PearsonCorrelationTest

PearsonCorrelationTest[v1,v2]
tests whether the vectors and are linearly independent.

PearsonCorrelationTest[,"property"]
returns the value of .

Details and OptionsDetails and Options

  • PearsonCorrelationTest performs a hypothesis test on and 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 and 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 .
  • 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 and properties is controlled by the SignificanceLevel option. This value is also used in diagnostic tests of normality. By default is set to .
  • Named settings for VerifyTestAssumptions in IndependenceTest include:
  • "Normality"verify that all data is normally distributed
Introduced in 2012
(9.0)