Analysis of Mean Absolute Deviation for Randomized Block Design under Laplace Distribution

Elsayed A. H. Elamir

doi:doi:10.11648/j.ajtas.20150403.19

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Analysis of Mean Absolute Deviation for Randomized Block Design under Laplace Distribution

Elsayed A. H. Elamir

Published in American Journal of Theoretical and Applied Statistics (Volume 4, Issue 3)

Received: 2 April 2015 Accepted: 11 April 2015 Published: 21 April 2015

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Abstract

Analysis of mean absolute deviation (ANOMAD) for randomized block design is derived where the total sum of absolute deviation (TSA) is partition into exact block sum of absolute deviation (BLSA), exact treatment sum of absolute deviation (TRSA) and within sum of absolute deviation (WSA). The exact partitions are derived by getting rid of the absolute function from MAD by using the idea of re-expressing the mean absolute deviation as a weighted average of data with sum of weights zero. ANOMAD has advantages: offers meaningful measure of dispersion, does not square data, and can be extended to other location measures such as median. Two ANOMAD graphs are proposed. However, the variance-gamma distribution is used to fit the sampling distributions for the mean of BLSA and the mean of TRSA. Consequently, two tests of equal means and medians are proposed under the assumption of Laplace distribution.

Published in	American Journal of Theoretical and Applied Statistics (Volume 4, Issue 3)
DOI	10.11648/j.ajtas.20150403.19
Page(s)	138-149
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), 2015. Published by Science Publishing Group

Keywords

ANOVA, Effect Sizes, Laplace Distribution, MAD, Variance-Gamma Distribution

References

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APA Style

Elsayed A. H. Elamir. (2015). Analysis of Mean Absolute Deviation for Randomized Block Design under Laplace Distribution. American Journal of Theoretical and Applied Statistics, 4(3), 138-149. https://doi.org/10.11648/j.ajtas.20150403.19

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ACS Style

Elsayed A. H. Elamir. Analysis of Mean Absolute Deviation for Randomized Block Design under Laplace Distribution. Am. J. Theor. Appl. Stat. 2015, 4(3), 138-149. doi: 10.11648/j.ajtas.20150403.19

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AMA Style

Elsayed A. H. Elamir. Analysis of Mean Absolute Deviation for Randomized Block Design under Laplace Distribution. Am J Theor Appl Stat. 2015;4(3):138-149. doi: 10.11648/j.ajtas.20150403.19

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@article{10.11648/j.ajtas.20150403.19,
  author = {Elsayed A. H. Elamir},
  title = {Analysis of Mean Absolute Deviation for Randomized Block Design under Laplace Distribution},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {4},
  number = {3},
  pages = {138-149},
  doi = {10.11648/j.ajtas.20150403.19},
  url = {https://doi.org/10.11648/j.ajtas.20150403.19},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150403.19},
  abstract = {Analysis of mean absolute deviation (ANOMAD) for randomized block design is derived where the total sum of absolute deviation (TSA) is partition into exact block sum of absolute deviation (BLSA), exact treatment sum of absolute deviation (TRSA) and within sum of absolute deviation (WSA). The exact partitions are derived by getting rid of the absolute function from MAD by using the idea of re-expressing the mean absolute deviation as a weighted average of data with sum of weights zero. ANOMAD has advantages: offers meaningful measure of dispersion, does not square data, and can be extended to other location measures such as median. Two ANOMAD graphs are proposed. However, the variance-gamma distribution is used to fit the sampling distributions for the mean of BLSA and the mean of TRSA. Consequently, two tests of equal means and medians are proposed under the assumption of Laplace distribution.},
 year = {2015}
}

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TY  - JOUR
T1  - Analysis of Mean Absolute Deviation for Randomized Block Design under Laplace Distribution
AU  - Elsayed A. H. Elamir
Y1  - 2015/04/21
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.20150403.19
DO  - 10.11648/j.ajtas.20150403.19
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  - 138
EP  - 149
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20150403.19
AB  - Analysis of mean absolute deviation (ANOMAD) for randomized block design is derived where the total sum of absolute deviation (TSA) is partition into exact block sum of absolute deviation (BLSA), exact treatment sum of absolute deviation (TRSA) and within sum of absolute deviation (WSA). The exact partitions are derived by getting rid of the absolute function from MAD by using the idea of re-expressing the mean absolute deviation as a weighted average of data with sum of weights zero. ANOMAD has advantages: offers meaningful measure of dispersion, does not square data, and can be extended to other location measures such as median. Two ANOMAD graphs are proposed. However, the variance-gamma distribution is used to fit the sampling distributions for the mean of BLSA and the mean of TRSA. Consequently, two tests of equal means and medians are proposed under the assumption of Laplace distribution.
VL  - 4
IS  - 3
ER  -

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Author Information

Elsayed A. H. Elamir

Department of Statistics and Mathematics, Benha University, Benha, Egypt & Management & Marketing Department, College of Business, University of Bahrain, Manama, Kingdom of Bahrain

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APA Style

Elsayed A. H. Elamir. (2015). Analysis of Mean Absolute Deviation for Randomized Block Design under Laplace Distribution. American Journal of Theoretical and Applied Statistics, 4(3), 138-149. https://doi.org/10.11648/j.ajtas.20150403.19

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ACS Style

Elsayed A. H. Elamir. Analysis of Mean Absolute Deviation for Randomized Block Design under Laplace Distribution. Am. J. Theor. Appl. Stat. 2015, 4(3), 138-149. doi: 10.11648/j.ajtas.20150403.19

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AMA Style

Elsayed A. H. Elamir. Analysis of Mean Absolute Deviation for Randomized Block Design under Laplace Distribution. Am J Theor Appl Stat. 2015;4(3):138-149. doi: 10.11648/j.ajtas.20150403.19

Copy | Download

@article{10.11648/j.ajtas.20150403.19,
  author = {Elsayed A. H. Elamir},
  title = {Analysis of Mean Absolute Deviation for Randomized Block Design under Laplace Distribution},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {4},
  number = {3},
  pages = {138-149},
  doi = {10.11648/j.ajtas.20150403.19},
  url = {https://doi.org/10.11648/j.ajtas.20150403.19},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150403.19},
  abstract = {Analysis of mean absolute deviation (ANOMAD) for randomized block design is derived where the total sum of absolute deviation (TSA) is partition into exact block sum of absolute deviation (BLSA), exact treatment sum of absolute deviation (TRSA) and within sum of absolute deviation (WSA). The exact partitions are derived by getting rid of the absolute function from MAD by using the idea of re-expressing the mean absolute deviation as a weighted average of data with sum of weights zero. ANOMAD has advantages: offers meaningful measure of dispersion, does not square data, and can be extended to other location measures such as median. Two ANOMAD graphs are proposed. However, the variance-gamma distribution is used to fit the sampling distributions for the mean of BLSA and the mean of TRSA. Consequently, two tests of equal means and medians are proposed under the assumption of Laplace distribution.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Analysis of Mean Absolute Deviation for Randomized Block Design under Laplace Distribution
AU  - Elsayed A. H. Elamir
Y1  - 2015/04/21
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.20150403.19
DO  - 10.11648/j.ajtas.20150403.19
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  - 138
EP  - 149
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20150403.19
AB  - Analysis of mean absolute deviation (ANOMAD) for randomized block design is derived where the total sum of absolute deviation (TSA) is partition into exact block sum of absolute deviation (BLSA), exact treatment sum of absolute deviation (TRSA) and within sum of absolute deviation (WSA). The exact partitions are derived by getting rid of the absolute function from MAD by using the idea of re-expressing the mean absolute deviation as a weighted average of data with sum of weights zero. ANOMAD has advantages: offers meaningful measure of dispersion, does not square data, and can be extended to other location measures such as median. Two ANOMAD graphs are proposed. However, the variance-gamma distribution is used to fit the sampling distributions for the mean of BLSA and the mean of TRSA. Consequently, two tests of equal means and medians are proposed under the assumption of Laplace distribution.
VL  - 4
IS  - 3
ER  -

Copy | Download