I've been admitted to more than one PhD program, and I'm having a very hard time making a decision.
The programs I'm accepted to have advantages and disadvantages with respect to one another. How do I weigh the relative importance of difference aspects of the program in order to make an optimal decision?
Ultimately, this is not a decision that anybody else can make for me, because everyone has different values and priorities, and the right decision for me may not be the right decision for somebody else. However, you can help by giving me more information about how different features of a program will affect my experience in graduate school and my future career.
The offers under consideration differ in a variety of ways:
I need to know more about what kinds of things are important and how these will affect me, so that I can make an informed decision about balancing competing criteria.
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This is a special community wiki 'canonical' question that aggregates advice on a very broad topic - see more information in this meta post.
Each answer here relates to a different metric that one might take under consideration. If you have a new "critical" metric not in the list above that you believe should be an important part of the decision, post a new answer. If you want to add something related a metric that's already represented in its own answer, edit that answer.
In deciding how to weigh the ranking of each department under consideration in your decision, it's important to realize how the ranking of the department where you get your PhD will affect your future.
In this answer, JeffE says that the quality of your research is by far the most important factor in faculty hiring in his field:
Nobody in theoretical computer science cares where you got your degree. Really. We. Do. Not. Care. We only care about the quality and visibility of your results. Publish strong papers and give brilliant talks at top conferences. Convince well-known active researchers to write letters raving about your work. Make a good product and get superstars to sell it for you. Do all that, and we'll definitely want to hire you, no matter where you got your degree.
but suggests that the quality of the research you produce during your PhD will depend on the environment you're in, which in turn depends on your department ranking:
In my experience, where you get your degree is strongly correlated with successful research. I got my Master's degree at UC Irvine in 1992 and my PhD at UC Berkeley in 1996. The biggest difference I saw between the two departments was the graduate-student research culture. Every theory student at Berkeley regularly produced good results and published them at top conferences. When the FOCS deadline rolled around each year, the question I heard in the hallways from other students was not "You know the deadline is coming up?" or "Are you submitting anything?" but "What are you submitting?", because "nothing" was the least likely answer. Everyone simply assumed that if you were there, you were ready and able to do publishable research. Publishing a paper wasn't exceptional, it was just what you did. That cloud of free-floating confidence/arrogance had a huge impact on my own development as a researcher.
In other words, he concludes:
getting a PhD from a top department definitely helps, but more by helping you become a better researcher than by making you look better on paper.
xLeitix offers similar advice here: don't go to a particular university just because of its high ranking, but make sure that the environment in which you do your PhD is one that enables you to do high-quality research.
Corvus strongly emphasizes the importance of surrounding yourself with high-quality peers, which you're more likely to find in a highly ranked program:
I think what matters most is the quality of the students who will be your peers. You need to surround yourself with students who, from day 1, expect nothing less of themselves than to produce novel scientific research of the highest caliber, present it at top meetings, publish it in top journals, and forth. Ultimately you will learn more from your peers than from your advisor. A sufficiently talented and ambitious cohort will hold the bar high for you and push you to excel whereas a sufficiently talentless and unambitious cohort will help you make excuses for your own failures to reach your potential.
In my experience, top schools with top graduate programs have the sorts of students you want to surround yourself with. Second tier regional programs may, but I have yet to see it.
eykanal adds that if you're interested in a career outside of academia, then ranking matters more, even irrespective of its impact on the quality of your research:
When looking for a job in academia, potential employers will look at many factors, including publication record, research success, research track, who your advisor was, etc. The school is important but other factors are involved.
When looking for a job outside of academia, they will look at your GPA and the name of the university from which you graduated. In this case, your university could easily be a "make it or break it" part of the deal.
If you're concerned about being outclassed by the other students in your program at a top school, Dnuorg Spu says not to worry:
My experience as a student at a Extremely Well-Ranked School is that other students are very supportive, and empathetic to the experience of getting through a tough program. In short: don't worry. It will be ok.
and JeffE adds:
Do not listen to the Impostor Syndrome.
(More on that insidious impostor syndrome here.)