BUILT-IN MATHEMATICA SYMBOL

# SignedRankTest

SignedRankTest[data]
tests whether the median of data is zero.

SignedRankTest[{data1, data2}]
tests whether the median of is zero.

SignedRankTest[dspec, 0]
tests a location measure against .

SignedRankTest[dspec, 0, "property"]
returns the value of .

## Details and OptionsDetails and Options

• SignedRankTest performs a hypothesis test on data with null hypothesis that the true population median is some value , and alternative hypothesis that .
• Given and , SignedRankTest performs a test on the paired differences of the two datasets.
• By default a probability value or -value is returned.
• A small -value suggests that it is unlikely that is true.
• The data in dspec can be univariate or multivariate .
• If two samples are given, they must be of equal length.
• The argument can be a real number or a real vector with length equal to the dimension of the data.
• SignedRankTest assumes that the data is symmetric about the median in the univariate case and elliptically symmetric in the multivariate case. For this reason, SignedRankTest is also a test of means.
• SignedRankTest[dspec, 0, "HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
• SignedRankTest[dspec, 0, "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 a test "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 SignedRankTest is a more powerful alternative to the SignTest.
• For univariate samples SignedRankTest performs the Wilcoxon signed rank test for medians of paired samples. A correction for ties is applied for permutation-based -values. By default, the test statistic is corrected for continuity and an asymptotic result is returned.
• For multivariate samples, SignedRankTest performs an affine invariant test for paired samples using standardized spatial signed ranks. The test statistic is assumed to follow a where dim is the dimension of the data.
• The following options can be used:
•  AlternativeHypothesis "Unequal" the inequality for the alternative hypothesis MaxIterations Automatic max iterations for multivariate median tests Method Automatic the method to use for computing -values SignificanceLevel 0.05 cutoff for diagnostics and reporting VerifyTestAssumptions Automatic what assumptions to verify
• For the SignedRankTest, 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 assumptions including a test for symmetry. By default is set to .
• Named settings for VerifyTestAssumptions in SignedRankTest include:
•  "Symmetry" verify that all data is symmetric

## ExamplesExamplesopen allclose all

### Basic Examples (4)Basic Examples (4)

Test whether the median of a population is zero:

 Out[2]=
 Out[3]=

Compare the median difference for paired data to a particular value:

 Out[2]=
 Out[3]=

Report the test results in a table:

 Out[4]=

Test whether the spatial median of a multivariate population is some value:

 Out[2]=

Compute the test statistic:

 Out[3]=

Create a HypothesisTestData object for repeated property extraction:

 Out[2]=

A list of available properties:

 Out[3]=

Extract a single property or a list of properties:

 Out[4]=
 Out[5]=