If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
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I sometimes come across an interesting scientific paper where the study being done seems easy and/or low-budget enough to make me think "hey, I could do that" (on this occasion, this paper on theanine levels in tea, which I skimmed too quickly the first time to notice that they used big, proper and presumably expensive lab equipment to measure it because I was reading it for practical reasons (reading about modafinil amplifying the side-effects of caffeine, while beginning an all-nighter powered by those chemicals)), and to me there's a strong "coolness factor" to being someone who's published real research, especially if that also means a finite Erdos number. How easy/difficult is it to become author or co-author of a scientific paper as an amateur, given that you're trying to actually accomplish something and not munchkin for "get my name published as easily as possible"?
Unrelatedly, I'm pretty sure posting under the influence of caffeine and modafinil is a terrible idea for me. I just spent two hours writing and re-writing that question, and I'm only stopping now because I'm giving up on trying to get it right. That's only exacerbating a tendency I already have, but damn.
As someone who is published, I can tell you that it depends entirely on the field. One possibility is obtaining data from other people and analyzing it in new ways. There are many free public sources of data, and a lot of researchers will share old data sitting on their hard drives if they think it could result in publications. Off the top of my head, genomics, bioinformatics, microscopy, medical imaging/radiology, and biometrics are all fields where there is a glut of data and people would gladly welcome new, more powerful analysis tools and procedures.