weighted and relative GPAs: pros and cons

LynnG's article, Weighted GPA, confused me for a moment, until I realized that high schools were using the term, "weighted GPA" to mean something very different from the way universities use the term:

Our High School is proposing to change the way high school grade point average is calculated. We currently use a a weighted GPA scale that gives more "credit" to Honors and AP level courses. Honors and AP are graded on a 6.25 scale (an A+ gets a 6.25) and the non-Honors/AP courses use a 5.25 scale. Also, health and physical ed courses are not included in the GPA calculation.

The high school administration proposes to end this and grade all students on a single 4.0 scale that includes all graded courses (scooping in band, pe, health, maybe others). I'm on the fence on this because I really don't know what the pros and cons are and I am hoping maybe some of you out there might help clarify.

If I were an admissions officer (I am not), I would back the high school administration, if only because this sort of system, where schools can have different scales for different courses, would be a nightmare. However, making life easier for bureaucrats isn't necessarily the best reason for supporting a system (or not).

It seems that the biggest disadvantage of this sort of weighted system is that it is based solely on the designation of the course. Perhaps I'm being cynical (it's happened before), but I have seen enough "honors" courses at the university that were utter crap that the idea of giving a student a higher GPA solely because he was enrolled in an advanced course is pointless, at least without some objective way to judge the rigor of the course.

She brings up an excellent point here:

Here's what we've come up with so far -- the change would primarily affect the class "rank." By taking easier courses and getting an A, you'll get a better GPA and a better class rank than if you take AP and Honors courses and get a B. The kids graduating in that all important (is it?) top 10% might be those that avoid AP and Honors and take easier courses for a better grade. Would this new system penalize kids that stretch themselves in AP and Honors? Or do colleges really not care about GPA and class rank, caring much more about the courses on the transcript rather than the grades achieved?

The issue here, of course, is the existence of "easier" courses, but that's a series of books in itself, so I won't address it. Her point is valid, though: Will going to a flat 4.0 scale penalize students who take more difficult courses (assuming that they are, indeed, more difficult)?

Yes, this is a potential problem. One solution -- though not a perfect one, as I'll point out -- is to use what universities call a "weighted GPA" (I'll use the alternative "relative GPA" to avoid the confusion I originally experienced).

A relative GPA is relative to the mean GPA for the class (universities also assign relative GPAs to courses calculated relative to the overall mean GPA for all the courses in the department or school, in order to determine difficulty). The advantage of this (over the weighted GPA above) is that the relative GPA is not calculated as a function of class label, but the performance of all the students in the class. A relative GPA is, therefore, a real statistic, whereas a weighted GPA is not -- that is, a relative GPA is meaningful to an admissions officer (or a parent), because he can see not only what grade the student received, but also how well the student did relative to the other students in the course, while a weighted GPA is meaningless to an admissions officer, because he has no way of knowing whether the course was, in fact, advanced or more difficult beyond the certification of the student's school.

When relative GPAs are calculated and reported, they are always (in my knowledge) reported with the student's raw GPA. A relative GPA is essentially a curve, in the traditional (and not "raise my grade") sense of the term.

One way to calculate a relative GPA is to divide the student's raw GPA by the class mean GPA. Let's say we have three students, Hyung-Sik, Mary, and Tomoyuki, who receive As in three different courses, Organic Chemistry I, Introduction to Philosophy, and Overview of Ethnic Studies, respectively. If only raw GPAs are calculated and reported to the university, Hyung-Sik, Mary, and Tomoyuki will all receive As. But if the university uses relative GPAs, the grades reported for the three students will be calculated by dividing the raw GPAs by the class mean GPAs. So if the class mean GPAs for Organic Chemistry I, Introduction to Philosophy, and Overview of Ethnic Studies are 1.0 (a D), 2.5 (mid-range C), and 4.0 (A), Hyung-Sik, Mary, and Tomoyuki will receive relative GPAs of 4.0, 1.6, and 1.0. Unlike the weighted GPA LynnG described, the difficulty of the course in the relative GPA system is determined wholly by the performance of the class as a whole, and not by a class description, label, or determination, all subjective criteria.

Here is an example table of nine students in nine classes (I have no idea why blogger is forcing the table so far down the page, but it's there -- just scroll):

Student	Raw GPA	Class Mean GPA	Relative GPA
Hyung-Sik	4.0	1.0	4.0
Mary	4.0	2.5	1.6
Tomoyuki	4.0	4.0	1.0
John	3.0	1.0	3.0
Sue	3.0	2.5	1.2
Gerald	3.0	4.0	0.8
Bill	2.0	1.0	2.0
Lisa	2.0	2.5	0.8
Cindy	2.0	4.0	0.5

In this system, a student whose raw GPA is identical to the mean GPA of the course will receive a 1.0, which becomes the mean standard score. Relative GPAs can also be calculated by reporting the student's raw GPA and percentile rank, or by reporting the student's standardized score, or z-score (the difference of the student's score and the class mean score divided by the class standard deviation).

Another advantage of using relative GPAs is that it counters the administrative bias toward college-track courses. Why, for example, should Jim, who loves working with wood and excels at it, and wants to be a carpenter or woodworker, not receive the same advantage with respect to his GPA in shop? With a weighted system, Jim will likely only take 4.0-0.0 courses; with a relative system, Jim's superior work will be accurately reflected in his GPA.

The relative GPA is not a perfect solution. Whereas the relative GPA does give an objective assessment of the student's performance relative to the other students in the class, its major disadvantage is in small classes. One very low score (at the university, it would be that inevitable student who fails to drop the class in time, and there's always at least one), will drastically alter the class mean, and therefore, the student's relative GPA.

This presents a possible problem for using the relative GPA in pre-university schools, where class sizes are as a rule significantly smaller than university classes. One might counteract the effects of small classes by calculating the relative GPA with a trimmed mean (the outliers are removed from the sample). Confidence intervals can also be calculated to counteract this effect.

Either way, the relative GPA is a far more accurate and useful assessment tool than the weighted GPA, whether the school is primary, secondary, or the university.