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One part of the work of any researcher is to referee the work of other scientists in his field. This is a time-consuming and volunteer work, that is made with the idea of service for the community.

My main question: What are the standards of organization for the referee report of an article?

For instance, is a "general comment" section (mostly, explaining why the paper should be accepted or rejected) and a "specific comments" (in the form of a list of precise comments e.g. "Page $2$ line $4$: typo. It should read X instead of Y") enough? Or do people organize the review under specific sections like "Typos and writing", "Missing definitions", "Scope of the paper",etc...

I wish my report to be as useful as it could for the author, so I am inquiring about the best practices for referee reports.

PS: It may be a field-dependant question. I am mostly interested about standards in mathematics, but answers for other fields would be interesting too.

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    There are no real standards (at least in math). But I've never seen specific sections for "typos" versus "missing definitions." Typically, there is a general review (summary and context of paper with your opinions on ot), then a single list of specific comments (e.g., p. 4, l.2 xxx is undefined...). – Kimball Jan 21 '15 at 16:13
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There are no standards but there is a reasonable logical progression that can be followed from the general and larger to the smaller points. I would therefore structure a letter as follows:

  • An introduction highlighting the merits of the topic and the study. Often this paragraph ends by stating that certain revisions may be necessary. It i snot the reviewers task to state whether he or she feels the manuscript should be rejected, under go revisions or be accepted. That should be stated to the editor only.

  • Following the introduction would be more general aspects such as structure, language etc.

  • Next larger scientific issues that concern more general aspects of the study, not tiny details. The points would concern entire chapters or sets of paragraphs and usually be the cause for significant reworking of the manuscript.

  • The final part, and usually the longest may be small issues or questions concerning aspects that need clarification or correction, usually pointing at the page and line where the problems occur.

  • The letter should be capped off by summarizing the review and making a statement as to whether you think significant or minor reworking is necessary. Note that I am not speaking about a verdict but an assessment of how much work you think is necessary to complete the short-comings you have identified.

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    "It is not the reviewers task to state whether he or she feels the manuscript should be rejected, under go revisions or be accepted. That should be stated to the editor only." (As ever, I wonder about field-dependence, but...) In most reports I have written and received the referee does make a recommendation as to whether the manuscript should be accepted and whether there should be revisions. In fact this is probably the most important part of the report, and the language used is read carefully by all parties. What would be gained by not including this as part of the report? – Pete L. Clark Jan 21 '15 at 19:16
  • So you write to the author about a decision an editor will make later? Well, you can and I have also seen it done but I feel that undermines the editor to some extent. – Peter Jansson Jan 21 '15 at 20:32
  • @PeterJansson I'm comfortable pushing the editor when I really dislike a paper... – jakebeal Jan 21 '15 at 22:29
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    @PeterJansson: As a referee, I am not writing about the editor's decision. I am writing my own recommendation, which is what I was asked to provide. If a referee makes a recommendation which is not the one the journal ultimately follows, then it seems to me that the author has the right to know. – Pete L. Clark Jan 21 '15 at 22:58
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I organize my reviews in the way that I would like to receive them, sorted from most important from least important. My general structure is:

  • First, I summarize my understanding of the the key ideas and contributions of the paper.
  • Next, I give my judgement and main reasons for this judgement.
  • Third, I have a "Major Issues" list of other scientific problems that I think absolutely must be addressed before publications
  • Finally, I give a "Minor Points" list of nitpicking, language issues, typos, etc.

The first two sections show that I have understood what the authors are trying to say, and the big picture issues. The third gives the contributing factors, but tries to make it clear that fixing these without fixing the big picture issues won't change my basic judgement (if that judgement was negative). The final is things that will improve the paper but aren't really affecting my judgement.

  • When you say sorted from most-to-least important, do you mean overall (as in the sections you listed) or within each section also? For instance, when you go through your "minor points," do you list them in the order they appear as you read the paper, or in some order of importance regardless of where they appear in the paper? – tpg2114 Jan 21 '15 at 22:11
  • @tpg2114 I'm not anal-retentive enough to organize within a section as well. So within a section, I tend to write them down in no particular order, which ends up generally in order appearance in the paper. – jakebeal Jan 21 '15 at 22:28
  • Fair enough -- just wanted to clarify. – tpg2114 Jan 21 '15 at 22:34

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