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https://issues.apache.org/jira/browse/MATH-814?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
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Thomas Neidhart updated MATH-814:
---------------------------------
Affects Version/s: (was: 4.0)
3.2
> Kendalls Tau Implementation
> ---------------------------
>
> Key: MATH-814
> URL: https://issues.apache.org/jira/browse/MATH-814
> Project: Commons Math
> Issue Type: New Feature
> Affects Versions: 3.2
> Environment: All
> Reporter: devl
> Assignee: Phil Steitz
> Labels: correlation, rank
> Fix For: 4.0
>
> Attachments: kendalls-tau.patch
>
> Original Estimate: 840h
> Remaining Estimate: 840h
>
> Implement the Kendall's Tau which is a measure of Association/Correlation
> between ranked ordinal data.
> A basic description is available at
> http://en.wikipedia.org/wiki/Kendall_tau_rank_correlation_coefficient however
> the test implementation will follow that defined by "Handbook of Parametric
> and Nonparametric Statistical Procedures, Fifth Edition, Page 1393 Test 30,
> ISBN-10: 1439858012 | ISBN-13: 978-1439858011."
> The algorithm is proposed as follows.
> Given two rankings or permutations represented by a 2D matrix; columns
> indicate rankings (e.g. by an individual) and row are observations of each
> rank. The algorithm is to calculate the total number of concordant pairs of
> ranks (between columns), discordant pairs of ranks (between columns) and
> calculate the Tau defined as
> tau= (Number of concordant - number of discordant)/(n(n-1)/2)
> where n(n-1)/2 is the total number of possible pairs of ranks.
> The method will then output the tau value between -1 and 1 where 1 signifies
> a "perfect" correlation between the two ranked lists.
> Where ties exist within a ranking it is marked as neither concordant nor
> discordant in the calculation. An optional merge sort can be used to speed up
> the implementation. Details are in the wiki page.
> Although this implementation is not particularly complex it would be useful
> to have it in a consistent format in the commons math package in addition to
> existing correlation tests. Kendall's Tau is used effectively in comparing
> ranks for products, rankings from search engines or measurements from
> engineering equipment.
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