STATISTICS: HIERARCHY

https://en.wikipedia.org/wiki/List_of_statistics_articles

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