BUILT-IN MATHEMATICA SYMBOL
- 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:
Compare the median difference for paired data to a particular value:
Report the test results in a table:
Test whether the spatial median of a multivariate population is some value:
Compute the test statistic:
Create a HypothesisTestData object for repeated property extraction:
A list of available properties:
Extract a single property or a list of properties:
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