When it comes to the tenure review process, someone puts it like the way it's put below:
The tenure review process is designed to determine whether someone has "the ability to do their job." The junior faculty member has six years to construct a track record of success. During these six years, the junior faculty member acquires teaching evaluatons from students and colleagues. The junior faculty member acquires grants and sets up a lab with a productive research program. The junior faculty member develops a reputation of collegiality and service within the department and the university.
Though that's how it's done in name. Others, like Sean Carroll, say that research is far more important than teaching (which is probably true in the elite private universities).
What about things like successfully graduating PhD students though? Can a PhD student help an assistant professor gain tenure? I'm particularly curious about whether or not this applies for all universities - both in the elite privates and the public ones.
How many graduate students a professor helps through the program can have a number of impacts on tenure - including some I'll likely miss. Off the top of my head:
- As a former student, I have been asked to write a letter on behalf of a mentor of mine. The more students one helps launch off into bright, shiny, productive careers, the more of these letters should be positive and strong.
- PhD students are heavily correlated with research productivity. One person can only be so productive - having a thriving lab with graduate students passing through it can help boost publications, productivity, etc. all of which may very well help one's tenure portfolio.
- To address "like Sean Carroll, say that research is far more important than teaching" - your actual, direct supervised graduate students really don't fall under "teaching" in many cases, and are much closer to either the research or service end of things.
Keep in mind that, with the tenure clock of many universities, a junior professor may very reasonably not have graduated any students from their lab by the time they come up for tenure. But being a good mentor and building a pool of capable graduate students can help one's tenure application in a number of ways even if the committee doesn't look at it as a solitary number.