Portability	portable
Stability	experimental
Maintainer	bos@serpentine.com
Safe Haskell	None

Statistics.Test.WilcoxonT

Contents

Wilcoxon signed-rank matched-pair test
Data types

Description

The Wilcoxon matched-pairs signed-rank test is non-parametric test which could be used to whether two related samples have different means.

WARNING: current implementation contain critical bugs https://github.com/bos/statistics/issues/18

Synopsis

Wilcoxon signed-rank matched-pair test

wilcoxonMatchedPairTest Source

Arguments

:: TestType	Perform one-tailed test.
-> Double	The p-value at which to test (e.g. 0.05)
-> Sample	First sample
-> Sample	Second sample
-> Maybe TestResult	Return `Nothing` if the sample was too small to make a decision.

The Wilcoxon matched-pairs signed-rank test. The samples are zipped together: if one is longer than the other, both are truncated to the the length of the shorter sample.

For one-tailed test it tests whether first sample is significantly greater than the second. For two-tailed it checks whether they significantly differ

Check wilcoxonMatchedPairSignedRank and wilcoxonMatchedPairSignificant for additional information.

wilcoxonMatchedPairSignedRank :: Sample -> Sample -> (Double, Double)Source

The Wilcoxon matched-pairs signed-rank test.

The value returned is the pair (T+, T-). T+ is the sum of positive ranks (the ranks of the differences where the first parameter is higher) whereas T- is the sum of negative ranks (the ranks of the differences where the second parameter is higher). These values mean little by themselves, and should be combined with the wilcoxonSignificant function in this module to get a meaningful result.

The samples are zipped together: if one is longer than the other, both are truncated to the the length of the shorter sample.

Note that: wilcoxonMatchedPairSignedRank == ((x, y) -> (y, x)) . flip wilcoxonMatchedPairSignedRank

wilcoxonMatchedPairSignificant Source

Arguments

:: TestType	Perform one- or two-tailed test (see description below).
-> Int	The sample size from which the (T+,T-) values were derived.
-> Double	The p-value at which to test (e.g. 0.05)
-> (Double, Double)	The (T+, T-) values from `wilcoxonMatchedPairSignedRank`.
-> Maybe TestResult	Return `Nothing` if the sample was too small to make a decision.

Tests whether a given result from a Wilcoxon signed-rank matched-pairs test is significant at the given level.

This function can perform a one-tailed or two-tailed test. If the first parameter to this function is TwoTailed, the test is performed two-tailed to check if the two samples differ significantly. If the first parameter is OneTailed, the check is performed one-tailed to decide whether the first sample (i.e. the first sample you passed to wilcoxonMatchedPairSignedRank) is greater than the second sample (i.e. the second sample you passed to wilcoxonMatchedPairSignedRank). If you wish to perform a one-tailed test in the opposite direction, you can either pass the parameters in a different order to wilcoxonMatchedPairSignedRank, or simply swap the values in the resulting pair before passing them to this function.

wilcoxonMatchedPairSignificance Source

Arguments

:: Int	The sample size
-> Double	The value of T for which you want the significance.
-> Double	The significance (p-value).

Works out the significance level (p-value) of a T value, given a sample size and a T value from the Wilcoxon signed-rank matched-pairs test.

See the notes on wilcoxonCriticalValue for how this is calculated.

wilcoxonMatchedPairCriticalValue Source

Arguments

:: Int	The sample size
-> Double	The p-value (e.g. 0.05) for which you want the critical value.
-> Maybe Int	The critical value (of T), or Nothing if the sample is too small to make a decision.

Obtains the critical value of T to compare against, given a sample size and a p-value (significance level). Your T value must be less than or equal to the return of this function in order for the test to work out significant. If there is a Nothing return, the sample size is too small to make a decision.

wilcoxonSignificant tests the return value of wilcoxonMatchedPairSignedRank for you, so you should use wilcoxonSignificant for determining test results. However, this function is useful, for example, for generating lookup tables for Wilcoxon signed rank critical values.

The return values of this function are generated using the method detailed in the paper "Critical Values for the Wilcoxon Signed Rank Statistic", Peter Mitic, The Mathematica Journal, volume 6, issue 3, 1996, which can be found here: http://www.mathematica-journal.com/issue/v6i3/article/mitic/contents/63mitic.pdf. According to that paper, the results may differ from other published lookup tables, but (Mitic claims) the values obtained by this function will be the correct ones.

Data types

data TestType Source

Test type. Exact meaning depends on a specific test. But generally it's tested whether some statistics is too big (small) for OneTailed or whether it too big or too small for TwoTailed

Constructors

OneTailed
TwoTailed

Instances

Eq TestType
Ord TestType
Show TestType
Typeable TestType

data TestResult Source

Result of hypothesis testing

Constructors

Significant	Null hypothesis should be rejected
NotSignificant	Data is compatible with hypothesis

Instances

Eq TestResult
Ord TestResult
Show TestResult
Typeable TestResult