> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/990-misc/810-statistics/hierarchy.md). # STATISTICS: HIERARCHY ## Statistics * Descriptive statistics * Data collection * Statistical inference * Correlation * Regression analysis * Categorical * Multivariate * Time-series * Survival analysis ## Descriptive statistics * Continuous data * Center * Mean * arithmetic * geometric * harmonic * Median * Mode * Dispersion * Variance * Standard deviation * Coefficient of variation * Percentile * Range * Interquartile range * Shape * Central limit theorem * Moments * Skewness * Kurtosis * L-moments * Count data * Index of dispersion * Summary tables * Grouped data * Frequency distribution * Contingency table * Dependence * Pearson product-moment correlation * Rank correlation * Spearman's rho * Kendall's tau * Partial correlation * Scatter plot * Graphics * Bar chart * Biplot * Box plot * Control chart * Correlogram * Fan chart * Forest plot * Histogram * Pie chart * Q–Q plot * Run chart * Scatter plot * Stem-and-leaf display * Radar chart ## Data collection * Study design * Population * Statistic * Effect size * Statistical power * Optimal design * Sample size determination * Replication * Missing data * Survey methodology * Sampling * stratified * cluster * Standard error * Opinion poll * Questionnaire * Controlled experiments * Scientific control * Randomized experiment * Randomized controlled trial * Random assignment * Blocking * Interaction * Factorial experiment * Adaptive Designs * Adaptive clinical trial * Up-and-Down Designs * Stochastic approximation * Observational Studies * Cross-sectional study * Cohort study * Natural experiment * Quasi-experiment ## Statistical inference * Statistical theory * Population * Statistic * Probability distribution * Sampling distribution * Order statistic * Empirical distribution * Density estimation * Statistical model * Model specification * Lp space * Parameter * location * scale * shape * Parametric family * Likelihood * Monotone likelihood * Location–scale family * Exponential family * Completeness * Sufficiency * Statistical functional * Bootstrap * U * V * Optimal decision * loss function * Efficiency * Statistical distance * divergence * Asymptotics * Robustness * Frequentist inference * Point estimation * Estimating equations * Maximum likelihood * Method of moments * M-estimator * Minimum distance * Unbiased estimators * Mean-unbiased minimum-variance * Rao–Blackwellization * Lehmann–Scheffé theorem * Median unbiased * Plug-in * Interval estimation * Confidence interval * Pivot * Likelihood interval * Prediction interval * Tolerance interval * Resampling * Bootstrap * Jackknife * Testing hypotheses * 1- & 2-tails * Power * Uniformly most powerful test * Permutation test * Randomization test * Multiple comparisons * Parametric tests * Likelihood-ratio * Score/Lagrange multiplier * Wald * Specific tests * Z-test * Normal Z-test * Student's t-test * F-test * Goodness of fit * Chi-squared * G-test * Kolmogorov–Smirnov * Anderson–Darling * Lilliefors * Jarque–Bera Normality * Shapiro–Wilk * Likelihood-ratio test * Model selection * Cross validation * AIC * BIC * Rank statistics * Sign * Sample median * Signed rank * (Wilcoxon) * Hodges–Lehmann estimator * Rank sum * (Mann–Whitney) * Nonparametric anova * 1-way * (Kruskal–Wallis) * 2-way * (Friedman) * Ordered alternative * (Jonckheere–Terpstra) * Bayesian inference * Bayesian probability * prior * posterior * Credible interval * Bayes factor * Bayesian estimator * Maximum posterior estimator ## Correlation, Regression analysis * Correlation * Pearson product-moment * Partial correlation * Confounding variable * Coefficient of determination * Regression analysis * Errors and residuals * Regression validation * Mixed effects models * Simultaneous equations models * Multivariate adaptive regression splines (MARS) * Linear regression * Simple linear regression * Ordinary least squares * General linear model * Bayesian regression * Non-standard predictors * Nonlinear regression * Nonparametric * Semiparametric * Isotonic * Robust * Heteroscedasticity * Homoscedasticity * Generalized linear model * Exponential families * Logistic * (Bernoulli) * Binomial * Poisson regressions * Partition of variance * Analysis of variance (ANOVA, anova) * Analysis of covariance * Multivariate ANOVA * Degrees of freedom ## Categorical / Multivariate / Time-series / Survival analysis * Categorical Cohen's kappa Contingency table Graphical model Log-linear model McNemar's test * Multivariate Regression Manova Principal components Canonical correlation Discriminant analysis Cluster analysis Classification Structural equation model Factor analysis Multivariate distributions Elliptical distributions Normal * Time-series * General Decomposition Trend Stationarity Seasonal adjustment Exponential smoothing Cointegration Structural break Granger causality * Specific tests Dickey–Fuller Johansen Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey * Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional heteroskedasticity (ARCH) Vector autoregression (VAR) * Frequency domain Spectral density estimation Fourier analysis Wavelet Whittle likelihood * Survival * Survival function Kaplan–Meier estimator (product limit) Proportional hazards models Accelerated failure time (AFT) model First hitting time * Hazard function Nelson–Aalen estimator * Test Log-rank test