In case it has not been clear: Ph.D. candidates make up most of the teaching assistants in research institutions; these are graduate students who are becoming experts in the field but have not yet completed their Ph.D. Typically, the professor (who has completed their Ph.D.), teaches the large lecture class several times a week, and that is supplemented by smaller discussion or lab sections led by TAs. TAs may do the grading of the students who are in their discussion section, subject to parameters set by the professor, and often lead supplemental review sessions etc. before exams. At some schools, Ph.D. candidates may be the “lead” instructor for a class, typically as they get closer to completion of their Ph.D. program (including, I believe, some of Columbia’s introductory core curriculum classes, which are highly competitive positions to get). Largely, Ph.D. programs are funded by the department, students are not paying tuition to participate in the program. For a Ph.D. student, working as a TA is part of the department’s funding, particularly to get the stipend which covers a grad student’s bare-bones living expenses.
A school with TAs is neither “good” nor “bad.” It simply means that the institution is a research institution which has Ph.D. students who are preparing to enter the academic field. There has been lots of commentary about the move to use adjuncts to cover teaching responsibilities, and that is a whole different dilemma if an institution is using adjuncts as TAs or as a big part of its teaching.
The Common Data Set does show the number, and percentage, of part-time, non-tenure track teaching faculty. But even looking at that number, one has to drill further down, because often professionals in a field may serve as part-time instructors, particularly in music and fine art programs. A related point is that the student-faculty ration can appear low when a school offers a lot of private music lessons – 100 different students having private, one on one lessons, per semester on various instruments, can throw off that ratio. Looking at the Common Data Set to see how many classes are offered at the different class sizes is more revealing than the student-faculty ration alone.