Intrinsically Ties Adjusted Tau (C-Tat) Correlation Coefficient

OYEKA CYPRIL ANENE; OSUJI GEORGE AMAEZE; NWANKWO CHRISTIAN CHUKWUEMEKA

doi:doi:10.11648/j.ajtas.20130206.26

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Intrinsically Ties Adjusted Tau (C-Tat) Correlation Coefficient

OYEKA CYPRIL ANENE, OSUJI GEORGE AMAEZE, NWANKWO CHRISTIAN CHUKWUEMEKA

Published in American Journal of Theoretical and Applied Statistics (Volume 2, Issue 6)

Received: 23 November 2013 Published: 10 January 2014

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Abstract

This paper proposes a method for correcting and adjusting the usual or regular estimates of Tau correlation coefficients for the possibility of ties within and between observations in the population being correlated. The index here called C-Tat for ‘ties adjusted Tau correlation coefficient’ is formulated to intrinsically and structurally adjust and correct the estimated Tau correlation coefficient for the possible presence of tied observations in the sampled populations and for the fact that the estimates obtained are often dependent on, that is, vary depending on which of the two populations under study has its assigned ranks arranged in their natural order and which has its assigned ranks arranged in their natural order and which has its assigned ranks tagged along. The proposed method is illustrated with some sample data and shown to yield more reliable and efficient estimates of tau correlation coefficients than the usual method which is able to give the same estimates only if there are no tied observations what-so-ever in the sampled populations.

Published in	American Journal of Theoretical and Applied Statistics (Volume 2, Issue 6)
DOI	10.11648/j.ajtas.20130206.26
Page(s)	273-281
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Tau Correlation Coefficient, C-Tat, Tied Observations and Ties Adjusted

References

[1]	Gibbion, J.D. (1973): Non parametric Statistical Inference "Mc Graw.Hills book Company, New York.
[2]	Hollander, M. and Woife, D.A. (1999); Non parametric Statistical methods (2nd edition) Wiley-Inter Science, New York.
[3]	Kendall, M. G. (1962); rank Correlation Methods Hafner Publishing Company, Inc., New York.
[4]	Oyeka, C.A. etal (2009). A method of analyzing paired data intrinsically adjusted for tie Global Journal of maths and Statistics Vol.1, Pg 1-6.
[5]	Oyeka, C.A. (1996). An introduction to applied Statistical Method , Nobern avocation Publishing Company, Enugu- Nigeria

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OYEKA CYPRIL ANENE, OSUJI GEORGE AMAEZE, NWANKWO CHRISTIAN CHUKWUEMEKA. (2014). Intrinsically Ties Adjusted Tau (C-Tat) Correlation Coefficient. American Journal of Theoretical and Applied Statistics, 2(6), 273-281. https://doi.org/10.11648/j.ajtas.20130206.26

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OYEKA CYPRIL ANENE; OSUJI GEORGE AMAEZE; NWANKWO CHRISTIAN CHUKWUEMEKA. Intrinsically Ties Adjusted Tau (C-Tat) Correlation Coefficient. Am. J. Theor. Appl. Stat. 2014, 2(6), 273-281. doi: 10.11648/j.ajtas.20130206.26

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AMA Style

OYEKA CYPRIL ANENE, OSUJI GEORGE AMAEZE, NWANKWO CHRISTIAN CHUKWUEMEKA. Intrinsically Ties Adjusted Tau (C-Tat) Correlation Coefficient. Am J Theor Appl Stat. 2014;2(6):273-281. doi: 10.11648/j.ajtas.20130206.26

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@article{10.11648/j.ajtas.20130206.26,
  author = {OYEKA CYPRIL ANENE and OSUJI GEORGE AMAEZE and NWANKWO CHRISTIAN CHUKWUEMEKA},
  title = {Intrinsically Ties Adjusted Tau (C-Tat) Correlation Coefficient},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {2},
  number = {6},
  pages = {273-281},
  doi = {10.11648/j.ajtas.20130206.26},
  url = {https://doi.org/10.11648/j.ajtas.20130206.26},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20130206.26},
  abstract = {This paper proposes a method for correcting and adjusting the usual or regular estimates of Tau correlation coefficients for the possibility of ties within and between observations in the population being correlated. The index here called C-Tat for ‘ties adjusted Tau correlation coefficient’ is formulated to intrinsically and structurally adjust and correct the estimated Tau correlation coefficient for the possible presence of tied observations in the sampled populations and for the fact that the estimates obtained are often dependent on, that is, vary depending on which of the two populations under study has its assigned ranks arranged in their natural order and which has its assigned ranks arranged in their natural order and which has its assigned ranks tagged along. The proposed method is illustrated with some sample data and shown to yield more reliable and efficient estimates of tau correlation coefficients than the usual method which is able to give the same estimates only if there are no tied observations what-so-ever in the sampled populations.},
 year = {2014}
}

