Glossary of Common Statistical Tests
This glossary provides a comprehensive overview of widely used and well established statistical tests in applied research. Where a test is known by more than one name, the alternative names are also stated.
A
ADF Test (Augmented Dickey–Fuller)
Tests for a unit root in time series data. Also called the Dickey–Fuller test with lagged differences.
ANOVA (Analysis of Variance)
Tests equality of means across multiple groups.
Anderson–Darling Test
Tests whether data follow a specified distribution.
Armitage Trend Test (Cochran–Armitage test)
Tests for linear trend in proportions across ordered groups.
Aitchison Test
Tests hypotheses for compositional data.
ANCOVA (Analysis of Covariance)
ANOVA adjusted for one or more covariates.
Ansari–Bradley Test
Nonparametric test for equality of scale between two groups.
B
Barnard’s Test
Exact test of independence in 2×2 tables.
Bera–Jarque Test (Jarque–Bera test)
Tests normality using skewness and kurtosis.
Binomial Test
Tests a single proportion against a hypothesised value.
Box–Pierce Test
Tests for autocorrelation in time series residuals.
Box’s M Test
Tests equality of covariance matrices across groups.
Brown–Forsythe Test
Robust alternative to Levene’s test for equality of variances.
Bartlett’s Test
Tests equality of variances across groups.
Bhattacharyya Test
Measures similarity between probability distributions.
Bowker’s Test
Tests symmetry in square contingency tables.
Box–Ljung Test
Modified version of Box–Pierce with better small sample performance.
Breslow–Day Test
Tests homogeneity of odds ratios across strata. Used with Mantel–Haenszel analysis.
C
Cochran’s Q Test
Tests differences in matched proportions across more than two groups.
Cochran–Mantel–Haenszel Test
Tests association between two variables controlling for stratification. Often called the Mantel–Haenszel test.
Clark–West Test
Compares predictive accuracy of nested regression models.
Cramér–von Mises Test
Tests goodness of fit of a distribution.
Cochran–Armitage Test
Tests trend in proportions across ordered categories.
Chi Square Test
Tests association between categorical variables. Also called Pearson’s chi square test.
Conover–Iman Test
Nonparametric multiple comparisons following Kruskal–Wallis.
D
Davies Test
Tests for a change point in regression models.
Dickey–Fuller Test
Tests for unit roots in time series.
Durbin–Watson Test
Tests for first order autocorrelation in regression residuals.
DeLong Test
Tests difference between correlated ROC curves.
Durbin Test
Nonparametric test for balanced incomplete block designs.
E
Epps–Singleton Test
Tests equality of distributions using characteristic functions.
Exact McNemar Test
Exact version of McNemar’s test for small samples.
Exact Binomial Test
Exact inference for binomial proportions.
F
F Test
Tests equality of variances or compares nested linear models.
Fligner–Killeen Test
Nonparametric test for equality of variances.
Fisher’s Exact Test
Exact test of independence in contingency tables.
Friedman Test
Nonparametric alternative to repeated measures ANOVA.
G
Games–Howell Test
Post hoc comparison allowing unequal variances and sample sizes.
Granger Causality Test
Tests predictive causality in time series.
Gehan Test
Weighted log rank test emphasising early survival differences. Also called Gehan–Wilcoxon test.
H
Hartley’s Test
Tests equality of variances. Also called Fmax test.
Hosmer–Lemeshow Test
Tests goodness of fit for logistic regression models.
Hodges–Lehmann Test
Tests median differences using pairwise averages.
Hotelling’s T² Test
Multivariate generalisation of the one sample or two sample t test.
I
Intraclass Correlation Test
Tests reliability or agreement among measurements.
Interaction Test
Tests whether effects differ across subgroups. Often implemented via regression interaction terms.
J
Jonckheere–Terpstra Test
Tests ordered differences among independent groups.
K
Kaplan–Meier Log Rank Test
Tests equality of survival curves. Often simply called the log rank test.
Kolmogorov–Smirnov Test
Tests equality of distributions or goodness of fit.
Kendall’s Tau Test
Tests rank correlation between two variables.
Kruskal–Wallis Test
Nonparametric alternative to one way ANOVA.
L
Levene’s Test
Tests equality of variances across groups.
Lilliefors Test
Modified Kolmogorov–Smirnov test for normality.
Log Rank Variants
Includes Fleming–Harrington, Tarone–Ware, Peto–Peto tests.
Likelihood Ratio Test
Compares nested models using likelihoods.
Log Rank Test
Tests equality of survival distributions.
M
Mantel–Haenszel Test
Tests association controlling for stratification. Same as Cochran–Mantel–Haenszel.
McNemar Test
Tests paired categorical data.
Mann–Whitney U Test
Nonparametric test comparing two independent groups. Also called Wilcoxon rank sum test.
Mood’s Median Test
Tests equality of medians.
N
Newey–West Test
Provides robust standard errors for autocorrelation and heteroskedasticity.
Normal Score Test
Rank based test using normal scores. Also called Van der Waerden test.
O
Omnibus Test
Tests for any overall difference without specifying direction.
One Sample T Test
Tests whether a sample mean differs from a hypothesised value.
P
Paired T Test
Tests mean difference in paired observations.
Phillips–Perron Test
Unit root test for time series.
Permutation Test
Distribution free test based on resampling.
Peto–Peto Test
Weighted log rank test emphasising early events.
Q
Q Test (Dixon)
Tests for a single outlier in small samples.
R
Rank Sum Test
Another name for Mann–Whitney U test.
Royston Test
Tests whether a multivariate dataset follows a multivariate normal distribution.
Repeated Measures ANOVA
Tests mean differences across repeated observations.
Runs Test
Tests randomness in a sequence.
S
Scheffé Test
Conservative post hoc comparison after ANOVA.
Shapiro–Wilk Test
Tests normality.
Spearman Rank Correlation Test
Tests monotonic association.
Score Test
Tests model parameters using score functions. Also called Lagrange multiplier test.
Sign Test
Nonparametric test for paired data.
Student’s t Test
Tests mean differences.
T
Tarone–Ware Test
Weighted log rank test balancing early and late events.
Tukey HSD Test
Post hoc test controlling family wise error.
Trend Test
Tests ordered alternatives. Often refers to Cochran–Armitage.
Two Sample t Test
Tests difference between two independent means.
U
Unit Root Tests
Family including ADF, Phillips–Perron, KPSS tests.
V
Van der Waerden Test
Rank based normal score test.
Variance Ratio Test:
Tests for random walk behaviour in time series.
W
Wald Test
Tests individual parameters in regression models.
Wilcoxon Signed Rank Test
Nonparametric test for paired data.
Welch t Test
t test allowing unequal variances.
Wilcoxon Rank Sum Test
Same as Mann–Whitney U test.
X
X² test (Chi-square test)
Tests for association or independence between categorical variables. Also known as Pearson’s Chi-square test.
Y
Yates Corrected Chi Square Test
Continuity corrected chi square test for small samples.
Z
Z test
A hypothesis test based on the standard normal distribution, commonly used to test means or proportions when sample sizes are large or population variance is known.