BUILT-IN MATHEMATICA SYMBOL
SignedRankTest
- 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 ChiSquareDistribution[dim] where dim is the dimension of the data.
- The following options can be used:
-
- 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 |
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]= |  |
New in 8
is zero.
.
.
-values
