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I have been reviewing a paper where the authors apply a computational method from an earlier paper they published to a specific system of general relevance. The paper seemed ok, and I recommended major revision in the review.

After submitting the review, I've been working with this computational method myself and discovered that the way the authors applied the method is seriously flawed, so that it makes in general no sense to interpret the result in any way without further tests. If I had noted this problem earlier, I would probably have recommended rejection in my review.

What's the recommended course of action in this situation? Should I notify the editor of this additional discovery, so that the authors can directly take care of it in their (presumably ongoing) revision, or is it better to just wait for a request to review the revised version?

I haven't heard any decision from the journal so far, but I don't think that the paper will be accepted without revisions.

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    I'm not an academic, but I would say that you'll look more a "fool" by not seeing it at all (or not telling it's the same) than seeing it late. – user23652 Oct 31 '14 at 8:25
  • Tell the editor that you have gained additional knowledge and you have changed your stance to reject. Also the authors might appreciate being told directly what the problem is. Consider conferring with your more experienced colleagues who can tell you what is expected of you in your circles. – Thorbjørn Ravn Andersen Nov 1 '14 at 12:57
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What's the recommended course of action in this situation? Should I notify the editor of this additional discovery, so that the authors can directly take care of it in their (presumably ongoing) revision,

Yes, I think so. This seems to be in the best interest of all involved: you, the authors and the journal. It may be tempting to feel "embarrassed" about this or feel loathe to hold up the stately train of the editorial process, but you should resist these temptations: part of being a professional academic is being completely willing to change and adjust to new information and/or new insight you've acquired.

or is it better to just wait for a request to review the revised version?

No, I don't think so. Put yourself in the authors' shoes: wouldn't you like to have this information as soon as possible? Revising a paper without knowing about a serious -- potentially fatal -- error sounds like it could be a waste of their valuable time. Moreover, the longer they think that the paper will be accepted with revisions, the more disappointed they will be when they learn about the true situation.

I would write up carefully your description of the error as though it were part of the original referee report. In effect this does become a new referee report, but you don't necessarily need to edit this into the old referee report: having already submitted that, the matter of it is to convey the new information. Of course, the final decision about in what manner to inform the authors lies with the editor.

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    I don't know about computer science journals, but most of the journals our lab publishes in don't send revised papers back to reviewers, the editor has final say. If you wait for a second chance to look at the paper, you might not get one. – user137 Oct 30 '14 at 22:31
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    @user137 In theoretical computer science I'd expect, as a reviewer, to see the paper again if and only if significant changes had been requested or made. – David Richerby Oct 31 '14 at 9:23
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You should definitely contact the editor as soon as possible. It is not certain that the editor has provided your review to the authors yet and even if the editor has done so, receiving the additional information allows the editor to make additional decisions concerning additional revisions or even rejecting the paper altogether.

So it is vital that you send your additional information as soon as possible.

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It is certainly advisable to notify the editor, so that she/he can pass on the information to the authors. The editor may or may not take this information into account for the decision.

When sending the information, you may want to offer to write a revised version of the review.

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In addition to all other excellent recommendations I would just highlight that reporting a flaw in the paper is in your own best interest. Imagine the paper is accepted. Then others will try to reproduce the results or scrutinize the computational methods. If other researchers find flaws in the paper that may force a retraction. Depending on the popularity of the paper that may lead to wonder how it could have been accepted on the first place. In that case the blame usually goes to journals and referees. Although referees are frequently anonymous this hypothetical situation may damage your reputation as a referee in that journal. If referees are not anonymous then your reputation can be even more affected.

On the other side of the coin, if you report a potential flaw and it turns out the flaw does not exists, then probably means the authors needed to give extended explanations- your report will give them the opportunity to do so. That would not affect your reputation- referees' job is to question what its in the manuscript- even when sometimes we may be wrong.

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