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8.01 Preliminary Renormalization of Recitation Quizzes, Fall 1998

November 20, 1998

To give you preliminary feedback on how to interpret your own Recitation Quiz scores, we have computed preliminary renormalization numbers based on the first three Recitation Quizzes, and the first two Review Quizzes. Since significantly more quiz data will exist by the end of the term, you should bear in mind that the numbers presented here are very much subject to change.

In this document I will give you the formulas for computing your own renormalized Recitation Quiz grade, and also a set of grade cuts and a histogram so that you can see where you stand. The Recitation Quiz grade will count for 20% of your final grade in the course.

HOW TO COMPUTE YOUR GRADE:

STEP 1: Computation of Raw Grade

To simulate the fact that the lowest of the 5 Recitation Quiz grades will in the end be dropped, for the preliminary calculation we dropped the lowest 3/5 of a quiz for each student who has taken all the quizzes. The dropping a fractional quiz is accomplished by weighting the lowest quiz less than the others. The implementation of this procedure was further complicated by the fact that the Mon-Wed recitations had 3 full Recitation Quizzes, while in the Tues-Thurs recitations the last quiz is to count only half.

Monday-Wednesday sections:

3 out of 5 quizzes have happened, so you should drop the lowest 3/5 of a quiz. That means that one should compute a weighted average of the three quiz scores, with the lowest quiz counting as 2/5 of a quiz. Specifically, if Q1 is the lowest quiz score and Q2 and Q3 are the two others, then the desired average is:

                     0.4*Q1 + Q2 + Q3
             <Q> =  -------------------
                           2.4

If the grades were not based on 100 as the maximum possible grade, then you should scale them so that they are based on 100.

Tuesday-Thursday sections:

2.5 out of 4.5 quizzes have happened, and in the end you will be allowed to drop one quiz of the 4.5. For the preliminary calculation, your grade was computed by dropping the 0.5 quizzes. Specifically, let Q_1/2 denote the score on the quiz that counts half, and Q1 and Q2 denote the other two scores. I am assuming that the maximum possible score is 100 for all three quizzes. If Q_1/2 is the lowest score, then just drop it, so the average is

                    Q1 + Q2
             <Q> = ----------
                       2

If Q_1/2 is not the lowest, then let Q1 denote the lowest. The desired average is

                    0.5*Q_1/2 + 0.5*Q1 + Q2
             <Q> = --------------------------
                               2

Students with excused absenses, any day of the week:

If you have any excused absences on the Recitation Quizzes, then click here to find out how to compute your raw grade.

STEP 2: Computation of Renormalized Grade

We experimented with three different methods of renormalization, but found that none of them seemed to be fair in all cases. We have therefore decided to use all three, and for each student the maximum of the three calculations will be used for the renormalized grade. For each instructor, four parameters were determined by comparing the Recitation Quiz grades and the Review Quiz grades of the instructor's students. A table of these parameters is as follows:

TABLE OF RENORMALIZATION FACTORS:

Sections	Instructor	R	Q	M	B
1	Busza	1.276	0.580	0.990	19.2
2 & 3	Burgess	0.916	1.526	2.185	-106.7
4 & 5	Hauer	1.037	0.913	1.093	-3.764
6, 7, & 8	Javan	0.815	2.300	1.066	-22.7
9, 10, & 11	Joss	1.074	0.833	0.799	18.2
12	Koster	1.022	0.970	0.497	40.619
12 & 14	Falus	0.939	1.160	1.273	-26.0
15, 16, & 17	Burke	0.868	1.641	1.445	-48.6
18 & 19	Su	0.984	1.046	0.890	7.0
20	Wiese	1.111	0.774	1.115	0.5
21 & 22	Millar	1.064	0.856	1.529	-32.6
23 & 24	Graham	0.940	1.142	1.312	-28.7
25 & 26	Katz	1.204	0.673	1.103	6.3

Use the parameters in the above table to compute your renormalized Recitation Quiz grades by each of the following three methods, and then take the maximum of the three:

Method 1:

Renormalized Grade = R * (Raw Grade)

Method 2:

Renormalized Grade = 100 - Q*(100 - Raw Grade)

Method 3:

Renormalized Grade = M * (Raw Grade) + B

WHERE DO YOU STAND?

The passing grade for the renormalized Recitation Quiz average has been set at 60.0, and other numerical grades can be translated into letter grades according to the following chart:

A histogram of the grades is shown below:

RECOMPUTATIONS BEFORE AND AFTER THE FINAL EXAM:

After the final examination, when the final data is available to compare the classes with each other, the renormalized grades will be calculated one last time. If your renormalized grade is increased by this recalculation, then the new value will be used; if not, then the value computed before the final exam will be retained.

IF YOU ARE INTERESTED:

• How were the renormalization parameters computed?

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