Normalizing Section Grades
Barnes-Billingsley contraction formula
To even out differences in grading standards between section instructors, I am issuing standard scores to which to normalize your Quiz sections. The idea is to avoid altering any scores near zero (or near perfect).
FIRST: You must normalize your scores so that a perfect score equals Gmax(see table below).
SECOND: Now that you have your section scores on a basis where Gmax is a perfect score, obtain YOUR average, A, for ALL your sections (of a given type), as a group. Do NOT make separate averages for each individual section. We want to correct only for your grading standards, not for statistical fluctuations in the students in each separate section. Also, omit people who have large numbers of zero quiz scores or are clearly not performing. We want your average to reflect how you grade people. For example, use only students who did at least 80% of the work, on average (quizzes + homework sets).
You now have your average, A. Get the appropriate value of AA, the overall average for the course, from the table below. Let G be the grade you calculated for the student in part ONE above, and let G' be the final grade you are about to calculate.
1) If G < A, normalize in the usual way:
G' = (AA/A) G = p G
(p will, of course, be a constant for a particular REC TA.)\
2) If G > A, normalize such that a score of Gmax is the fixed point:
G' = Gmax (1 - f) + f G = K Gmax + f G
where
f = (Gmax - AA)/(Gmax - A) and K = 1 - f
Once you have calculated p, K, and f, check that 0à 0, Gmax à Gmax, and (two ways) Aà A. Your algorithm is now ready. Again, the product K Gmax is a single number, constant for a given TA, as is f.
Here are the specified average and maximum values for recitations: AA = 45 Gmax =60