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You would surely have read the quote which says
If you can't explain it to a six-year-old, you don't understand it yourself.
I'm a Master's student in Physics currently in my first sem. Soon, We have to choose an advisor for our Ph.D. There are instructors whose teaching doesn't fit to me (really saying to most of my fellow students). I wanted to ask, If I can consider that they aren't good at research as well? How much correlation there is between teaching and research?
I would strongly disagree with the quote, as teaching requires very different skills than conducting research. There are many great researchers, who are bad at teaching, and vice versa.
However, this does not mean that you should not take a supervisor's teaching ability into account when looking for a potential supervisor for your PhD. Supervising a PhD candidate requires a complex set of skills, of which conducting research and teaching are two important ones. Another one is more subtle, concerning the interpersonal relations, essentially how well you two get along. The latter is an aspect that you sometimes can already assess from the lectures or classes you had with the instructor.
No.
Counterexample: Einstein's English is fairly heavily accented, making him hard to understand. Therefore if he were to teach in English, it won't be outstanding. That doesn't say anything of the quality of his research, of course.
I would think that the correlation is low in general. But that is because tenured faculty get to choose, to some extent, whether to focus primarily on teaching or research rather than to both "equally". Both take effort, but a different kind of effort. And some faculty change focus over their career.
But it is certainly possible for someone to be great at both, for example, someone who can give insight into deep topics, not just detailed (pedantic?) explanations.
Using teaching ability (or a match between what they do and what you like them to do) as a predictor of their research is probably not a win for you. And, the ability to guide your research is also important along with the quality of their own.
For purposes of making a choice, I suggest you look farther than just those two "variables". How helpful they are likely to be when you need it (some research focused people are terrible at this). How successful other student advisees have been, both in their degree work and in starting their careers.
There are a lot of variables. Don't ignore other important factors.
I've known people who were excellent at both; one of my mentors. I've known people who excelled at one or the other but not both.
One example, that seems like a counterexample, is Robert Lee Moore who was both a pioneer in Topology, but also in a certain teaching method (Moore Method). His method was very effective, if you could stand to bear it. He didn't lecture and he didn't let students read mathematics. Instead he had them spend their time writing and developing math from the barest of hints. Most people would hate this, since it is very difficult, but it worked for the few that stayed with him.
The quote is wrong. There are plenty of things you cannot explain to a six year old but can still understand perfectly well.
Almost all the people I know who do not care about teaching are also not good at research. This does not mean those who care about teaching are good researchers or good instructors, but if they care about teaching it’s usually a good sign.
Based solely on my personal observation, I would estimate that prowess in research and teaching are weakly positively correlated (i.e., I think there is some positive correlation here, but it is not strong). There is some theoretical reason to believe that these things ought to be positively correlated, due to some overlap in the requires skills for the two activities, but as others have pointed out, there is also some degree of competition between the two roles in academia.
In any case, if you particularly want to identify the most successful researchers in your department then ---rather than relying on a weak proxy measure--- you could probably just ask around the faculty and get their opinions. Professors in your department might be willing to tell you who they identify as a particularly strong or successful researcher, and who they think would be a good supervisor for you if you were to pursue a PhD candidature. Research success (for the supervisor) is just one thing that is helpful in a PhD supervisor; there are other important factors, including having shared research interests and having a good "fit" in terms of learning style, etc.
There is a persistent myth that sloppy, unprepared, handwaving, wishy-washy, arrogant, condescending, etc... teachers must be brilliant researchers.
And one can climb the greasy pole quite nicely exploiting this.
However, it has been my observation that such people are also sloppy, unprepared, handwaving, wishy-washy, arrogant, condescending, etc... in their research, and it is usually best to steer clear of them.
