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SignedRankTest—Wolfram Documentation

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SignedRankTest[{data₁,data₂}]

tests whether the median of data₁-data₂ is zero.

• SignedRankTest tests the null hypothesis against the alternative hypothesis :
• where μ is the population median for data and μ₁₂ is the median of 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 {x₁,x₂,…} or multivariate {{x₁,y₁,…},{x₂,y₂,…},…}.
• If two samples are given, they must be of equal length.
• The argument μ₀ 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,μ₀,"HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
• SignedRankTest[dspec,μ₀,"property"] can be used to directly give the value of "property".
• Properties related to the reporting of test results include:
• 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 "TestConclusion" and "ShortTestConclusion" 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 0.05.
• 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:

Test versus :

The -values are typically large when the median is close to μ₀:

The -values are typically small when the location is far from μ₀:

Using Automatic is equivalent to testing for a median of zero:

Test versus :

The -values are typically large when median is close to μ₀:

The -values are typically small when the location is far from μ₀:

Test whether the median vector of a multivariate population is the zero vector:

Alternatively, test against {0.1,0,-.5,0}:

Test versus :

The -values are generally small when the locations are not equal:

The -values are generally large when the locations are equal:

Test versus :

The order of the datasets affects the test results:

Test whether the median difference vector of two multivariate populations is the zero vector:

Alternatively, test against {1,0,-1,0}:

Create a HypothesisTestData object for repeated property extraction:

The properties available for extraction:

Extract some properties from a HypothesisTestData object:

The -value and test statistic:

Extract any number of properties simultaneously:

The -value and test statistic:

Tabulate the test results:

Retrieve the entries from a test table for customized reporting:

Tabulate -values or test statistics:

The -value from the table:

The test statistic from the table:

A two-sided test is performed by default:

Test versus :

Perform a two-sided test or a one-sided alternative:

Test versus :

Test versus :

Test versus :

Perform tests with one-sided alternatives when μ₀ is given:

Test versus :

Test versus :

Set the maximum number of iterations to use for multivariate tests:

By default, 500 iterations are allowed:

Setting the maximum number of iterations may result in lack of convergence:

The -values are not equivalent:

By default, -values are computed using asymptotic test statistic distributions:

Permutation methods can be used:

Set the number of permutations to use:

By default, random permutations are used:

Set the seed used for generating random permutations:

The significance level is used for "TestConclusion" and "ShortTestConclusion":

Diagnostics can be controlled as a group using All or None:

Verify all assumptions:

Check no assumptions:

Diagnostics can be controlled independently:

Check for symmetry:

Set the symmetry assumption to True:

Twelve sets of identical twins were given psychological tests to measure aggressiveness. It is hypothesized that the first-born twin will tend to be more aggressive than the second-born:

There is insufficient evidence to reject that birth order has no effect on aggressiveness:

The SignedRankTest is generally more powerful than the SignTest:

The univariate Wilcoxon signed rank test statistic:

In the absence of ties, Ordering can be used to compute ranks:

The asymptotic two-sided -value:

For univariate data, the test statistic is asymptotically normal:

For multivariate data, the test statistic follows a ChiSquareDistribution under :

The degree of freedom is equal to the dimension of the data:

For multivariate data, the SignedRankTest effectively tests uniformity about a unit sphere:

A function for computing the spatial signed ranks of a matrix:

Deviations from μ₀ yield clustering of spatial signed ranks and larger test statistics:

The test statistic is affine invariant for multivariate data:

The signed rank test works with the values only when the input is a TimeSeries:

The signed rank test works with all the values together when the input is a TemporalData:

Test all the values only:

Test the difference of the medians of the two paths:

SignedRankTest requires that the data be symmetric about a common median:

Use SignTest if the data is not symmetric:

Compute the statistic when the null hypothesis is true:

The test statistic given a particular alternative:

Compare the distributions of the test statistics:

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