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I am currently reviewing an applied math paper that I don't think is great; indeed, I am hesitant to accept it even with major revisions. The language is poor, I'm not convinced by the arguments, and the numerical results are difficult to interpret based on how they are presented. However, based on other work this journal has published (in particular, other papers by the same authors), I think the quality of the journal I'm reviewing for is a bit lower than my personal standards.

Should I based my final recommendation on my own standards, or the journal's?

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    Too much nonsense is published. If the paper has poor language and is not convincing, it just should not be published, even if the journal published other similar papers before. – J. Fabian Meier Jun 26 at 15:27
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    Rather than consulting the journal's previous publications or Stack Exchange, consider the instructions the journal provides to reviewers. – Anonymous Physicist Jun 27 at 3:54
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    If you don't think a journal has appropriate standards, you should not review for the journal. – Alexander Woo Jun 27 at 15:20
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There are many different notions of quality of a paper:

  1. accessibility of the presentation,
  2. soundness of the arguments and conclusions,
  3. relevance of the research.

Ideally, the level of journals only differs in Point 3. Realistically, there are some differences in Point 1 as well (ironically, I find that middle-level journal score best here, but that’s a different story). However, even mega journals aspire Point 2 – and outrage ensues if they clearly fail.

I would therefore not let the level of the journal influence assessment of deficiencies with respect to soundness, i.e., if I consider a paper unsound, I recommend to reject it, no matter the level of the journal. Also, think for a second what would happen if all reviewers would recommend to accept all papers that are better than the worst paper in the journal in question: Due to the variability and laziness of reviewers (and the abundance of bad papers), the threshold would decrease perpetually. Nobody wants this.

Also, irrespective of the journal’s level, I note everything I see wrong with a paper, and let the editor decide whether this is a sufficient reason for rejection. As language problems (and some other presentation issues) can be fixed by a copy editor or similar, I would not even let them influence my main recommendation, but just recommend heavy copy-editing or similar to the editor.

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    Minor language problems can be fixed by line-editors. The big problems (clarity and flow, calques, organization, poor notation, etc) cannot. These only authors can fix. In these cases, I would recommend major revision or even rejection (on 2nd/3rd iteration in absence of improvements). – Boris Bukh Jun 27 at 18:55
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Actually, it is the editor's decision to accept or reject. Give an honest recommendation according to your best judgement.

I suggest you make your best effort to help the author(s) improve the paper. Your recommendation to the editor can be whatever you think best. But don't give it a higher rating than you think it deserves (or lower, for that matter) as that will skew the information the editor has to work with. If you think it has low quality you can certainly say that to the editor.

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    I replaced "decision" with "recommendation." ;) – artificial_moonlet Jun 26 at 12:27
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As a reviewer, your role is to provide sufficient information to the editor that they can make a decision about how to proceed with a manuscript (accept, accept if major amendments are made, reject). I have reviewed some manuscripts, and used many more in research. From my perspective:

  1. manuscripts should have been peer reviewed prior to submission, particularly if there are multiple authors. This solves most manuscript problems.

  2. language should be clear. Everyone has their own writing style. I don't suggest changes to language in a manuscript unless there are major problems in my understanding of the prose, and I therefore assume that the journal readers will have the same problem. I don't edit prose, my edit is a comment about what precisely is unclear with a request to amend the text to clarify the content. I do not know if this is what you mean by "the language is poor" or whether you mean that the person does not have English as a first language and therefore their translations into English are poor. See how clarity is good?

  3. state how the arguments are unconvincing. Also, your interpretation of how the arguments are unconvincing may not be at the same standard as those of others. Sometimes this has little impact on whether the manuscript is published.

  4. explain exactly how the numeric results are hard to understand. You may be the only reviewer with expertise in how those numbers should be reported.

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    "whether you mean that the person does not have English as a first language" When peer reviewing, please try to avoid the appearance of bias or discrimination on the basis of language background. – Anonymous Physicist Jun 27 at 3:53
  • @AnonymousPhysicist my point is that the OP did not clarify what they meant by "The language is poor". If it was due to ESOL, then the OP is suggesting that one reason for recommending rejection is due to the ESOL. – Michelle Jun 29 at 23:06
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Just explain the strengths and weaknesses of the paper without judging, give constructive critique where possible. Also try to be concrete, e.g. say that theorem 3.5 is not obviously true as claimed, in fact you don't see how XYZ follows trivially, instead of just saying that it is not convincing.
In the end, you can give a recommendation and you could base that on the level of the journal, yes. However, the final decision is made by the editor, and for them, your observations about flaws and good points are much more important than your personal opinion (unless, of course, you are the most famous researcher in this area^^).

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    One kind of has to judge though, because one has to check "revise" or "reject". – Allure Jun 26 at 12:49
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    That's a completely unhelpful answer from an editor-in-chief's perspective: We want the reviewer to judge. That's the role of a reviewer. – Wolfgang Bangerth Jun 26 at 13:14
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One thing that would be good to know here is the exact meaning of "accept with major revisions". The emphasis may be on "accept" or on "major revisions". In many (probably most) journals I'm familiar with (I'm from statistics), a "major revision" actually means that the reviewers get the paper again and can still reject it if issues are not appropriately addressed. This is however not everywhere the case (and may in any case depend on what other reviewers think).

My understanding of the question is that there's nothing clearly wrong about the paper, and that there is a contribution with at least some originality and some use to somebody. Such papers should in my opinion be publishable somewhere, and whether the standard of the current journal is low enough is ultimately the editor's call, although you may have your opinion. However it seems that things are unclear, so that currently it cannot be appropriately evaluated whether the paper is correct and/or a contribution of some value.

Many journals offer "reject with encouragement to resubmit" as option in cases like this, in which from the current version it isn't quite clear whether or not a revised version will be publishable, whereas "major revision" in my view implies that my subjective probability that this will be OK after (maybe more than one) revision is substantially larger than 50% (in case "reject with encouragement to resubmit" is not offered I'd cut out the "substantially").

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    I don't think I've ever seen "accept with major revisions" as an option; usually the distinction for requiring major revisions rather than minor is that in the former case you will need to see the revisions before deciding whether to accept. – Especially Lime Jun 27 at 10:22

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