Wolfram Language & System Documentation Center

SignedRankTest

SignedRankTest[data]

tests whether the median of data is zero.

SignedRankTest[{data₁,data₂}]

tests whether the median of data₁-data₂ is zero.

SignedRankTest[dspec,μ₀]

tests a location measure against μ₀.

SignedRankTest[dspec,μ₀,"property"]

returns the value of "property".

Details and Options

SignedRankTest tests the null hypothesis against the alternative hypothesis :
data

{data₁,data₂}
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:

	"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:

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 "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

Examples

open all close all

Basic Examples (4)

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:

Scope (13)

Testing (10)

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:

Reporting (3)

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:

Options (12)

AlternativeHypothesis (3)

A two-sided test is performed by default:

Test versus :

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

Test versus :

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

Test versus :

MaxIterations (2)

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:

Method (4)

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:

SignificanceLevel (1)

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

VerifyTestAssumptions (2)

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:

Applications (1)

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:

Properties & Relations (8)

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:

Possible Issues (1)

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

Use SignTest if the data is not symmetric:

Neat Examples (1)

Compute the statistic when the null hypothesis is true:

The test statistic given a particular alternative:

Compare the distributions of the test statistics:

Top

More Learning

Tech Support

Wolfram Solutions

Wolfram Solutions For Education

Get Started

Grow Your Skills

Work with Us

Educational Programs for Adults

Educational Programs for Youth

Read

SignedRankTest

Details and Options

Examples

Basic Examples (4)