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Computer Science PhD admit here.

Is it crazy of me to turn down a top school (MIT/Stanford) for a lower-ranked school (think Cornell/UW/Columbia/Michigan) if I think there is better advisor fit?

Obviously all of these are fantastic schools and I am very lucky to be choosing from them. However, I felt like I got along really well with my would-be advisor at the lower-ranked school than I did at MIT/Stanford. People have told me that it's crazy of me to turn down MIT/Stanford since they are, along with Berkeley/CMU, on a different "level" than the other schools.

(My field is somewhat narrow so there is only 1~2 faculty at each of the schools doing research in the area. So regardless of which school I go to, if the advisor doesn't work out, I would be in a dire position.)

EDIT: Both advisors are well known in the field (and both have produced outstanding graduates), but the MIT/Stanford professor is good deal more senior. Also, talking with their current students, the MIT/Stanford professor is known to be pushy and have a "strong" personality (which may work for some people, but not sure whether it will work for me, as I've never worked with such people before).

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    In my humble opinion, it is your research output in the future you really should be concerned. If I think I can do better research with a better advisor, I would choose that advisor, regardless of the school. – scaaahu Apr 6 '15 at 4:34
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    Also to consider is the city the university is in. Are any friends or family living there or nearby? What is the lifestyle in the city like? This probably isn't so important as choosing your advisor, but you don't want to be miserable in the new city if you knew you would not like living there. – Moriarty Apr 6 '15 at 6:49
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    Make sure that a potential advisor has money/time to actually take you on before deciding to go to a school based largely or solely upon that advisor. – NeutronStar Apr 6 '15 at 15:28
  • This question reminds me of a previous one I read on this site. It was discussing the idea of adviser type (something about a good adviser will make you cry at least once). I think the idea was that look out for advisers that are too nice. You are not looking for a friend here. Liking eachother/being likable could actually get in the way of a successful working relationship. – Jonathon Apr 7 '15 at 1:38
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All of the schools that you are discussing are first-rank computer science schools with global leadership in their areas of specialty. In this area at least, the only real difference between the "top" and "top of the top" schools that you are considering is the number of different areas in which the school is a global leader. Thus, if you already have a clear, narrow focus that you know that you want to work in, and there are 1-2 people in that area at all of the schools you are choosing between, the distinction between "top" and "top of the top" is pretty much null.

Furthermore, your graduate career will be primarily determined by your advisor relationship rather than the school within which it will occur. Beware of being misled by first impressions, but a good match with your Ph.D. advisor is worth much more than the incremental difference between schools.

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There are some aspects of the decision that are independent of your advisor, such as having a large pool of impressive peers to learn from and work with, but the degree of fit with your advisor is certainly a major factor.

If you believe you can't work effectively with the potential advisors at the higher-ranked schools, then there's no point in choosing one of those schools. If the advisor at the lower-ranked school is performing at or above the level of the other possible advisors (as judged by influential papers and successful students), then again you don't have to worry. But your phrasing makes me a little uncomfortable:

I felt like I got along really well with my would-be advisor at the lower-ranked school

This sounds like you are describing how quickly you clicked and became comfortable, but you can learn an enormous amount from someone even if you never develop an easy rapport with them or feel you could be friends. It's worth thinking about whether the less comfortable relationship could nevertheless be productive. Maybe it can't - it depends on the personalities and the details of your interaction - but it's important to distinguish how much you like the advisor from how fruitful the intellectual relationship might be.

I wouldn't stress out too much about this decision, though. My impression is that Cornell and UW are not so markedly far behind MIT and Stanford in computer science. (There's a gap, but not a huge gap.) If one of them feels like a better fit, you are not jeopardizing your career.

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As previous responders have already answered, both your options are top-notch institutions and no sane future employer will think less of you for having gone somewhere on step lower on a league table. I know I can only present a single case, my own, but beware of first impressions! My worst advisor ever, who treated me worse than an unwanted brat, was oh-so charming and pleasant during the one-day interview and during our pre-employment e-mail contact. That said, my best advisor ever was lovely during the interview too, so all I can say is: Beware of first impressions! maybe the MIT guy just was having a bad stressful day?

It is worth looking also at the breadth of work within realated fields at the two places too. It is not necessarily great if they are brilliant and have huge teams working on your subject, what would you be doing then? incremental work? if there is a breadth then you can expand and learn from experts in complementary subject too, expand your work and bring a fresh view or implementation for it? Not that I know what you are working with, but it helped me in material science.

Final point: It's not only the Advisor that counts. Did you get a chance to talk to others in the dept? it can help to get a feel of the collegiality, how friendly, open and helpful a place is it? or is it super-competitive? Also what are their pet peeves? do they struggle to get instrument time? (or whatever the equivalent is for computer scientists) do they ever get to present their work at significant conferences?

I know this makes for an impossible spreadsheet, you might end up flipping a coin. If you're being offered a place at both MIT and Cornell, you must be a smart dude or dudette! I doubt you'll struggle to get a new place if the first one turns out to be impossible. It is allowed to quit. Worked for me. Then I took a year off to milk cows (über-cool!) and now am happily back in the lab at a better uni than I started :-)

EDIT:: As previous responders also said, dont' forget the rest of life too. Don't move somewhere you don't want to live. Friends, family, hobbies, and/or the ease of travelling to fun places or home at weekends and holidays counts for a lot too! Remember, you'll be living there for at least a couple of years.

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All of the above answers are correct. However, do trust your first impressions. I didn't click with my first prospective advisor and picked someone else. That prospective advisor failed to get tenure after his next couple of graduate students opted to switch advisors and start new research projects in the 3-4th year of their theses. These choices were made in spite of the fact that he was a really bright guy and working in a hot research field.

He was apparently a nightmare to work for.

It wouldn't hurt to confirm your first impressions by communicating with people who have worked with and for the advisors you are considering. Former research students, collaborators, et cetera. Being personable and likeable is a moderately positive sign, but there are a lot of different components to being a good PhD mentor.

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