BUILT-IN MATHEMATICA SYMBOL

# CorrelationTest

CorrelationTest[{{x1, y1}, {x2, y2}, ...}]
tests whether the correlation coefficient for a bivariate population is zero.

CorrelationTest[{{x1, y1}, {x2, y2}, ...}, 0]
tests whether the correlation coefficient is .

CorrelationTest[{{x1, y1}, {x2, y2}, ...}, {{u1, v1}, {u2, v2}, ...}]
tests whether the correlation coefficients for two populations are equal.

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

## Details and OptionsDetails and Options

• CorrelationTest[{{x1, y1}, {x2, y2}, ...}, 0] performs a hypothesis test on the bivariate sample with null hypothesis that the population correlation coefficient , and alternative hypothesis that .
• CorrelationTest[{{x1, y1}, {x2, y2}, ...}, {{u1, v1}, {u2, v2}, ...}] performs a hypothesis test on the bivariate samples with null hypothesis that the population correlation coefficients , and alternative hypothesis that .
• By default, a probability value or -value is returned.
• A small -value suggests that it is unlikely that is true.
• The data and can be any real-valued bivariate matrices.
• The argument can be any real number such that .
• CorrelationTest[{{x1, y1}, {x2, y2}, ...}, 0] will choose the most powerful test that applies to the data.
• CorrelationTest[..., All] will choose all tests that apply to the data.
• CorrelationTest[..., "test"] reports the -value according to .
• The following tests can be used:
•  "PearsonCorrelation" based on Pearson product-moment "SpearmanRank" based on Spearman's
• The test assumes the data was drawn from a normal distribution.
• CorrelationTest[..., "HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
• CorrelationTest[..., "property"] can be used to directly give the value of .
• Properties related to the reporting of test results include:
•  "AllTests" list of all applicable tests "AutomaticTest" test chosen if Automatic is used "PValue" list of -values "PValueTable" formatted table of -values "ShortTestConclusion" a short description of the conclusion of a test "TestConclusion" a description of the conclusion of a test "TestData" list of pairs of test statistics and -values "TestDataTable" formatted table of -values and test statistics "TestStatistic" list of test statistics "TestStatisticTable" formatted table of test statistics
• The following options can be used:
•  AlternativeHypothesis "Unequal" the inequality for the alternative hypothesis SignificanceLevel 0.05 cutoff for diagnostics and reporting VerifyTestAssumptions Automatic what assumptions to verify
• For tests of correlation, 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 CorrelationTest include:
•  "Normality" verify that all data is normally distributed

## ExamplesExamplesopen allclose all

### Basic Examples (3)Basic Examples (3)

Test whether the population correlation coefficient is zero:

 Out[2]=
 Out[3]=

Test whether the population correlation coefficient is 0.25:

 Out[2]=

Compare two correlation coefficients:

 Out[2]=
 Out[3]=

Report the test statistics and -values in a table:

 Out[4]=

## See AlsoSee Also

New in 9
New to Mathematica? Find your learning path »
Have a question? Ask support »