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TY  - JOUR
T1  - Intrinsically Ties Adjusted Tau (C-Tat) Correlation Coefficient
AU  - OYEKA CYPRIL ANENE
AU  - OSUJI GEORGE AMAEZE
AU  - NWANKWO CHRISTIAN CHUKWUEMEKA
Y1  - 2014/01/10
PY  - 2014
N1  - https://doi.org/10.11648/j.ajtas.20130206.26
DO  - 10.11648/j.ajtas.20130206.26
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 273
EP  - 281
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20130206.26
AB  - This paper proposes a method for correcting and adjusting the usual or regular estimates of Tau correlation coefficients for the possibility of ties within and between observations in the population being correlated. The index here called C-Tat for ‘ties adjusted Tau correlation coefficient’ is formulated to intrinsically and structurally adjust and correct the estimated Tau correlation coefficient for the possible presence of tied observations in the sampled populations and for the fact that the estimates obtained are often dependent on, that is, vary depending on which of the two populations under study has its assigned ranks arranged in their natural order and which has its assigned ranks arranged in their natural order and which has its assigned ranks tagged along. The proposed method is illustrated with some sample data and shown to yield more reliable and efficient estimates of tau correlation coefficients than the usual method which is able to give the same estimates only if there are no tied observations what-so-ever in the sampled populations.
VL  - 2
IS  - 6
ER  -

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Author Information

OYEKA CYPRIL ANENE

Department of Statistics, Nnamdi Azikiwe University, Awka, Nigeria
OSUJI GEORGE AMAEZE

Department of Statistics, Nnamdi Azikiwe University, Awka, Nigeria
NWANKWO CHRISTIAN CHUKWUEMEKA

Department of Statistics, Nnamdi Azikiwe University, Awka, Nigeria

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APA Style

OYEKA CYPRIL ANENE, OSUJI GEORGE AMAEZE, NWANKWO CHRISTIAN CHUKWUEMEKA. (2014). Intrinsically Ties Adjusted Tau (C-Tat) Correlation Coefficient. American Journal of Theoretical and Applied Statistics, 2(6), 273-281. https://doi.org/10.11648/j.ajtas.20130206.26

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ACS Style

OYEKA CYPRIL ANENE; OSUJI GEORGE AMAEZE; NWANKWO CHRISTIAN CHUKWUEMEKA. Intrinsically Ties Adjusted Tau (C-Tat) Correlation Coefficient. Am. J. Theor. Appl. Stat. 2014, 2(6), 273-281. doi: 10.11648/j.ajtas.20130206.26

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AMA Style

OYEKA CYPRIL ANENE, OSUJI GEORGE AMAEZE, NWANKWO CHRISTIAN CHUKWUEMEKA. Intrinsically Ties Adjusted Tau (C-Tat) Correlation Coefficient. Am J Theor Appl Stat. 2014;2(6):273-281. doi: 10.11648/j.ajtas.20130206.26

Copy | Download

@article{10.11648/j.ajtas.20130206.26,
  author = {OYEKA CYPRIL ANENE and OSUJI GEORGE AMAEZE and NWANKWO CHRISTIAN CHUKWUEMEKA},
  title = {Intrinsically Ties Adjusted Tau (C-Tat) Correlation Coefficient},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {2},
  number = {6},
  pages = {273-281},
  doi = {10.11648/j.ajtas.20130206.26},
  url = {https://doi.org/10.11648/j.ajtas.20130206.26},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20130206.26},
  abstract = {This paper proposes a method for correcting and adjusting the usual or regular estimates of Tau correlation coefficients for the possibility of ties within and between observations in the population being correlated. The index here called C-Tat for ‘ties adjusted Tau correlation coefficient’ is formulated to intrinsically and structurally adjust and correct the estimated Tau correlation coefficient for the possible presence of tied observations in the sampled populations and for the fact that the estimates obtained are often dependent on, that is, vary depending on which of the two populations under study has its assigned ranks arranged in their natural order and which has its assigned ranks arranged in their natural order and which has its assigned ranks tagged along. The proposed method is illustrated with some sample data and shown to yield more reliable and efficient estimates of tau correlation coefficients than the usual method which is able to give the same estimates only if there are no tied observations what-so-ever in the sampled populations.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Intrinsically Ties Adjusted Tau (C-Tat) Correlation Coefficient
AU  - OYEKA CYPRIL ANENE
AU  - OSUJI GEORGE AMAEZE
AU  - NWANKWO CHRISTIAN CHUKWUEMEKA
Y1  - 2014/01/10
PY  - 2014
N1  - https://doi.org/10.11648/j.ajtas.20130206.26
DO  - 10.11648/j.ajtas.20130206.26
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 273
EP  - 281
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20130206.26
AB  - This paper proposes a method for correcting and adjusting the usual or regular estimates of Tau correlation coefficients for the possibility of ties within and between observations in the population being correlated. The index here called C-Tat for ‘ties adjusted Tau correlation coefficient’ is formulated to intrinsically and structurally adjust and correct the estimated Tau correlation coefficient for the possible presence of tied observations in the sampled populations and for the fact that the estimates obtained are often dependent on, that is, vary depending on which of the two populations under study has its assigned ranks arranged in their natural order and which has its assigned ranks arranged in their natural order and which has its assigned ranks tagged along. The proposed method is illustrated with some sample data and shown to yield more reliable and efficient estimates of tau correlation coefficients than the usual method which is able to give the same estimates only if there are no tied observations what-so-ever in the sampled populations.
VL  - 2
IS  - 6
ER  -

Copy | Download