Mentor says I cannot be first author of my paper because I am an undergraduate
My mentor tells me that no magazines will accept me as a first author
This is clearly wrong. Of course I cannot speak for every journal in your particular subfield, but rejecting papers only because of the academic rank of the first author would be ethically dubious. At the very least, there are some megajournals that do not have such criteria and which should accept your work – given that it is scientifically sound, etc. (Mind that I am not saying that megajournals are your best or only choice; they are just the easiest counter example.)
Moreover, a typical journal won’t even ask for your academic rank and may not bother to investigate it and neither do the peer reviewers. The journal may even practice double-blind peer review, in which the reviewers won’t even know your name and thus probably lack all means of finding out your academic rank.
Finally, while there are some people who judge a work by whether they know the authors (though they shouldn’t), they usually do not look at authorship positions. If somebody is going to be more benign to your work because your mentor’s name is on it, they will likely not care whether they are the first or last author.
by the rules, mentor must to [the statistics]
There are certainly no universal rules for this. Where did this come from?
Anyway, your problems rather are these:
Doing the statistics almost certainly qualifies your mentor for authorship, so he must agree on all publishing decisions. (The opposite also applies.) Even if you re-do the statistics, it will be difficult to argue that you did so completely independently. Also mind that any intellectual contribution qualifies for authorship, so think about any feedback or advice you got from your mentor on this work.
Your mentor may have some power over you. I don’t know them, but you must consider the possibility that they freak out over this and try to sabotage your career and particular this very paper.
The biggest advantage of having an experienced mentor contributing to your paper is their experience in writing. It is very unlikely that anybody produces proper scientific writing on their first attempt without help from somebody experienced with it.
Unfortunately, you have to judge your mentor’s mentality yourself. However, unless you are sure that they do not abuse their power, I strongly suggest that you find another professor or similar who can advise you and possibly act as an arbiter in this situation.
if you have done most of the work that @Dmitry mentions, it is neither appropriate nor ethical your mentor to be the first author and, I can tell you from my experience, that in my field "no journal will accept the paper if the undergrad is the first author" is a total lie. As long as the paper stands as a proper scientific article written appropriately, you can even publish just yourself.
However, as Dmitry mentiones, if your "mentor" advises you throughout the research and writes the article, i.e contributes to the paper, s/he also needs to be a co-author.
But who should be the first author?
Well, that should be determined by the authors; you and your mentor. However, note that, having a second-author paper is way better than no paper. Therefore, don't let the authorship issue to prevent the publication of the research.
Lastly and most importantly, I can advise a clever solution to that authorship dilemma. Why not state who have done what? In your paper, you can list the contributions of each author, so that the author ordering, in a sense, made redundant. This way, even if the paper published with you as the second author, everyone would know what are your contributions and that of your mentor; i.e you have done the work and your mentor advised you.
Addedum 1:
If there is "enough research" done for a proper paper, I would suggest publishing now, since having a publication would greatly help you in your graduate applications. Plus, this way, you wouldn't have to stay in the same university just yo complete & publish a single paper.
Addedum 2:
From your comment to @Dmitry's answers, I suspect that your mentor either lies or s/he is very young and doesn't have much experience. In such a case, I would advise you to discuss the issue with other (more established) faculty members in your department who also work in the same field. In either case, they can talk with your mentor about the issue and advise them. Plus, that would prevent the possibility of damaging your relationship with your mentor while discussing the authorship issues.
Update: She has revealed in the comments that the "mentor" is a Professor at the Docent level, which makes me more inclined to advise her to take advice from the mentor. "Mentor" on its own sounds like it could be a grad student, in which case the answer would be different. Furthermore the Professor is suggesting more co-authors to save costs on publication, this suggests to me that it is going to a very good (expensive) journal or it could be going to a pay-to-publish journal, so I have asked for clarification. If it is going to a good journal that has for example $3000 publication fees and more authors are added, there's lots to say about that, but papers in "top" journals do not come by very often for people from every country, and adding co-authors can help: working together with several scientists that are more senior to you, is also in my opinion the best thing about doing science, as they often provide far more insights and improve the paper.
I agree with a lot of what the other answers say.
I will respond separately to some of your specific points though:
I performed some research and submitted it to a congress of biomedical sciences. Many professors told me that my research is very advanced compared to student work and that it could easily be my specialisation one day.
