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[{{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:
-
- 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 |
New in 9
.
-values in a table:
