Chi-squared test (or
test) is a statistical hypothesis test. It usually tests the hypothesis that "the experimental data does not differ from untreated data". That is a null hypothesis. The distribution of the test statistic is a chi-squared distribution when the null hypothesis is true.
The test results are regarded as 'significant' if there is only one chance in 20 that the result could be got by chance.
There are three main groups of tests:
- Tests for distribution check that the values follow a given probability distribution.
- Tests for independence check that the values are independent; if this is the case, no value can be left out without losing information.
- Tests for homogeneity: These check that all samples taken have the same probability distribution, or are from the same set of values.
|
---|
|
|
---|
Continuous data | |
---|
Count data | |
---|
Summary tables | |
---|
Dependence | |
---|
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
- Violin plot
|
---|
|
|
|
---|
Study design |
- Population
- Statistic
- Effect size
- Statistical power
- Optimal design
- Sample size determination
- Replication
- Missing data
|
---|
Survey methodology | |
---|
Controlled experiments | |
---|
Adaptive Designs |
- Adaptive clinical trial
- Up-and-Down Designs
- Stochastic approximation
|
---|
Observational Studies |
- Cross-sectional study
- Cohort study
- Natural experiment
- Quasi-experiment
|
---|
|
|
|
---|
Statistical theory | |
---|
Frequentist inference | Point estimation |
- Estimating equations
- Unbiased estimators
- Mean-unbiased minimum-variance
- Rao–Blackwellization
- Lehmann–Scheffé theorem
- Median unbiased
- Plug-in
|
---|
Interval estimation | |
---|
Testing hypotheses |
- 1- & 2-tails
- Power
- Uniformly most powerful test
- Permutation test
- Multiple comparisons
|
---|
Parametric tests |
- Likelihood-ratio
- Score/Lagrange multiplier
- Wald
|
---|
|
---|
Specific tests | | Goodness of fit | |
---|
Rank statistics |
- Sign
- Signed rank (Wilcoxon)
- Rank sum (Mann–Whitney)
- Nonparametric anova
- 1-way (Kruskal–Wallis)
- 2-way (Friedman)
- Ordered alternative (Jonckheere–Terpstra)
|
---|
|
---|
Bayesian inference | |
---|
|
|
|
---|
Correlation | |
---|
Regression analysis |
- Errors and residuals
- Regression validation
- Mixed effects models
- Simultaneous equations models
- Multivariate adaptive regression splines (MARS)
|
---|
Linear regression | |
---|
Non-standard predictors |
- Nonlinear regression
- Nonparametric
- Semiparametric
- Isotonic
- Robust
- Heteroscedasticity
- Homoscedasticity
|
---|
Generalized linear model | |
---|
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
- Multivariate distributions
|
---|
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)
- Cross-correlation (XCF)
- ARMA model
- ARIMA model (Box–Jenkins)
- Autoregressive conditional heteroskedasticity (ARCH)
- Vector autoregression (VAR)
|
---|
Frequency domain | |
---|
|
---|
Survival | Survival function |
- Kaplan–Meier estimator (product limit)
- Proportional hazards models
- Accelerated failure time (AFT) model
- First hitting time
|
---|
Hazard function | |
---|
Test | |
---|
|
---|
|
|
Applications |
---|
Biostatistics | |
---|
Engineering statistics |
- Chemometrics
- Methods engineering
- Probabilistic design
- Process / quality control
- Reliability
- System identification
|
---|
Social statistics | |
---|
Spatial statistics |
- Cartography
- Environmental statistics
- Geographic information system
- Geostatistics
- Kriging
|
---|
|
|