Modified Extended Median Test for C Matched Samples

Oyeka Ikewelugo Cyprian Anaene; Okeh Uchechukwu Marius

doi:doi:10.11648/j.cbb.20130105.11

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Modified Extended Median Test for C Matched Samples

Oyeka Ikewelugo Cyprian Anaene, Okeh Uchechukwu Marius

Published in Computational Biology and Bioinformatics (Volume 1, Issue 5)

Received: 21 October 2013 Accepted: Published: 30 November 2013

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Abstract

This work presented an extended median test for analyzing samples that are not independent but paired or matched given some criteria. Here, the data for analysis are presented in table form with the column corresponding to one factor with ‘c’ treatments or conditions considered as fixed, while the row as second factor with say ‘k’ subjects ,batches, blocks or levels which are considered random given that there is only one observation per cell. These observations themselves may be measurements on as low as the ordinal scale. The null hypothesis to be tested was that there is no difference between the ‘c’ treatments, thus having equal medians. This required the use of Friedman test and an alternative ties adjusted method. Although these methods lead to the same conclusions, the relative sizes of the calculated chi-square values suggest that the Friedman test is likely to lead to an acceptance of a false null hypothesis (Type II error) more frequently and hence likely to be less powerful than the ties adjusted modified extended median test. Nevertheless, the Friedman’s two-way analysis of variance test by ranks is here at least shown to be still more powerful than the usual extended median test.

Published in	Computational Biology and Bioinformatics (Volume 1, Issue 5)
DOI	10.11648/j.cbb.20130105.11
Page(s)	22-27
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), 2024. Published by Science Publishing Group

Keywords

Friedman Test, Treatment, Modified Extended Median Test, Measurements, Matched Samples, Ties Adjusted Method

References

[1]	Agresti A.(1992).Analysis of Ordinal Paired Comparison data. Appl Statist 41:287-297.
[2]	Gibbons, JD (1971). Nonparametric Statistical Inferences. McGraw Hill Book Company, New York.
[3]	Munzel U, Brunner E.(2002). An exact paired rank test. Biometrical Journal 44:584-593.
[4]	Oyeka I.C.A and Okeh U.M.(2012). Intrinsically Ties Adjusted Sign Test by Ranks. J Biom Biostat 2012, 3:8
[5]	Siegel, Sydney (1956): Nonparametric Statistics for the behavioral sciences. McGraw-Hill KOGAKUSHA,
[6]	LTD. International Student Edition.

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APA Style

Oyeka Ikewelugo Cyprian Anaene, Okeh Uchechukwu Marius. (2013). Modified Extended Median Test for C Matched Samples. Computational Biology and Bioinformatics, 1(5), 22-27. https://doi.org/10.11648/j.cbb.20130105.11

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ACS Style

Oyeka Ikewelugo Cyprian Anaene; Okeh Uchechukwu Marius. Modified Extended Median Test for C Matched Samples. Comput. Biol. Bioinform. 2013, 1(5), 22-27. doi: 10.11648/j.cbb.20130105.11

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AMA Style

Oyeka Ikewelugo Cyprian Anaene, Okeh Uchechukwu Marius. Modified Extended Median Test for C Matched Samples. Comput Biol Bioinform. 2013;1(5):22-27. doi: 10.11648/j.cbb.20130105.11

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@article{10.11648/j.cbb.20130105.11,
  author = {Oyeka Ikewelugo Cyprian Anaene and Okeh Uchechukwu Marius},
  title = {Modified Extended Median Test for C Matched Samples},
  journal = {Computational Biology and Bioinformatics},
  volume = {1},
  number = {5},
  pages = {22-27},
  doi = {10.11648/j.cbb.20130105.11},
  url = {https://doi.org/10.11648/j.cbb.20130105.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cbb.20130105.11},
  abstract = {This work presented an extended median test for analyzing samples that are not independent but paired or matched given some criteria. Here, the data for analysis are presented in table form with the column corresponding to one factor with ‘c’ treatments or conditions considered as fixed, while the row as second factor with say ‘k’ subjects ,batches, blocks or levels which are considered random given that there is only one observation per cell. These observations themselves may be measurements on as low as the ordinal scale. The null hypothesis to be tested was that there is no difference between the ‘c’ treatments, thus having equal medians. This required the use of Friedman test and an alternative ties adjusted method. Although these methods lead to the same conclusions, the relative sizes of the calculated chi-square values suggest that the Friedman test is likely to lead to an acceptance of a false null hypothesis (Type II error) more frequently and hence likely to be less powerful than the ties adjusted modified extended median test. Nevertheless, the Friedman’s two-way analysis of variance test by ranks is here at least shown to be still more powerful than the usual extended median test.},
 year = {2013}
}

