This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# SignTest

 SignTest[data] tests whether the median of data is zero. SignTesttests whether the median of is zero. SignTesttests a location measure against . SignTestreturns the value of .
• 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 returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
• SignTest 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 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 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. This value is also used in diagnostic tests of assumptions including a test for symmetry. By default is set to .
Test whether the median of a population is zero:
Test whether the spatial median of a multivariate population is some value:
Compute the test statistic:
Compare the median difference for paired data to a particular value:
Report the test results in a table:
Create a HypothesisTestData object for repeated property extraction:
A list of available properties:
Extract a single property or a list of properties:
Test whether the median of a population is zero:
 Out[2]=

Test whether the spatial median of a multivariate population is some value:
 Out[2]=
Compute the test statistic:
 Out[3]=

Compare the median difference for paired data to a particular value:
 Out[2]=
Report the test results in a table:
 Out[3]=

Create a HypothesisTestData object for repeated property extraction:
 Out[2]=
A list of available properties:
 Out[3]=
Extract a single property or a list of properties:
 Out[4]=
 Out[5]=
 Scope   (13)
Test versus :
The -values are typically large when the median is close to :
The -values are typically small when the location is far from :
Using Automatic is equivalent to testing for a median of zero:
Test versus :
The -values are typically large when the median is close to :
The -values are typically small when the location is far from :
Test whether the median vector of a multivariate population is the zero vector:
Alternatively, test against :
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 :
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:
 Options   (9)
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 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 the BinomialDistribution for univariate data:
Asymptotic methods can be used for univariate data:
For multivariate data only the asymptotic result is available:
The significance level is also used for and :
 Applications   (2)
A new sleeping aid was tested on eight patients. The number of minutes taken for each subject to fall asleep was recorded for a night taking the medication and for a night with a placebo:
The SignTest does not detect a difference in the sleep aid and placebo:
The datasets, while very small, do not fail a test for normality:
A more powerful PairedTTest shows a significant reduction in time to sleep with the sleep aid:
A group of 10 students with low assessments in mathematics and science was asked to participate in tutoring program. A test similar to the original assessment was administered after the program. The students' scores on the math and science portions of both assessments are as follows:
There is a significant improvement in scores overall:
The Bonferroni-corrected tests of the individual components suggest that math scores alone account for the detected improvement:
Conceptually, the SignTest counts the number of positive signs in a dataset:
For univariate data the test statistic follows a BinomialDistribution, ignoring zeros:
The SignTest is generally less powerful than other hypothesis tests for location:
For multivariate data spatial signs are used when computing the test statistic:
Spatial signs tend to cluster when the spatial median is nonzero:
The amount of clustering is quantified by the test statistic:
The test statistic follows a ChiSquareDistribution[p]:
The test statistic is affine invariant for multivariate data:
The distribution of spatial signs in three dimensions shows that larger deviations from a zero mean vector produce more highly clustered spatial signs and larger sign statistics:
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