devl created MATH-814:
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Summary: 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
Fix For: 4.0
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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