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 ChiSquareDistribution[dim] where dim is the dimension of dspec.
  • The following options can be used:
  • AlternativeHypothesis"Unequal"the inequality for the alternative hypothesis
    MaxIterationsAutomaticmax iterations for multivariate median tests
    MethodAutomaticthe method to use for computing -values
    SignificanceLevel0.05cutoff 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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