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BUILT-IN MATHEMATICA SYMBOL
PearsonCorrelationTest
PearsonCorrelationTest[v1, v2]
tests whether the vectors 
and 
are linearly independent.
PearsonCorrelationTest[..., "property"]
returns the value of 
.
Details 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 
-valuesSignificanceLevel 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
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