Intrinsically Ties Adjusted Partial Tau (C-Tap) Correlation Coefficient

Oyeka Ikewelugo Cyprian Anaene; Osuji George Amaeze; Obiora-Ilouno Happiness Onyebuchi

doi:doi:10.11648/j.ajtas.20160505.14

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Intrinsically Ties Adjusted Partial Tau (C-Tap) Correlation Coefficient

Oyeka Ikewelugo Cyprian Anaene, Osuji George Amaeze, Obiora-Ilouno Happiness Onyebuchi

Published in American Journal of Theoretical and Applied Statistics (Volume 5, Issue 5)

Received: 21 December 2015 Accepted: 24 May 2016 Published: 10 August 2016

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Abstract

This paper present a non-parametric statistical method for the estimation of partial correlation coefficient intrinsically adjusted for tied observations in the data. The method based on a modification of the method of estimating Tau correlation coefficient may be used when the population of interest are measurements on as low as the ordinal scale that are not necessary continuous or even numeric. The estimated partial correlation coefficient is a weighted average of the estimates obtained when each of the observations whose assigned ranks are arranged in their natural order as well as the observations whose assigned ranks are tagged along, with the weights being functions of the number of tied observations in each population. It is shown that failure to adjust for ties tends to lead to an underestimation of the true partial correlation coefficient, an effect that increases with the number of ties in the data. The proposed method is illustrated with some data and shown to compare favorably with the Kendall approach.

Published in	American Journal of Theoretical and Applied Statistics (Volume 5, Issue 5)
DOI	10.11648/j.ajtas.20160505.14
Page(s)	270-279
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), 2016. Published by Science Publishing Group

Keywords

Intrinsically, Ties, Adjusted Partial Tau (C-Tap), Correlation, Coefficient, Estimation

References

[1]	Ebuh G. U, Oyeka I. C. A (2012) “A Nonparametric Method for Estimating Partial Correlation Coefficient” J Biom Biostat 3: 156. doi:10.4172/2155-6180.1000156.
[2]	Fraser, D. A. S. (1957) “Nonparametric Methods in Statistics” John Wiley & Sons, Inc., New York.
[3]	Gibbon, J. D (1973), “Non parametric statistical inference” Mc Graw Hills book company, New York.
[4]	Hollander, m and Woife, D. A. (1999), “Non parametric statistical Methods (2nd edition) Wiley-Inter Science, New York.
[5]	Kendall, M. G. (1948), Rank Correlation Methods, Hafiner Publishing Company. Inc. New York.
[6]	Noether, G. E. (1967) “Elements of Nonparametric Statistics” John Wiley & Sons, Inc., New York.
[7]	Siegel Sidney (1956) Nonparametric Statistics for the Behavioral Sciences. McGraw-Hill Series in Psychology, New York.
[8]	Oyeka, C. A Osuji, G. A and Nwankwo, C. C. (2013), “Intrinsically ties adjusted Tau (C – Tat) Correlation Coefficient” American Journal of Theoretical and Applied Statistics Vol 2 pp 273–281.
[9]	Oyeka I. C. A., Ebuh G. U., Nwosu C. R., Utazi E. C., Ikpegbu P. A., Obiora-Ilouno H & Nwankwo C. C. (2009) “A Method of Analyzing Paired Data Intrinsically Adjusted for Ties”. Global Journal of Mathematics and Statistics, India. Volume1, Number 1, 2009. 1-6.
[10]	Oyeka, C. A. (1996) “An introduction to applied statistical method. Nobern avocation Publication Company, Enugu-Nigeria.

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APA Style

Oyeka Ikewelugo Cyprian Anaene, Osuji George Amaeze, Obiora-Ilouno Happiness Onyebuchi. (2016). Intrinsically Ties Adjusted Partial Tau (C-Tap) Correlation Coefficient. American Journal of Theoretical and Applied Statistics, 5(5), 270-279. https://doi.org/10.11648/j.ajtas.20160505.14

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ACS Style

Oyeka Ikewelugo Cyprian Anaene; Osuji George Amaeze; Obiora-Ilouno Happiness Onyebuchi. Intrinsically Ties Adjusted Partial Tau (C-Tap) Correlation Coefficient. Am. J. Theor. Appl. Stat. 2016, 5(5), 270-279. doi: 10.11648/j.ajtas.20160505.14

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AMA Style

Oyeka Ikewelugo Cyprian Anaene, Osuji George Amaeze, Obiora-Ilouno Happiness Onyebuchi. Intrinsically Ties Adjusted Partial Tau (C-Tap) Correlation Coefficient. Am J Theor Appl Stat. 2016;5(5):270-279. doi: 10.11648/j.ajtas.20160505.14

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@article{10.11648/j.ajtas.20160505.14,
  author = {Oyeka Ikewelugo Cyprian Anaene and Osuji George Amaeze and Obiora-Ilouno Happiness Onyebuchi},
  title = {Intrinsically Ties Adjusted Partial Tau (C-Tap) Correlation Coefficient},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {5},
  pages = {270-279},
  doi = {10.11648/j.ajtas.20160505.14},
  url = {https://doi.org/10.11648/j.ajtas.20160505.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160505.14},
  abstract = {This paper present a non-parametric statistical method for the estimation of partial correlation coefficient intrinsically adjusted for tied observations in the data. The method based on a modification of the method of estimating Tau correlation coefficient may be used when the population of interest are measurements on as low as the ordinal scale that are not necessary continuous or even numeric. The estimated partial correlation coefficient is a weighted average of the estimates obtained when each of the observations whose assigned ranks are arranged in their natural order as well as the observations whose assigned ranks are tagged along, with the weights being functions of the number of tied observations in each population. It is shown that failure to adjust for ties tends to lead to an underestimation of the true partial correlation coefficient, an effect that increases with the number of ties in the data. The proposed method is illustrated with some data and shown to compare favorably with the Kendall approach.},
 year = {2016}
}

