Before publishing, I found a minor mistake in a study that took a month to do. The mistake will not affect the main conclusion of the work, it just shifts a curve on one of the plots ever so slightly. My advisor says it is not worth the time to redo the work to correct the mistake, because it will not make a big difference in the results. (This is a month-long project). My field is engineering.
Is it unethical to publish the results with the known mistake?
If you try to cover up the mistake by manipulating data, or omitting critical information that is needed for reproducibility, then yes, it is unethical.
If you include a mention of the issue, and describe any applied correction, then it is fine and it is up for the peer reviewers to (hopefully) pick up on and decide if they are concerned about the impact it may have on your results.
When you publish a paper, you are asserting that everything in it is true. If you know before submitting for publication that something in the paper is false, then (excuse my bluntness) you are lying. Lying is unethical (at least almost always).
As a separate issue, if you don’t fix the problem before publication and a reader spots the error, they may wonder if there are other errors in your paper.
In conclusion, I recommend fixing the mistake before submitting for publication.
From the example you provide it sounds like the work that has to be re-done is remaking a figure or re-analyzing the data (since you mention that you already know what will happen: a curve will shift to the right).
This is very different from redoing actual experiments/measurements (even there, one could argue that a month is nothing, unless your contract or funds have run out to prevent you from redoing the work).
If it's the latter, you might want to leave the data as they are and discuss the suboptimal setup in the discussion. In that case I would also argue it is not so much a "mistake" as an ill designed experiment.
If it's the former and you catch a mistake in the writing stage, then by all means fix it. Transparency and your reputation are key.
No, it is not unethical to publish results with a known mistake. As long as you state clearly what the mistake was, what the effects on the results were and give your reasoning why the main conclusion is not affected. Point out the shift in the curve and explain it. All of that is perfectly ethical.
What would be unethical would be shift the curve to match, change the data to match or in any other way prevent the results from being reproducible.
As long as you state something along the lines of
"The first three data sets were collected according to these standards and resulted in these curves; the final dataset was collected according to these slightly different standards and resulted in almost the same curve"
then there is nothing to say against publication.
Is it unethical to publish the results with the known mistake?
Of course, it is, unless you disclose your mistake. If you disclose your mistake in a publication, the only way to publish your findings would naturally be a submission to a low-quality venue. Junk results belong to a junk venue. This might be fine with you.
As for the impact of a hidden mistake, in some fields, folks will read your publication and perhaps care or reuse the data, whereas in other fields, your paper would be write-only. It's hard to say what the impact of a hidden mistake would be.
However, ethics is not the main point here. Regardless of ethics, and even if the impact of your mistake is zero:
If you value your own self, in particular, what you say and write, then tell the truth, or at least don't knowingly lie. Lying is not healthy and doesn't do you any good in the long run. Build and maintain the habit of being truthful as much as you can. For your very own benefit.
It’s not completely clear what the nature of the mistake is, but from your description in the question and comments it sounds like, in broad terms, the data you have collected do not reflect the experiment you claim in the paper to have performed. That means that publishing the results without redoing the work would be knowingly misleading. This is academically unethical.
It might be worth considering the potential consequences for attempting to publish in this case:
Compare these possibilities to a one-month delay before publication when making your decision.
Redo the experiments during review.
If you are certain, you could send the paper for review, with a cover letter explaining the problem and stating that results will not shift nowhere close to changing the conclusion of the paper. Then, during the review you could rerun the experiment.
This might result in one of few outcomes: your paper is reviewed and then you fix the problem before publication, editor might reject it before you fix the issue, or one or more reviewers might reject reviewing due to this issue. In any case, you will not be doing anything unethical and will have chance to reduce time to publication.
If there is no time right now or the process is to far, publish an erratum if the error may hinder another team to reproduce your results.
