For whom the ‘Bell Curve’ tolls

The title of the post is inspired by the title of a famous novel, however unlike experiences of Robert Jordan, the hero in the novel, we would look here at pros and cons of a hypothetical scenario of incorporating ‘Bell curve grading’ in Indian Law Schools.

So let us begin by understanding what bell curve is: it is a normal distribution curve or graphical representation of the Gaussian function. It refers to a continuous probability distribution that describes data that clusters around a mean or average. The graph of the associated probability density function is bell-shaped, with a peak at the mean, hence the name Bell Curve. An example (courtesy wiki) of a bell and bell curve is as below, (Disclaimer: The use of cracked Liberty Bell as an example to illustrate bell curve does not refer to comment by Earnest Ernest as ‘ Surely the hallowed bell-shaped curve has cracked from top to bottom. Perhaps, like the Liberty Bell, it should be enshrined somewhere as a memorial to more heroic days.’ as published in Philadelphia Inquirer on 10 November 1974.)

Click on the graph or bell above to enlarge (opens in same tab).

When bell curve is implemented for grading (the part which interests us), it simply means that the professor who is grading the copies would keep in mind that the numbers of recipient of a particular grade must yield a desired distribution of grades among the students in a class, i.e. assigning of grades should be according to the frequency distribution. Below is an example of bell curve grading where the parameters for the teacher, in a 6 point grade system, is to place 2.3% students between grade 0-1, 13.6% students between 1-2, 34.1% between 2-3, 34.1% between 3-4, 13.6% between 4-5 and again 2.3% between 5-6.

Click on the graph above to enlarge (opens in same tab)

In other word out of 100 students, the professor has to mark in a manner that, we ought to find 3 students score poor, 13 score below average, 68 score average, 13 score above average and 3 score excellent marks (as per the curve above). This ensures that there is a homogenized marking pattern in all the subjects and the final result is also homogenous, i.e. according to Gaussian function and thereby eliminating chances of an unusually harsh professor or an inexperienced tutor.

Among the pros the system would ensure that results in a subject are not very poor or incredibly excellent or extremely average but follow the distribution pattern as fixed by the university administration, thus there would be more objectivity and less subjectivity and consequently less allegation of faulty/careless grading can be raised against the professors. Among other benefits the curve ameliorates the problem of deciding grades that fall very near a grade margin (so no more pulling/splitting hairs on missing a grade by .25 marks). So the professors would now mark the students first (raw marks) and then use Microsoft Excel (one more reason to bash Microsoft) or any other curve fitting software to get the final grades. However before we move on to the cons let us see an example of graphical representation of normal distribution of assessment of a five subject semester (represented in five different colors) where five different professor evaluate the exam papers of students, four of them follow Gaussian function but with different parameters and one of them doesn’t, the diagram below is revealing;

Click on the graph above to enlarge (opens in same tab)

Even in a bell curve grading, patterns of extreme can be achieved by merely tweaking the mean and standard deviation, thus the university authority would fix the mean curve, commonly know simply as the curve, this is the GPA around which 70% of the student should be placed. In USA the mean curve varies with university to university and sometimes with ‘demand’ the mean curve is changed. Cornell Law School has a mean curve of 3.35; George Washington University has mean curve of 3.0 similarly the top law universities in USA have 3.2 or 3.3 curve. But that does not mean all US law schools follow the curve, notable exceptions are Harvard, Columbia, Yale, Vanderbilt, Berkley among others. The usual reasons given by these law schools are that students should be graded as per their quality and not what the administration thinks is the mean quality of the students and how many students can be Gaussianly placed on two sides of the mean.

• And indeed this is the very first critique of Bell curving of gradation at Indian law schools, it curtails the academic freedom of the professor to grade a paper as per the quality rather now the faculty will have to first grade and them fit the result into the Gaussian function with the ‘constant’ coming from the Registrar or the VC. So what about a class where about 60% submitted a ‘brilliant paper’ yet to maintain the curve 3/4th of the brilliant papers are going to be given a lower grade although they deserved better. To quote Prof. Goertzel ‘instructors should grade papers according to their intrinsic merit and give out whatever grades result even if the distribution results in a lot of A's or F's’ (More on history of Bell Curve and examples of disastrous consequence of strict implementation of curving of grades by administration can be found in a condensed article titled The Myth of the Bell Curve by Prof. Goertzel.)
  
• The second problem is that of lack of uniformity, under Indian law school system we have already been hard pressed to come up with a common GPA system thus some follow 8 GPA system while some follow 6. With introduction of grade curves there will be further confusion and the system will be unfair as aptly explained by Prof. Kerr ‘The unfairness of using a lower curve was made particularly clear by the experience of one of my colleagues who covered a class at Georgetown one semester, and ended up giving the same exam to Georgetown and GW students at the same time. According to him, the raw scores of the GW students were slightly higher than the raw scores of the Georgetown students. But because Georgetown used a 3.3 curve and GW used a 3.0 curve, he was required to give GW students lower grades than the Georgetown students for the same raw score.’
• The third disadvantage would be implement bell curve grading in a smaller seminar/optional paper, there isn’t enough data points for categorizing students in various grade quotas (Much similar to the problem faced by Prof. Seldon when he failed to use psychohistory to predict future of one person due to dearth in statistical data points on one person).

Just to compare the present system with curve grading, I decided to record the grade pattern in a non curve CGPA system based on calculation of the CGPA of an entire 5th year batch comprising of 94 students of an elite law school in India, these students have passed about 40 papers under a 7 point grading system in last four years. If the university was using a grade curve of 3.5 then the number of students in each grade in ascending order would be 2, 13, 32, 32, 13, 2 (results can be obtained by using the data provided in second chart from the beginning of this post or using a curve fitting software), however as per available data we find the corresponding numbers are 3, 13, 23, 27, 23, 5 (much like the brown line in the 3rd chart from the beginning of this post). This shows a tendency to cluster students at the higher end of the spectrum, give the fact that these students come through a rigorous selection criteria there would be little question on their merit; thus the logic to solely deny a student a higher grade on the basis of maintaining the curve and preserving a grade quota is bit shaky.

Thus finally to conclude, Prof. Volokh may support the curve grading but the disadvantages of implementing implementing curve grading in India simply outweighs any perceived benefits especially when the absolute marking system (each student marked out of 100 in percentage) still rules the roost. Hence to summarize in one sentence given the disparate nature of legal education in India it would be an unwise decision to implement bell curve grading at Indian law schools.
On a lighter note there are several other ‘more effective’ staggered grading systems available as advocated by Prof. Solove.