BUILT-IN MATHEMATICA SYMBOL

# SignTest

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

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

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

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

## Details and OptionsDetails and Options

• SignTest performs a hypothesis test on data with null hypothesis that the true population median is some value , and alternative hypothesis that .
• Given and , SignTest 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.
• SignTest[dspec, 0, "HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
• SignTest[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
• For univariate samples, SignTest performs the sign test for medians of paired samples. The test statistic is assumed to follow a BinomialDistribution[n, 1/2] where n is the number of elements in dspec not equal to .
• For multivariate samples, SignTest performs an affine invariant test for paired samples using spatial signs. The test statistic is assumed to follow a where dim is the dimension of dspec.
• 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
• For the SignTest, a cutoff is chosen such that is rejected only if . The value of used for the and properties is controlled by the SignificanceLevel option. By default is set to .

## ExamplesExamplesopen allclose all

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

Test whether the median of a population is zero:

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

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Compute the test statistic:

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

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Report the test results in a table:

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Create a HypothesisTestData object for repeated property extraction:

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A list of available properties:

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Extract a single property or a list of properties:

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