statistics-0.13.1.0: A library of statistical types, data, and functions

Portability portable experimental bos@serpentine.com None

Statistics.Test.WilcoxonT

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 serious bug and couldn't be used with samples larger than 1023. https://github.com/bos/statistics/issues/18

Synopsis

# Wilcoxon signed-rank matched-pair test

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.

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.

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.

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

data TestResult Source

Result of hypothesis testing

Constructors

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