PONE-D-21-14331

An Alternative Approach for Comparison of Univariate Normality Tests

PLOS ONE

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Academic Editor

PLOS ONE

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

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2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

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3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: No

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4. Is the manuscript presented in an intelligible fashion and written in standard English?

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Reviewer #1: Yes

Reviewer #2: Yes

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5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: I found the paper very interesting and opening up a new debate on Normality testing. On balance, this is a technically sound piece of research which explores the power properties of normality tests using a diversified alternative distributional space. The data generation, simulation design, and finite sample properties are handled well. The proposed min-max approach definitely reduces the calculation cost in terms of computing power envelope which is the contribution of this paper. However, I have the following minor comments:

1. In section 2, distribution of the RJB test should be mentioned as well.

2. In table 3 & 5, how the ranks are defined for tests with small differences in losses?

3. Fig. 1 & 2 highlight the deviations of JB and RJB test against the worst alternatives at sample of sizes 25 and 75. Do the tests behave alike at sample of size 50? If yes, add this information as footnote or in the main text.

4. Table numbers are not aligned, e.g., there are two tables titled as table 5.

5. It is evident from literature that the JB and RJB tests behave well against long-tailed alternatives. This study should acknowledge the same (as it is evident from this study results as well) and particularly mention that there are only few long-tailed worst alternatives which should be taken care of while testing normality assumption by applying the JB and RJB tests.

Reviewer #2: The paper presents an extensive simulation study on normality tests. It could be useful for researchers in order to select the most appropriate normality test. I have two suggestions to the authors:

1. More details on the simulations should be disclosed. For example, which software do you use? Additionally, in order to facilitate the reproduction of the study you should provide data. If you generate your distributions with Python, R, Matlab, etc, you could include the code as a supplementary material or upload at a repository such as Github.

2. Probably you could complement your results using a classification or a clustering algorithm. In other words, which features of the distribution influences the loss function the most? Do some tests perform better at detecting non normality against a Beta rather than against a Laplace distribution? You could use Self Organizing Maps or K-means or many other techniques in order to produce such representation. IN this way instead of a ranking such as in tables 5,6,7, you could produce a ranking that informs on the different dimensions that affect the normality detection.

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Reviewer #1: Yes: Asad ul Islam KHAN

Reviewer #2: No

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Min-Max Approach for Comparison of Univariate Normality Tests

PONE-D-21-14331R1

Dear Dr. Islam,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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Kind regards,

Saeed Mian Qaisar, Ph.D.

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

I am pleased to tell you that your work has now been accepted for publication in the PLOS ONE Journal.

Thank you for submitting your work to this journal.

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

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2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

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5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: All of the comments have been addressed by the author. My recommendation is "accept" without further comments.

Reviewer #2: The author correctly addressed all the previous comments of this reviewer.

Just please check the URL of github you provided, as I could not reach it, and include it in a footnote in the paper.

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Reviewer #1: Yes: Asad ul Islam KHAN

Reviewer #2: No