The student/faculty ratio, which represents on average how many students there are for each faculty member, is a common metric of educational quality. The ratio shows up in the Common Data Set (CDS) and college guides, presumably so prospective students can compare colleges.
The standard way to count students and faculty for the CDS calculation is to equate the total number of students into a smaller number of artificial standardized units. That's because some students may take a single class, while others take ten or more an academic year, and faculty teaching loads similarly vary. This is usually done by converting each population into Full Time Equivalent (FTE) units. The idea is that a part time student isn't the same as a full time student, but we might count, say, three part time students as equal to one full time student. This is the CDS approach, which we can write as FTE = FT + PT/3.
The part time conversion formula is ad hoc, chosen for convenience instead of meaningfulness. It considers all part timers (students or faculty) as averaging a third of a full load, when that will vary across institutions and across time. Additionally, "full time" is defined by policy, and this also varies by institution. A full time faculty load at a research institution is probably less than the load at a teaching college. The full-time definition for students is usually a range of numerical values, e.g. a full load is somewhere between 12 and 20 credits. There's a big difference between 12 and 14 or 16 or 18 credits, when
averaged over the whole student population, because it directly impacts
how many course sections need to be taught. So the student FTE works
okay as a measure of revenue (paying tuition for full load), but not as a
demand measure (how many classes do we need to teach).
Similarly, faculty members who get release time from teaching or conversely teach overloads may be "full time" for contractual purposes, but not reflect their classroom presence. There are complicated adjustments in the CDS definition, which refers to the AAUP definition of full time faculty. For example, a faculty member on leave for research (e.g. sabbatical) still counts even though they are not in the classroom, but if they have a replacement hired, that replacement should not be counted. A certain amount of judgment is required to decide if a hire is a replacement or not, resulting in "house rules" for counting faculty.
These effects combine to erode the meaningfulness of an FTE-based student/faculty ratio. But we might take a step back and ask what the ratio is intending to do anyway.
Deriving the Raw Ratio
If we focus on the student classroom experience, we might think of a student in a class as the basic unit for counting. How many of these are there? If there are \(N_s\) students, and on average each student has a class load of \(L_s\) each academic year, then there are a total of \(N_s L_s\) units of "student-classes." That's how many of these experiential units were consumed.
From the faculty perspective--the production side--if there are \(N_f\) faculty members, with an average teaching load of \(L_f\) classes, and average class size of \(A\), then the total student-classes is those three numbers multiplied together. Since student-classes taught (produced) must equal student-classes taken (consumed), these can be set against each other as
$$ N_s L_s = N_f L_f A $$
Using these raw counts (not FTEs) of students and faculty, the ratio is then
$$ \frac{N_s}{ N_f} = A \frac{L_f }{ L_s} $$
The average loads for faculty and students are largely determined by policy. For example, if six classes per year is the contractual load for a full-time faculty member, and ten courses per year is necessary to complete a bachelor's degree in four years, then the load fraction is 6/10. Because of part-timers and overloads, the measured load averages won't be exact, but they should be close to that and relatively stable over time for an institution--as long as policies don't change.
The raw student-faculty ratio is then measuring average class size times an index of institutional policy, the load ratio \(L_f / L_s\), including the prevalence of part-timers and overloads. This load ratio won't be the same between institutions, so including it as a factor is not appropriate if we want a comparable index. If we drop the load ratio from the right side, we have average class size, which is a comparable index of student experience. It's crude--a distribution would be better--but as a single metric it's not terrible.
The FTE Ratio
With that understanding, we can now see what the FTE ratio is all about. Suppose we create a "true" FTE calculation for faculty by dividing the total number of classes taught by the policy's specification for a full load. So if 3000 courses are taught in an academic year, and the faculty handbook says the load for a full-time faculty member is six courses, then the FTE faculty is 3000/6 = 500. We can do a similar calculation with students, e.g. using twelve credits as a full time student load.
In the terms defined earlier, the number of classes taught is \(N_f L_f\), which we need to divide by the faculty policy-defined load \(P_f\) to get \( \text{FTE}_f = N_f L_f / P_f \). Similarly for students, \( \text{FTE}_s= N_s L_s/ P_s \). In each case, the \( L/P\) fraction is expressing the measured average load as compared to the policy load. If there are a lot of adjuncts teaching, the average load per faculty member might be 5.1, whereas the full-time load is 6. Putting this together we have
$$ \frac{\text{FTE}_s}{\text{FTE}_f} = \frac{N_s L_s}{N_f L_f} \cdot \frac{P_f}{P_s} $$
The derivation in the previous section shows that
$$ A = \frac{N_s L_s}{N_f L_f} $$
so the FTE ratio is:
$$ \frac{\text{FTE}_s}{\text{FTE}_f} = A \frac{P_f}{P_s} $$
The difference between the raw ratio and the FTE ratio is that the former uses empirical average loads for students and faculty, whereas the FTE version uses policy-defined loads. In both cases, these vary by institution.
In the actual CDS calculations, the house rules and approximations, like FT = PT/3, will add error, so you probably won't get exactly the formula above.
Discussion
The student/faculty ratio conflates two types of educational quality. Average class size crudely evaluates the quality of in-class instruction, as a measure of accessibility to faculty while teaching. The load ratio (empirical or policy-based) assesses how much time faculty have to devote to each class, as well as how much students must spread themselves around to cover the required load. These are related to classroom experience, but are different dimensions. I suggest we adopt a rule for measures of "one dimension per dimension," in which case we could describe classroom quality as (1) average class size, (2) average teaching load, and (3) average student load. Attempting to combine all that information into one metric just creates a mess.
I've never seen the above derivation before, and until I did it I didn't know what was going into the ratio calculation. I suspect that most producers and consumers of the metric don't really understand it, and probably misuse it. For many purpose, the average class size is a convenient summary measure of student experience that also represents operational efficiency: financially it represents both revenue and cost in the same scale. It can be aggregated or disaggregated to whatever level of analysis you care do to do. And it's easily understood and communicated.
Bottom line: use average class size instead of student/faculty ratio.
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