Hypothesis tests give quantitative answers to common questions, such as how good the fit is between data and a particular distribution, whether these distributions have the same mean or median, and whether these datasets have the same variability. The Wolfram Language provides high-level functions for these types of questions and will automatically select the tests applicable for the data and distributions given. The high-level functions typically run more than one test and are able to produce full reports, but there are also specific named hypothesis tests such as the Kolmogorov–Smirnov goodness-of-fit test, or paired -test. These give more direct control over settings and performance for specific tests.

Goodness-of-Fit Tests

DistributionFitTest — test for goodness-of-fit to a distribution of data

LogRankTest — test whether hazard functions are equal

AndersonDarlingTest  ▪  BaringhausHenzeTest  ▪  CramerVonMisesTest  ▪  JarqueBeraALMTest  ▪  KolmogorovSmirnovTest  ▪  KuiperTest  ▪  MardiaCombinedTest  ▪  MardiaKurtosisTest  ▪  MardiaSkewnessTest  ▪  PearsonChiSquareTest  ▪  ShapiroWilkTest  ▪  WatsonUSquareTest

Location Tests

LocationTest — test means or mean differences of one or two datasets

LocationEquivalenceTest — compare means or medians of two or more datasets

MannWhitneyTest  ▪  PairedTTest  ▪  PairedZTest  ▪  SignTest  ▪  SignedRankTest  ▪  TTest  ▪  ZTest

Variance Tests

VarianceTest — test variances or variance ratios of one or two datasets

VarianceEquivalenceTest — compare variances of two or more datasets

ConoverTest  ▪  BrownForsytheTest  ▪  FisherRatioTest  ▪  LeveneTest  ▪  SiegelTukeyTest

Dependency Tests

IndependenceTest — test whether vectors are independent

CorrelationTest — test for particular correlations between vectors

PearsonCorrelationTest  ▪  SpearmanRankTest  ▪  KendallTauTest  ▪  HoeffdingDTest  ▪  GoodmanKruskalGammaTest  ▪  BlomqvistBetaTest  ▪  WilksWTest  ▪  PillaiTraceTest

Time Series Tests

UnitRootTest — test whether time series data is stationary

AutocorrelationTest — test whether time series data is autocorrelated

Options and Objects for Hypothesis Tests

HypothesisTestData — hypothesis test data generated by hypothesis tests

SignificanceLevel — significance level to use for reporting test conclusions

AlternativeHypothesis — alternative hypothesis for location and variance tests

VerifyTestAssumptions — whether to verify data assumptions through diagnostic tests