Hypothesis Tests

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 KolmogorovSmirnov goodness-of-fit test, or paired -test. These give more direct control over settings and performance for specific tests.

ReferenceReference

Goodness-of-Fit Tests

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

LogRankTest test whether hazard functions are equal

AndersonDarlingTest  ▪  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