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TY  - JOUR
T1  - Intrinsically Ties Adjusted Partial Tau (C-Tap) Correlation Coefficient
AU  - Oyeka Ikewelugo Cyprian Anaene
AU  - Osuji George Amaeze
AU  - Obiora-Ilouno Happiness Onyebuchi
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T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
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AB  - This paper present a non-parametric statistical method for the estimation of partial correlation coefficient intrinsically adjusted for tied observations in the data. The method based on a modification of the method of estimating Tau correlation coefficient may be used when the population of interest are measurements on as low as the ordinal scale that are not necessary continuous or even numeric. The estimated partial correlation coefficient is a weighted average of the estimates obtained when each of the observations whose assigned ranks are arranged in their natural order as well as the observations whose assigned ranks are tagged along, with the weights being functions of the number of tied observations in each population. It is shown that failure to adjust for ties tends to lead to an underestimation of the true partial correlation coefficient, an effect that increases with the number of ties in the data. The proposed method is illustrated with some data and shown to compare favorably with the Kendall approach.
VL  - 5
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Author Information

Oyeka Ikewelugo Cyprian Anaene

Derpartment of Statistics, Physical Science Faculty, Nnamdi Azikiwe University, Awka, Nigeria
Osuji George Amaeze

Derpartment of Statistics, Physical Science Faculty, Nnamdi Azikiwe University, Awka, Nigeria
Obiora-Ilouno Happiness Onyebuchi

Derpartment of Statistics, Physical Science Faculty, Nnamdi Azikiwe University, Awka, Nigeria

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APA Style

Oyeka Ikewelugo Cyprian Anaene, Osuji George Amaeze, Obiora-Ilouno Happiness Onyebuchi. (2016). Intrinsically Ties Adjusted Partial Tau (C-Tap) Correlation Coefficient. American Journal of Theoretical and Applied Statistics, 5(5), 270-279. https://doi.org/10.11648/j.ajtas.20160505.14

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ACS Style

Oyeka Ikewelugo Cyprian Anaene; Osuji George Amaeze; Obiora-Ilouno Happiness Onyebuchi. Intrinsically Ties Adjusted Partial Tau (C-Tap) Correlation Coefficient. Am. J. Theor. Appl. Stat. 2016, 5(5), 270-279. doi: 10.11648/j.ajtas.20160505.14

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AMA Style

Oyeka Ikewelugo Cyprian Anaene, Osuji George Amaeze, Obiora-Ilouno Happiness Onyebuchi. Intrinsically Ties Adjusted Partial Tau (C-Tap) Correlation Coefficient. Am J Theor Appl Stat. 2016;5(5):270-279. doi: 10.11648/j.ajtas.20160505.14

Copy | Download

@article{10.11648/j.ajtas.20160505.14,
  author = {Oyeka Ikewelugo Cyprian Anaene and Osuji George Amaeze and Obiora-Ilouno Happiness Onyebuchi},
  title = {Intrinsically Ties Adjusted Partial Tau (C-Tap) Correlation Coefficient},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {5},
  pages = {270-279},
  doi = {10.11648/j.ajtas.20160505.14},
  url = {https://doi.org/10.11648/j.ajtas.20160505.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160505.14},
  abstract = {This paper present a non-parametric statistical method for the estimation of partial correlation coefficient intrinsically adjusted for tied observations in the data. The method based on a modification of the method of estimating Tau correlation coefficient may be used when the population of interest are measurements on as low as the ordinal scale that are not necessary continuous or even numeric. The estimated partial correlation coefficient is a weighted average of the estimates obtained when each of the observations whose assigned ranks are arranged in their natural order as well as the observations whose assigned ranks are tagged along, with the weights being functions of the number of tied observations in each population. It is shown that failure to adjust for ties tends to lead to an underestimation of the true partial correlation coefficient, an effect that increases with the number of ties in the data. The proposed method is illustrated with some data and shown to compare favorably with the Kendall approach.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Intrinsically Ties Adjusted Partial Tau (C-Tap) Correlation Coefficient
AU  - Oyeka Ikewelugo Cyprian Anaene
AU  - Osuji George Amaeze
AU  - Obiora-Ilouno Happiness Onyebuchi
Y1  - 2016/08/10
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160505.14
DO  - 10.11648/j.ajtas.20160505.14
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  - 270
EP  - 279
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160505.14
AB  - This paper present a non-parametric statistical method for the estimation of partial correlation coefficient intrinsically adjusted for tied observations in the data. The method based on a modification of the method of estimating Tau correlation coefficient may be used when the population of interest are measurements on as low as the ordinal scale that are not necessary continuous or even numeric. The estimated partial correlation coefficient is a weighted average of the estimates obtained when each of the observations whose assigned ranks are arranged in their natural order as well as the observations whose assigned ranks are tagged along, with the weights being functions of the number of tied observations in each population. It is shown that failure to adjust for ties tends to lead to an underestimation of the true partial correlation coefficient, an effect that increases with the number of ties in the data. The proposed method is illustrated with some data and shown to compare favorably with the Kendall approach.
VL  - 5
IS  - 5
ER  -

Copy | Download