I very much believe that they said those things, but also keep in mind to try to take everything with a slight grain of salt. Since the mentor was involved in the work (you said they did the statistics), your mentor will know some things that random professors at a conference will not. At the moment I would recommend to try to remain modest, as this is indeed your first time on the verge of publishing, and PhDs with 10 publications worth of experience often still don't have much of a clue how the outside world "truly" thinks of their research.
You seem off to a great start though, and you've come to the right place for advice :)
I am an undergraduate student (sixth year veterinary science). My mentor tells me that no journal will accept me as a first author although the entire research is mine. I did everything except the statistics, because by the rules, the mentor must to it. I spent four months on the field, alone, taking samples, and an idea of gifting my own blood, sweat and tears is very painful.
I completely understand you.
Many people spent 48 months like that, and did not end up with any publication, and it is indeed very painful. Specifically, I'm thinking about all the 2-year (sometimes 3-year) masters students I know who graduated with no publication. This is not "rare" either: it actually happens all the time.
However it would indeed be nice (and even perhaps preferred!) for this work to get published. For that you do not have to, but might want to consider the advantages of having your mentor as first author (it is already understood that the mentor will be a co-author because they did the "statistics" for the paper):
Your mentor might get very angry at you if you try to oppose their authority or advice. When asked for a letter of reference at the student level, often we're asked whether the student is a "team player": if your mentor is not too disappointed at you to outright decline writing a reference letter for you, there is still the possibility that they do not give you the best letter you might think you deserve. This can damage your future. If you maintain a good relationship with your mentor, this paper might just be the first of dozens in your career, many of them probably being far more important and impactful than what your present paper in question, because it will be at an even more advanced stage in your academic career.
Without experience, you are more than likely to struggle severely in getting your paper past the gate keepers. Also, with no record of publication history, the referees might not take your paper seriously at all, no matter how good it is (this is why I alluded to taking what the professors at the conference said, with a grain of salt, because not many people behave the same way at a conference as they would when they are "anonymous referees". There's a lot of things that have to go right, and not a lot of room for anything to go wrong, if a paper written solely by an undergraduate is to get published in a good journal. If the mentor writes the article, the paper usually has a much better chance of being published. People might agree that the mentor can claim first authorship if they write the article (although a lot of people, including me, would not ourselves be that type of mentor).
Since you describe the "blood, sweat and tears" you poured into this project, you might like the paper to be published in a good journal, that will be widely seen. The mentor will most likely be able to help you with this, much more than you can help yourself at it.
Do you think I should wait for a year or a bit more to publish it as a graduate or should I let them take credits for my work.
No I don't think so, and here's why:
- The mentor does not want you publishing it alone (or as first author), and that's why they said that you "can't" do it. What they said about undergraduates, applies to graduate students too. Waiting a year won't help.
- The work might not be publishable anymore (or in the best potential journal) if you wait a year.
The research is about horse welfare in my country and it has never been done before.
You might be 100% right, but almost always when I hear "never been done before", it actually had been done before in some way, shape, or form. Many journals do not even allow words such as "new", or "never been done before", because it's impossible to prove it.
This means a world to me. I want to devote my life to this area and publishing my paper as mine would be only right thing to do, right?
I'm very delighted to hear your passion for research :)
I disagree that anything is the "right" thing to do, let alone "the only right thing to do".
The paper is still yours if you are a co-author. If you are a student, it will usually be known that you were the one that did the 4 months of field work and not the "mentor".
If you seriously do want to have any career in research, you will have to remove this way of thinking that being the first author is "the only right thing to do". You will have to make compromises. As long as you are not paying for everything yourself, you will always have a "boss": you will never be 100% free to do things in whatever way you want best, independent of what other people want.
Should I accept publishing the paper with someone else’s name as a first author?
Ask yourself this: is it better than not publishing at all?
If so, I will console you by saying that if you really want to devote your life to research, you are likely to be doing 60 more years of this, and possibly publishing 200 papers, and maybe 50-100 of them being first author.
This paper is not the end of the world, unless you cause that to be, by burning bridges with the people that might best be able to help you.
I would be happy to provide more advice if you have questions. I recommend you also tell us how many other co-authors might be involved (only you and your mentor, or even more co-authors?) and what the status of your mentor is (professor, assistant professor, post-doctoral researcher, graduate student, etc.).