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Research group

This answer by JeffE is so perfect, I'm just going to quote it verbatim. He says that asking about the quality of a research group is the wrong question,

What you should be asking is "How can I judge which research group will best support my educational and career goals?" And yes, this is a very different question. And while lab productivity may be correlated with the future career prospects of its members, the two are not identical. Some great researchers are terrible advisors.

  • Do the lab's students have a consistent strong track record of publishing new results?

  • Are the lab's students strongly represented at conferences, workshops, and the like? In particular: Are the lab's students given ample opportunity to present their research outside their home department?

  • Are the lab's students given ample mentoring and support, both in developing their own research agendas and in applying for external fellowships, lab exchanges, internships, postdoctoral positions, faculty positions, and so on?

  • Are the lab's students given ample opportunity for substantial intellectual contributions to the lab's published research, or are they just lab/code monkeys?

  • Does the lab's research agenda closely match your own research interests and abilities?

  • Most importantly: Where do the lab's former students work now? (The worst possible answer is "We don't know.")

Almost none of these questions can be answered accurately without physically visiting the lab and talking directly to the students without the PI present. If travel is impractical, use Skype / Google hangout / Facetime / whatever. Or telephone. Or, if all else fails, email.

Publishing is key in academia, so to get a sense of a research group, it's also a good idea to look at publications that have come out of the group, as suggested here:

  • How many articles are published, particularly in high quality journals relevant to the field of interest

  • Is there a consistent strong track record of publishing new results?

  • Their history of representation and contributions to conferences, workshops and the like