard deviations. It protects ag...
Robust repeated measures ANOVA
Robust repeated measures ANOVA tests whether population trimmed means differ across three or more repeated conditions or time points measured on the same subjects. By replacing ordinary means with 20% trimmed means and replacing variances w...
Robust two-way ANOVA
Robust two-way ANOVA tests main effects and interactions of two categorical factors on a continuous outcome using trimmed means and Winsorized variances, providing valid inference when standard ANOVA assumptions — normality, homoscedasticit...
Rogers-Castro Migration Schedule
The Rogers-Castro migration schedule is a parametric model that captures the remarkably regular way migration rates vary with age. Across countries and eras, the probability of moving is high in infancy, falls through childhood, surges to a...
Roll-Call Analysis
Roll-call analysis is the study of recorded legislative votes to recover the structure of political conflict — the ideological positions of legislators, the dimensionality of the issue space, and the cohesion of parties. It encompasses para...
Royston-Parmar Model
The Royston-Parmar model, introduced by Royston and Parmar in 2002, is a modern parametric approach to survival analysis that replaces the rigid distributional assumptions of classical models with a restricted cubic spline fitted to the log...
Ruin Theory
Ruin Theory models the stochastic surplus process of an insurance company to quantify the probability that accumulated losses eventually exceed available capital. Introduced by Filip Lundberg in his 1903 doctoral thesis and rigorously unifi...
Runs Test
The Wald-Wolfowitz runs test is a nonparametric hypothesis test that determines whether a sequence of observations — coded as a series of binary symbols — follows a random pattern or contains systematic structure. Introduced by Abraham Wald...
S-Estimator
The S-estimator is a robust linear-regression method, introduced by Rousseeuw and Yohai in 1984, that estimates the coefficients by minimising a robust M-estimate of the residual scale rather than the variance of the residuals. By driving d...
SABR Model
The SABR (Stochastic Alpha-Beta-Rho) model is a stochastic volatility framework introduced by Hagan et al. in 2002 for valuing interest rate derivatives. It captures the smile effect in implied volatility through correlated Brownian motions...
SARIMA
SARIMA is a seasonal extension of the Box-Jenkins ARIMA model that adds seasonal differencing and seasonal autoregressive and moving-average terms. Developed within the Box, Jenkins, Reinsel and Ljung framework (5th edition, 2015), it forec...
SARIMA model
SARIMA extends ARIMA by adding seasonal autoregressive and moving-average operators to capture repeating patterns at fixed intervals — such as monthly, quarterly, or annual cycles. Denoted SARIMA(p,d,q)(P,D,Q)s, it is the standard workhorse...
SARIMAX
SARIMAX extends the seasonal ARIMA (Box-Jenkins) model by adding exogenous explanatory variables, so it can capture the effect of holidays, economic indicators, or policy variables on a time series. It combines non-seasonal and seasonal aut...
SEM
Structural equation modeling is a multivariate statistical framework that simultaneously estimates a measurement model — relating observed indicators to latent constructs — and a structural model specifying directional or reciprocal relatio...
SEM Power Analysis
Power analysis for SEM and other multivariate procedures determines the minimum sample size required to detect a model misfit of a specified magnitude with adequate probability. The dominant approach, introduced by MacCallum, Browne, and Su...