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TY  - JOUR
T1  - Modified Extended Median Test for C Matched Samples
AU  - Oyeka Ikewelugo Cyprian Anaene
AU  - Okeh Uchechukwu Marius
Y1  - 2013/11/30
PY  - 2013
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JF  - Computational Biology and Bioinformatics
JO  - Computational Biology and Bioinformatics
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PB  - Science Publishing Group
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AB  - This work presented an extended median test for analyzing samples that are not independent but paired or matched given some criteria. Here, the data for analysis are presented in table form with the column corresponding to one factor with ‘c’ treatments or conditions considered as fixed, while the row as second factor with say ‘k’ subjects ,batches, blocks or levels which are considered random given that there is only one observation per cell. These observations themselves may be measurements on as low as the ordinal scale. The null hypothesis to be tested was that there is no difference between the ‘c’ treatments, thus having equal medians. This required the use of Friedman test and an alternative ties adjusted method. Although these methods lead to the same conclusions, the relative sizes of the calculated chi-square values suggest that the Friedman test is likely to lead to an acceptance of a false null hypothesis (Type II error) more frequently and hence likely to be less powerful than the ties adjusted modified extended median test. Nevertheless, the Friedman’s two-way analysis of variance test by ranks is here at least shown to be still more powerful than the usual extended median test.
VL  - 1
IS  - 5
ER  -

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Author Information

Oyeka Ikewelugo Cyprian Anaene

Department of Statistics, Nnamdi Azikiwe University, Awka, Anambra State, Nigeria
Okeh Uchechukwu Marius

Department of Industrial Mathematics and Applied Statistics, Ebonyi State University Abakaliki, Nigeria

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APA Style

Oyeka Ikewelugo Cyprian Anaene, Okeh Uchechukwu Marius. (2013). Modified Extended Median Test for C Matched Samples. Computational Biology and Bioinformatics, 1(5), 22-27. https://doi.org/10.11648/j.cbb.20130105.11

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ACS Style

Oyeka Ikewelugo Cyprian Anaene; Okeh Uchechukwu Marius. Modified Extended Median Test for C Matched Samples. Comput. Biol. Bioinform. 2013, 1(5), 22-27. doi: 10.11648/j.cbb.20130105.11

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AMA Style

Oyeka Ikewelugo Cyprian Anaene, Okeh Uchechukwu Marius. Modified Extended Median Test for C Matched Samples. Comput Biol Bioinform. 2013;1(5):22-27. doi: 10.11648/j.cbb.20130105.11

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@article{10.11648/j.cbb.20130105.11,
  author = {Oyeka Ikewelugo Cyprian Anaene and Okeh Uchechukwu Marius},
  title = {Modified Extended Median Test for C Matched Samples},
  journal = {Computational Biology and Bioinformatics},
  volume = {1},
  number = {5},
  pages = {22-27},
  doi = {10.11648/j.cbb.20130105.11},
  url = {https://doi.org/10.11648/j.cbb.20130105.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cbb.20130105.11},
  abstract = {This work presented an extended median test for analyzing samples that are not independent but paired or matched given some criteria. Here, the data for analysis are presented in table form with the column corresponding to one factor with ‘c’ treatments or conditions considered as fixed, while the row as second factor with say ‘k’ subjects ,batches, blocks or levels which are considered random given that there is only one observation per cell. These observations themselves may be measurements on as low as the ordinal scale. The null hypothesis to be tested was that there is no difference between the ‘c’ treatments, thus having equal medians. This required the use of Friedman test and an alternative ties adjusted method. Although these methods lead to the same conclusions, the relative sizes of the calculated chi-square values suggest that the Friedman test is likely to lead to an acceptance of a false null hypothesis (Type II error) more frequently and hence likely to be less powerful than the ties adjusted modified extended median test. Nevertheless, the Friedman’s two-way analysis of variance test by ranks is here at least shown to be still more powerful than the usual extended median test.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - Modified Extended Median Test for C Matched Samples
AU  - Oyeka Ikewelugo Cyprian Anaene
AU  - Okeh Uchechukwu Marius
Y1  - 2013/11/30
PY  - 2013
N1  - https://doi.org/10.11648/j.cbb.20130105.11
DO  - 10.11648/j.cbb.20130105.11
T2  - Computational Biology and Bioinformatics
JF  - Computational Biology and Bioinformatics
JO  - Computational Biology and Bioinformatics
SP  - 22
EP  - 27
PB  - Science Publishing Group
SN  - 2330-8281
UR  - https://doi.org/10.11648/j.cbb.20130105.11
AB  - This work presented an extended median test for analyzing samples that are not independent but paired or matched given some criteria. Here, the data for analysis are presented in table form with the column corresponding to one factor with ‘c’ treatments or conditions considered as fixed, while the row as second factor with say ‘k’ subjects ,batches, blocks or levels which are considered random given that there is only one observation per cell. These observations themselves may be measurements on as low as the ordinal scale. The null hypothesis to be tested was that there is no difference between the ‘c’ treatments, thus having equal medians. This required the use of Friedman test and an alternative ties adjusted method. Although these methods lead to the same conclusions, the relative sizes of the calculated chi-square values suggest that the Friedman test is likely to lead to an acceptance of a false null hypothesis (Type II error) more frequently and hence likely to be less powerful than the ties adjusted modified extended median test. Nevertheless, the Friedman’s two-way analysis of variance test by ranks is here at least shown to be still more powerful than the usual extended median test.
VL  - 1
IS  - 5
ER  -

Copy | Download