What statistical test is used for categorical data?

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General tests[edit]
Binomial data[edit]
2 × 2 tables[edit]
Measures of association[edit]
Categorical manifest variables as latent variable[edit]
See also[edit]
What measure is best for categorical data?
What techniques of statistical analysis are used for categorical data?

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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.

1 General tests
2 Binomial data
3 2 × 2 tables
4 Measures of association
5 Categorical manifest variables as latent variable
6 See also

General tests[edit]

Bowker's test of symmetry
Categorical distribution, general model
Chi-squared test
Cochran–Armitage test for trend
Cochran–Mantel–Haenszel statistics
Correspondence analysis
Cronbach's alpha
Diagnostic odds ratio
G-test
Generalized estimating equations
Generalized linear models
Krichevsky–Trofimov estimator
Kuder–Richardson Formula 20
Linear discriminant analysis
Multinomial distribution
Multinomial logit
Multinomial probit
Multiple correspondence analysis
Odds ratio
Poisson regression
Powered partial least squares discriminant analysis
Qualitative variation
Randomization test for goodness of fit
Relative risk
Stratified analysis
Tetrachoric correlation
Uncertainty coefficient
Wald test

Binomial data[edit]

Bernstein inequalities (probability theory)
Binomial regression
Binomial proportion confidence interval
Chebyshev's inequality
Chernoff bound
Gauss's inequality
Markov's inequality
Rule of succession
Rule of three (medicine)
Vysochanskiï–Petunin inequality

2 × 2 tables[edit]

Chi-squared test
Diagnostic odds ratio
Fisher's exact test
G-test
Odds ratio
Relative risk
McNemar's test
Yates's correction for continuity

Measures of association[edit]

Aickin's α
Andres and Marzo's delta
Bangdiwala's B
Bennett, Alpert, and Goldstein’s S
Brennan and Prediger’s κ
Coefficient of colligation - Yule's Y
Coefficient of consistency
Coefficient of raw agreement
Conger’s Kappa
Contingency coefficient – Pearson's C
Cramér's V
Dice's coefficient
Fleiss' kappa
Goodman and Kruskal's lambda
Guilford’s G
Gwet’s AC1
Hanssen–Kuipers discriminant
Heidke skill score
Jaccard index
Janson and Vegelius’ C
Kappa statistics
Klecka's tau
Krippendorff's Alpha
Kuipers performance index
Matthews correlation coefficient
Phi coefficient
Press' Q
Renkonen similarity index
Prevalence adjusted bias adjusted kappa
Sakoda's adjusted Pearson's C
Scott's Pi
Sørensen similarity index
Stouffer’s Z
True skill statistic
Tschuprow's T
Tversky index
Von Eye's kappa

Categorical manifest variables as latent variable[edit]

Latent variable model
- Item response theory
  - Rasch model
- Latent class analysis

See also[edit]

Categorical distribution

Statistics

Outline
Index

Descriptive statistics

Continuous data

Center

Mean
- Arithmetic
- Cubic
- Generalized/power
- Geometric
- Harmonic
- 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

Count data

Index of dispersion

Summary tables

Contingency table
Frequency distribution
Grouped data

Dependence

Partial correlation
Pearson product-moment correlation
Rank correlation
- Kendall's τ
- Spearman's ρ
Scatter plot

Graphics

Bar chart
Biplot
Box plot
Control chart
Correlogram
Fan chart
Forest plot
Histogram
Pie chart
Q–Q plot
Radar chart
Run chart
Scatter plot
Stem-and-leaf display
Violin plot

Data collection

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

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)
- 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)
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

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
Cochran-Mantel-Haenszel statistics

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 Least-squares spectral 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

Applications

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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What measure is best for categorical data?

The mode is the only central tendency measure for categorical data, while a median works best with ordinal data.

Is t

For categorical variables, you can use a one-sample t-test for proportion to test the distribution of categories.

What techniques of statistical analysis are used for categorical data?

General tests.

Bowker's test of symmetry..

Categorical distribution, general model..

Chi-squared test..

Cochran–Armitage test for trend..

Cochran–Mantel–Haenszel statistics..

Correspondence analysis..

Cronbach's alpha..

Diagnostic odds ratio..

Is chi

Revised on November 10, 2022. A Pearson's chi-square test is a statistical test for categorical data. It is used to determine whether your data are significantly different from what you expected.

Is t Is chi Statistical significance test Statistical test McNemar test ANOVA analysis Correlation analysis Chi-square test

What statistical test is used for categorical data?

Contents

General tests[edit]

Binomial data[edit]

2 × 2 tables[edit]

Measures of association[edit]

Categorical manifest variables as latent variable[edit]

See also[edit]

What measure is best for categorical data?

Is t

What techniques of statistical analysis are used for categorical data?

Is chi

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