statistics-0.10.3.1: A library of statistical types, data, and functions

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

- wilcoxonMatchedPairTest :: TestType -> Double -> Sample -> Sample -> Maybe TestResult
- wilcoxonMatchedPairSignedRank :: Sample -> Sample -> (Double, Double)
- wilcoxonMatchedPairSignificant :: TestType -> Int -> Double -> (Double, Double) -> Maybe TestResult
- wilcoxonMatchedPairSignificance :: Int -> Double -> Double
- wilcoxonMatchedPairCriticalValue :: Int -> Double -> Maybe Int
- data TestType
  - = OneTailed
  - | TwoTailed
- data TestResult
  - = Significant
  - | NotSignificant

# Wilcoxon signed-rank matched-pair test

wilcoxonMatchedPairTest

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)

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

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

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

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

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

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 |