# Re: Using the Normal Distribution to Grade on a Curve

Gordon Sande wrote:
On 2006-08-14 00:17:48 -0300, "Reef Fish"
<Large_Nassau_Gr0uper@xxxxxxxxx> said:

DarkProtoman wrote:
Hi, I'm a Asst. Prof., and I need to learn how to grade on a curve
using the normal distribution. I've recently given a test where the max
score is 100 pts.,

Every time I hear some professor is grading a class on a curve
(whatever
that is), I cringe in horror.

As I tell my students, there is no theoretical nor practical reason why

ANY class should be graded on a curve, let alone a class of 20 or less.
Grading it on a curve would mean that if a class is populated by a
group of bright, hard-working, and exceptionally gifted students who
take my class because they expect to be challenged to learn, MOST
of them will get lower grades they deserved. I have had (graduate)
classes in which nearly 100% of the 20 students had A's.

The other side of the coin is that if my class happened to be populated
by a group of lazy, unprepared students unable and uninterested to
learn anything (there are increasingly many of those, especially at the
undergrad level of "required" courses), a class graded on a curve will
reward MOST of them with grades they don't deserve. I have had
classes of 40 to 50 in which half of them had F's or dropped out
before grades were given, and only 1 or 2 out of 50 had A's.

When you teach a course, you should KNOW what the students are
supposed to learn, and you teach accordingly. If 100% of them met
what is expected of a grade of A, why not give them all A's? OTOH,
if none of them performed what is expected of an A student, then
none should get an A.

The way I accomplish that kind of grade distribution is to set the
standards at Day 1, on the cutoff scores for A, B, C, D, and F, and
let the student performance determine the distribution of grades.

Yes, I had many disgruntled students who expected (under the
present educational system of everyone gets good grades for
paying the tuition) much higher grades than they earn. But that's
the sad reality of life. You either set the standards and keep it
or you "sell your soul to the devil" (there is a long thread on that
topic when I join this group early least year). It is my
conservative estimate that at least 75% of the college professors
had sold their souls to the Devil, while nearly 100% of the
administrators who call themselves "educators" had sold their
souls before the professors did.

That's only ONE of the reasons you find some in this group who
are the product of that educational system -- they learned nothing,
they did everything wrong, and some of them even said they
teach others, on the subjects they clearly don't deserve even a
passing grade.

and I need to set the grades so that the mean is
75%, and the standard deviation is 15%. How would I go about doing
this. Here are the raw mean and standard deviation:

Mean=80
Std. Dev=16

If you expect the scores to be normally distributed, you have
already set an inappropriate distribution a priori.

Even if you DO have scores that turned out to be approximately
normal, you have to set standards for where to make the CUT for
each grade anyway.

The net result of which is -- why not just imagine a normal
distribution centered at 60 (or elsewhere), with a standard
deviation that will make a near 100 score above 3 standard
deviations, and then PRE-assign grades based on that
distribution? Then you make very careful efforts to make your
tests and assignments that make up the total grade in such a
way that those FIXED cutoff points will determine the distribution
and let the chips fall where they may.

There are seven students in my class.

That's all the more reason why your grades shouldn't be curved.

-- Reef Fish Bob.

There is also the issue of selection bias.

Of course. And there are many more reasons than one can anticipate or
explain.

Students are fairly good at the "efficient market model" when it comes
to
selecting courses. Your example is the explainable bimodal or
U-shaped
distribution of grades.

When I was a freshman in the Honours stream there were separate course
numbers for many of the Honours versions of the courses. But freshman
calculus was an exception. There were calculus classes at all possible
timetable slots so most of the Honours stream was locked into a single
calculus class by the timings of the other courses. The instructor was
a fresh graduate of a major research school with this being his first
class. He was a PDE specialist but choose to illustrate how useful
mathematics was by explaining how he could tell "by statistics" that
there would a range of abilities in the class. By then I could already
recognize enough faces of the Honours stream to know this guy was out to
lunch because of the selection process. It turned out the rest of the
class were girls from the Agriculture faculty back in a time when farm
girls would go on to be either teachers or, for the brighter ones,
agriculture extension workers. So the workings of the timetable had
landed this guy with a class of two high side outlier groups.

Fortunately the statistics excursion was a one day wonder and he got
down to business and turned out to be a good instructor. This was all
back before grading to a curve was the way to go and it was even
considered quite OK, even by the students, that if you missed the
higher cut points for Honours that was it and you were relegated to
the Pass program.

Those who were in this group last year must have heard of my unique
grading method which I don't think anyone comes closed. First, all my
exams were open book and open notes (absolutely nothing to memorize).
But they are expected to know what to DO with the formulas on exams.
Then 75 or above is a guaranteed A, and 40 or above is passing, with
the other grades in-between.

The idea was to give enough variety of questions that the good student
can NEVER can get unlucky because the prof happened to ask something
he didn't know about the course. On the other hand, student can NEVER
get lucky either. Sort of my way of minimizing the Type I and Type II

error in assigning grades, given the imperfect methods of measurement.

But I warn the student at the beginning of each class that they
shouldn't
get the impression for a second that vacation was about to begin. :-)

Yes, that's the same scale that failed 50% of the class sometimes.

At first, some students flock to my class (especially the athletic
department which had students who needed passing grades badly,
sent their students to my section of the class). But they soon found
out that everyone had to work to EARN whatever grade they got.

The athletic department advisors learned fast. I did not have a
single athelete sent to my class in the past 20 years I taught. :-)
My favorite story was a student who was a star in the national
championship football team of the school. He wasn't sent to my
class. He went to Room 101 (in which the first stat. course for
math majors were taught, Mthsc 301), when he was supposed
to go to Mthsc 101. After the first quiz, it became obvious to me
something was terribly wrong because he attended the class
every day and scored 20 when the next lowest score was in
the 50s. That was the only time I ever asked a student to see
me after the first quiz because of their performance -- and we
both found out why. (He failed the 101 course also when he
found the right classroom).

At any rate, other students soon found out (from their frat
or dorm) that I was to be avoided (which was fine with me,
because I wouldn't want those students anyway). So, I would
get students who had to take the course at the time slot
and only an occasion outlier or two who wanted to take my
course because they WANTED to learn.

My grading scale stood unchanged during my entire teaching
career. Their distributions vary from 1 A out of 50 to 19 A
out of 20. Near the year of my voluntary early retirement, I
would teach one section of a 10 section course with 40 students
each say. Nobody failed from the other 9 and the drops and
Fs from my class would be close to 50 percent. 25 percent or
so would drop after the first 2-3 weeks to go to other sections
where they would get their grades without learning anything.

The free-market principle prevailed. Those who sold their souls
to the Devil became ever-increasingly popular; and the one who
held on to some standards and not sell their souls to the Devil
became the targets of complaints, first by students, and then by
the admininstrators who sold their souls to the Devil too. And
everyone lived miserably thereafter until my retirement. :-)

Today in academia, grades are a joke, but not a funny one.

Grading on a CURVE because the chairman wants it that way,
even for 7 students. That was the FUNNIEST joke I've heard
for some time.

DarkProtoman should print a copy of this cost and give it to his
chairman, and invite him to give his response. :-)

-- Reef Fish Bob.

.