I’m guessing that you have a theory that the % of TAs vs Profs is going to be a meaningful metric in assessing the relative merits of an engineering program. As somebody who has taught in an engineering school, and the parent of a grad student who has recently TA’d in an engineering program, I question that theory.
For a start, any university that offers a PhD in Engineering / Applied Physics / Math will have grad students teaching- they have to. Being able to teach your subject is one of the 3 pillars of earning a PhD, and pretty much every PhD program in the US has a requirement that every PhD candidate teach at least 1 semester (the requirements vary by university). As the teaching is a good source of revenue for PhD students, and as many PhD students hope to go into academia, many teach for many semesters more than they are required to. And yes, for the university grad students are cost-effective.
Which leads to the further point: what exactly is meant by “teach”? Typically there is a professor who “teaches” the course, and grad students lead smaller group discussions and labs. IME it is passing rare that a grad student is the primary “teacher”- as in, writing the syllabus, creating the assessments and structuring the class.
Then there is the question as to inherent quality: the theory that a class taught by a grad student is inherently ‘less’ than one taught by a prof is belied by the experience that many, many, many of us have had ourselves: the prof who is past their sell-by date, the prof who is the research star but isn’t good at introducing the subject to beginning students, etc. There are TAs who are much better at teaching introductory concepts than profs (I have seen students vote with their feet, choosing to go the TAs office hours over the Profs, b/c the TA was better at explaining the topic).
IMO, the relative impact of the “quality of faculty-student interactions” is also (perhaps surprisingly) somewhat dubious in engineering. Full disclosure: I believe that there is an engineering temperament- not in the lazy introvert/extrovert or nerdy detail person stereotypes, but one that is expressed by a particular kind of interest in understanding how things work. IME most profs and students share that temperament, and the ‘quality’ of that dynamic suits both sides pretty well.
Instead, I suggest two elements to consider:
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The department: what can you learn about how the department is run? When you look at the Engineering dept newsletters, the student newspaper, online RateMyProf-type sites, are there complaints about scheduling? frequent changing of requirements? inability to get responses from the Dept Chair? (expect some complaint everywhere ofc!). When you talk to current students what sort of gripes stand out?
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What is the peer networking like? Do students form study groups and help each other out, or do most students stick to themselves? Is there evidence of collaborative behaviour (the department websites are often good for this, but so are things like looking at the makerspace site, which may have pictures of some of the fun things that different student groups have done). Hand on heart, the thing that has made the most difference to their overall experience for the students that I have known is the peer group.
Sadly, neither of these suggestions lend themselves well to an Excel format. I understand the attractions of trying to quantify as many elements as possible, but the data has to reflect something meaningful.