List of analyses of categorical data

This a list of statistical procedures which can be used for the analysis of categorical data, also known as data on the nominal scale and as categorical variables.

General tests

Center	Mean Arithmetic Arithmetic-Geometric Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode
Dispersion	Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance
Shape	Central limit theorem Moments Kurtosis L-moments Skewness

Summary tables

Study design	Effect size Missing data Optimal design Population Replication Sample size determination Statistic Statistical power
Survey methodology	Sampling Cluster Stratified Opinion poll Questionnaire Standard error
Controlled experiments	Blocking Factorial experiment Interaction Random assignment Randomized controlled trial Randomized experiment Scientific control
Adaptive designs	Adaptive clinical trial Stochastic approximation Up-and-down designs
Observational studies	Cohort study Cross-sectional study Natural experiment Quasi-experiment

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) 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) Van der Waerden test

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

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 Least-squares spectral analysis Wavelet Whittle likelihood

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

Biostatistics	Bioinformatics Clinical trials / studies Epidemiology Medical statistics
Engineering statistics	Chemometrics Methods engineering Probabilistic design Process / quality control Reliability System identification
Social statistics	Actuarial science Census Crime statistics Demography Econometrics Jurimetrics National accounts Official statistics Population statistics Psychometrics
Spatial statistics	Cartography Environmental statistics Geographic information system Geostatistics Kriging

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