SignTest

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:

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 :

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: