Classification of Some Test of Normality Techniques into UMP and LMP Using Monte Carlo Simulation Technique

Awopeju Kabiru Abidemi; Ajibade Fatai Bright; Abuh Musa

doi:doi:10.11648/j.ml.20230901.12

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Classification of Some Test of Normality Techniques into UMP and LMP Using Monte Carlo Simulation Technique

Awopeju Kabiru Abidemi, Ajibade Fatai Bright, Abuh Musa

Published in Mathematics Letters (Volume 9, Issue 1)

Received: 29 September 2021 Accepted: 24 August 2022 Published: 29 May 2023

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Abstract

In Statistics, test of normality is of great importance and cannot be neglected in statistical analysis. However, there exist many techniques for such analysis and researchers usually face with the choice of test. From the literature, it has been established that power of test of normality vary significantly based on sample sizes. In this study, seven normality tests were reviewed and the classification into LMP and UMP were based on Power-of-Test. The test of hypothesis was done at 5% level of significance. The tests considered as; Shapiro-Wilk, Anderson-Darling, Bonett-Serial, Robust Jarque-Bera, Skewness, Lilliefors and Kurtosis tests. The sample sizes considered are 10, 20, 50 and 100 with 1000 replicates. Simulation was done from 3 distributions namely, normal, gamma and beta distributions. It was found that all methods were stronger for the detection of normality when normal distribution was used but the variation in their power was obvious when non-normal distributions were used. Among the methods, only three can be referred to as UMP while the rest are LMP. The UMP methods are Shapiro-Wilk, Anderson-Darling and Lilliefors as their Power-of-Test was not affected by sample sizes.

Published in	Mathematics Letters (Volume 9, Issue 1)
DOI	10.11648/j.ml.20230901.12
Page(s)	8-17
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

Distributions, Simulation, Monte Carlo Techniques, Power-of-Test, Type I Error

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APA Style

Awopeju Kabiru Abidemi, Ajibade Fatai Bright, Abuh Musa. (2023). Classification of Some Test of Normality Techniques into UMP and LMP Using Monte Carlo Simulation Technique. Mathematics Letters, 9(1), 8-17. https://doi.org/10.11648/j.ml.20230901.12

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ACS Style

Awopeju Kabiru Abidemi; Ajibade Fatai Bright; Abuh Musa. Classification of Some Test of Normality Techniques into UMP and LMP Using Monte Carlo Simulation Technique. Math. Lett. 2023, 9(1), 8-17. doi: 10.11648/j.ml.20230901.12

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AMA Style

Awopeju Kabiru Abidemi, Ajibade Fatai Bright, Abuh Musa. Classification of Some Test of Normality Techniques into UMP and LMP Using Monte Carlo Simulation Technique. Math Lett. 2023;9(1):8-17. doi: 10.11648/j.ml.20230901.12

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@article{10.11648/j.ml.20230901.12,
  author = {Awopeju Kabiru Abidemi and Ajibade Fatai Bright and Abuh Musa},
  title = {Classification of Some Test of Normality Techniques into UMP and LMP Using Monte Carlo Simulation Technique},
  journal = {Mathematics Letters},
  volume = {9},
  number = {1},
  pages = {8-17},
  doi = {10.11648/j.ml.20230901.12},
  url = {https://doi.org/10.11648/j.ml.20230901.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20230901.12},
  abstract = {In Statistics, test of normality is of great importance and cannot be neglected in statistical analysis. However, there exist many techniques for such analysis and researchers usually face with the choice of test. From the literature, it has been established that power of test of normality vary significantly based on sample sizes. In this study, seven normality tests were reviewed and the classification into LMP and UMP were based on Power-of-Test. The test of hypothesis was done at 5% level of significance. The tests considered as; Shapiro-Wilk, Anderson-Darling, Bonett-Serial, Robust Jarque-Bera, Skewness, Lilliefors and Kurtosis tests. The sample sizes considered are 10, 20, 50 and 100 with 1000 replicates. Simulation was done from 3 distributions namely, normal, gamma and beta distributions. It was found that all methods were stronger for the detection of normality when normal distribution was used but the variation in their power was obvious when non-normal distributions were used. Among the methods, only three can be referred to as UMP while the rest are LMP. The UMP methods are Shapiro-Wilk, Anderson-Darling and Lilliefors as their Power-of-Test was not affected by sample sizes.},
 year = {2023}
}

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TY - JOUR
T1 - Classification of Some Test of Normality Techniques into UMP and LMP Using Monte Carlo Simulation Technique
AU - Awopeju Kabiru Abidemi
AU - Ajibade Fatai Bright
AU - Abuh Musa
Y1 - 2023/05/29
PY - 2023
N1 - https://doi.org/10.11648/j.ml.20230901.12
DO - 10.11648/j.ml.20230901.12
T2 - Mathematics Letters
JF - Mathematics Letters
JO - Mathematics Letters
SP - 8
EP - 17
PB - Science Publishing Group
SN - 2575-5056
UR - https://doi.org/10.11648/j.ml.20230901.12
AB - In Statistics, test of normality is of great importance and cannot be neglected in statistical analysis. However, there exist many techniques for such analysis and researchers usually face with the choice of test. From the literature, it has been established that power of test of normality vary significantly based on sample sizes. In this study, seven normality tests were reviewed and the classification into LMP and UMP were based on Power-of-Test. The test of hypothesis was done at 5% level of significance. The tests considered as; Shapiro-Wilk, Anderson-Darling, Bonett-Serial, Robust Jarque-Bera, Skewness, Lilliefors and Kurtosis tests. The sample sizes considered are 10, 20, 50 and 100 with 1000 replicates. Simulation was done from 3 distributions namely, normal, gamma and beta distributions. It was found that all methods were stronger for the detection of normality when normal distribution was used but the variation in their power was obvious when non-normal distributions were used. Among the methods, only three can be referred to as UMP while the rest are LMP. The UMP methods are Shapiro-Wilk, Anderson-Darling and Lilliefors as their Power-of-Test was not affected by sample sizes.
VL - 9
IS - 1
ER -

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Author Information

Awopeju Kabiru Abidemi

Department of Statistics, Nnamdi Azikiwe University, Awka, Nigeria
Ajibade Fatai Bright

Petroleum Training Institute, Effurun, Warri, Nigeria
Abuh Musa

Department of Statistics, Federal Polytechnic, Idah, Nigeria

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APA Style

Awopeju Kabiru Abidemi, Ajibade Fatai Bright, Abuh Musa. (2023). Classification of Some Test of Normality Techniques into UMP and LMP Using Monte Carlo Simulation Technique. Mathematics Letters, 9(1), 8-17. https://doi.org/10.11648/j.ml.20230901.12

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ACS Style

Awopeju Kabiru Abidemi; Ajibade Fatai Bright; Abuh Musa. Classification of Some Test of Normality Techniques into UMP and LMP Using Monte Carlo Simulation Technique. Math. Lett. 2023, 9(1), 8-17. doi: 10.11648/j.ml.20230901.12

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AMA Style

Awopeju Kabiru Abidemi, Ajibade Fatai Bright, Abuh Musa. Classification of Some Test of Normality Techniques into UMP and LMP Using Monte Carlo Simulation Technique. Math Lett. 2023;9(1):8-17. doi: 10.11648/j.ml.20230901.12

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@article{10.11648/j.ml.20230901.12,
  author = {Awopeju Kabiru Abidemi and Ajibade Fatai Bright and Abuh Musa},
  title = {Classification of Some Test of Normality Techniques into UMP and LMP Using Monte Carlo Simulation Technique},
  journal = {Mathematics Letters},
  volume = {9},
  number = {1},
  pages = {8-17},
  doi = {10.11648/j.ml.20230901.12},
  url = {https://doi.org/10.11648/j.ml.20230901.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20230901.12},
  abstract = {In Statistics, test of normality is of great importance and cannot be neglected in statistical analysis. However, there exist many techniques for such analysis and researchers usually face with the choice of test. From the literature, it has been established that power of test of normality vary significantly based on sample sizes. In this study, seven normality tests were reviewed and the classification into LMP and UMP were based on Power-of-Test. The test of hypothesis was done at 5% level of significance. The tests considered as; Shapiro-Wilk, Anderson-Darling, Bonett-Serial, Robust Jarque-Bera, Skewness, Lilliefors and Kurtosis tests. The sample sizes considered are 10, 20, 50 and 100 with 1000 replicates. Simulation was done from 3 distributions namely, normal, gamma and beta distributions. It was found that all methods were stronger for the detection of normality when normal distribution was used but the variation in their power was obvious when non-normal distributions were used. Among the methods, only three can be referred to as UMP while the rest are LMP. The UMP methods are Shapiro-Wilk, Anderson-Darling and Lilliefors as their Power-of-Test was not affected by sample sizes.},
 year = {2023}
}

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