BUILT-IN MATHEMATICA SYMBOL

# 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 Method Automatic the method to use for computing -values SignificanceLevel 0.05 cutoff for diagnostics and reporting VerifyTestAssumptions Automatic what 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

## ExamplesExamplesopen allclose all

### Basic Examples (1)Basic Examples (1)

Test whether two vectors are independent:

 Out[2]=
 Out[3]=