tests whether the vectors v1 and v2 are linearly independent.


returns the value of "property".

Details and Options

  • PearsonCorrelationTest performs a hypothesis test on v1 and v2 with null hypothesis that the vectors are linearly independent, and alternative hypothesis that they are not.
  • By default, a probability value or -value is returned.
  • A small -value suggests that it is unlikely that is true.
  • The arguments v1 and v2 can be any real-valued vectors of equal length.
  • PearsonCorrelationTest is based on the Pearson product-moment correlation computed by Correlation[v1,v2]. Under , asymptotically follows a StudentTDistribution[n-2].
  • PearsonCorrelationTest[v1,v2,"HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
  • PearsonCorrelationTest[v1,v2,"property"] can be used to directly give the value of "property".
  • Properties related to the reporting of test results include:
  • "DegreesOfFreedom"the degrees of freedom used in the test
    "PValue"the -value of the test
    "PValueTable"formatted table containing the -value
    "ShortTestConclusion"a short description of the conclusion of the test
    "TestConclusion"a description of the conclusion of the test
    "TestData"a list containing the test statistic and -value
    "TestDataTable"formatted table of the -value and test statistic
    "TestStatistic"the test statistic
    "TestStatisticTable"formatted table containing the test statistic
  • The following options can be used:
  • AlternativeHypothesis"Unequal"the inequality for the alternative hypothesis
    MethodAutomaticthe method to use for computing -values
    SignificanceLevel0.05cutoff for diagnostics and reporting
    VerifyTestAssumptionsAutomaticwhat assumptions to verify
  • For tests of independence, a cutoff is chosen such that is rejected only if . The value of used for the "TestConclusion" and "ShortTestConclusion" properties is controlled by the SignificanceLevel option. This value is also used in diagnostic tests of normality. By default, is set to 0.05.
  • Named settings for VerifyTestAssumptions in IndependenceTest include:
  • "Normality"verify that all data is normally distributed


open allclose all

Basic Examples  (1)

Test whether two vectors are independent:

Click for copyable input
Click for copyable input
Click for copyable input

Scope  (7)

Options  (12)

Properties & Relations  (7)

Neat Examples  (1)

See Also

BlomqvistBetaTest  Correlation  CorrelationTest  GoodmanKruskalGammaTest  HoeffdingDTest  IndependenceTest  KendallTauTest  PillaiTraceTest  SpearmanRankTest  WilksWTest

Introduced in 2012