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panicking -- I messed up

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I've been in grad school for a few years now and have one first author paper that's been published for a while now (it was written well over a year ago).

I recently started working on something that requires the same numerical techniques as the work in this previous paper, so I revisited the methods that were used in this paper... and discovered to my horror that a key calculation in the paper was not done quite correctly. At first I thought that this would just mean one plot in our paper would need to be fixed (that was bad enough). I discussed it with my advisor and he said that we can submit errata to the journal. Fine, redoing a plot is bad, but I guess it happens.

But as I've been redoing the calculation correctly (it takes a long time), it is looking more and more like at least an entire section of my paper, as well as an appendix, are just plain wrong. I mean, not just the plots... like, the entire science we built behind them. And I am freaking out.

I can't imagine I'm the only person on the planet to ever have a stupid semester and discover after publishing that I'm horribly wrong, but what happens now? Obviously we have to see just how off our results are, but if they're really far off as I suspect then what?? Do we somehow withdraw the whole paper (can people even do that?), or do we just submit all the corrections in errata? And I know this might sound silly, but am I totally doomed here? I mean, this is my ONLY paper at all, and although I'll probably have one or two others by the time I defend, I'm not sure what long term consequences this screw up will have. It's a totally honest mistake -- I mean, it's a really hard calculation, and out of two journal referees, my advisor, and several other faculty members, as well as myself, no one noticed this mistake -- but I feel like a total moron, I should have been able to catch this. Why wasn't I being more careful?

Has this ever happened to anyone else here? What did you do? Any advice for a panicking student?

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Oh man, what a terrible situation to be in, I sympathize with your anxiety! I don't have experience with anything like this but what I imagine I would do is consult my advisor and see what they say to do. I guess it really depends on how much influence this mistake has on the paper - even if you have to revise a section or omit it entirely, is there still an original claim in the paper that stands? I'd imagine that if so, then you still have a claim to a first-author paper. You might want to submit an errata, but the rest of the paper remains intact. Integrity would suggest that you should correct the mistake and that ignoring it is wrong, but I wouldn't be surprised if many people would choose not to do that. If it's not large enough to affect the main point you're making, maybe it's a justified decision. The paper was published following peer review based on what you knew at the time, and things can change and improve. You'll correct the mistake and do better next time. In an event, you are definitely not the only person to have made a mistake that went to print. I can think of papers I've read recently that contain anything from small errors to large conceptual problems that in my opinion undermine the whole premise of the paper. I wish you luck -- will you come by to update us about what you decided to do?

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Going to your advisor is definitely the right thing to do here. You will probably have to discuss this with the other co-authors (if any) as well.

Papers do sometimes get retracted but this is a very serious thing and it is usually done if something very bad has happened -- e.g. plagiarism, falsified data, etc.

It doesn't sound like everything in the original paper was wrong. I don't think you did anything "wrong" because all of you honestly gave your best effort -- you were not trying to knowingly present false information. I think papers often have mistakes in them -- that's what happens when you do research. At least in astronomy, what I often see is the mistake being uncovered by someone else and a "response"/criticism is published. Sometimes if the mistake is found later by the same group, they write a follow-up paper explaining why the original stuff was wrong and presenting the new results.

I guess it also depends on what the journal's policy on errata is as well. I guess ideally, you'd be able to make a change to the paper but if the mistake is major enough, (e.g. the problem turned out to be much more complex and requiring much more computation/analysis) then you might need to write it up as a completely separate manuscript.

This may be field dependent, but I think it's not too rare to come across papers that mention that their previous work is wrong (although they usually phrase/spin it to make it sound like they had used an incorrect assumption, or "outdated" data/techniques/whatever), or that someone else's work is wrong. Obviously it's not a desirable thing to happen and it sucks when you find mistakes in published work (I've been there before), but I think science/research is all about putting forward your best idea/claim/results, then having it peer-reviewed by the journal, then having it actually peer-reviewed by the entire community and whatever stands becomes the addition to the community's knowledge. So, sometimes mistakes get past the first two stages, it's inevitable!

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I don't have experience with this, but I do want to say that you shouldn't put the weight of this on your shoulders. As the student in that situation, I think a lot of the responsibility is on your mentor/PI/collaborators to check through the work and notice mistakes like this. So, don't be hard on yourself. If the seasoned professonals and peer-reviewers at the journal didn't notice it, then really a student - who is new at writing/publishing/research/etc - shouldn't have this placed on their shoulders.

I imagine that there are many papers that are not "correct" that are published...these errors are most likely due to a variety of things (1) human error, (2) purposeful manipulation, (3) lack of knowledge, and (4) time - new methods, theories, programs, etc.

I think you're handling it with integrity and maturity. I think a lot of people (not just students, but professionals who have been at this a long time), would just brush their mistake under the table and avoid dealing with it or telling anyone. The fact that you went back, checked it, saw it, and then reported it shows that you have are really great appreciation for academic responsibility. Taking that step, and then going to your professor is the best thing you could do.

Lastly, I want to point out that I think a lot of students who take on the weight of publications stress over not making mistakes. I stress over writing and whether I have the best possible citations, the right editing, the right wording, the proper analysis- the proper DATA!! ahh- everything!!! I think we all do our best to make sure the product we submitted is done to our best abilities- but mistakes are going to happen...and I am sure they happen more than we think.

So try not to stress about put a lot of thought right now into what could happen...think more about this as a learning experience. Good luck!

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