Mathematica > Data Manipulation > Statistical Data Analysis > Hypothesis Tests
Mathematica > Mathematics and Algorithms > Statistical Data Analysis > Hypothesis Tests
Mathematica > Data Manipulation > Statistical Data Analysis > Probability & Statistics > Random Variables > Hypothesis Tests
MATHEMATICA GUIDE

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. Mathematica 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.

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

Other Tests

LogRankTest — test whether hazard rates are equivalent

UnitRootTest — test whether time series data is stationary

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

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