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https://issues.apache.org/jira/browse/MATH-814?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13808595#comment-13808595
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Matt Adereth commented on MATH-814:
-----------------------------------
Apologies in advance for not being consistent with SpearmansCorrelation. I
couldn't bring myself to make these methods non-static or to use the approach
of having the constructor take the data. If this is a problem, I have no issue
making the requisite change.
Another consideration that I didn't do, but would be willing to try, would be
to make a new Correlation interface that exposes the methods that should be
common to Spearmans, Kendalls, and Pearsons. It would probably make sense to
then have an AbstractCorrelation base class that handles the sheparding of data
between Matrix, double[][], and double[], double[].
Finally, if you do think a Correlation interface makes sense, I'd also like to
propose a NonParametricCorrelation interface for Spearmans and Kendalls which
would have an additional method for computing the Correlation between two
List<Comparable> objects.
> Kendalls Tau Implementation
> ---------------------------
>
> Key: MATH-814
> URL: https://issues.apache.org/jira/browse/MATH-814
> Project: Commons Math
> Issue Type: New Feature
> Affects Versions: 4.0
> 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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