Self-Adjusting Weighted Averages in Standard Scoring

Abstract

Like many of their counterparts in university teaching, law professors routinely rely on all-or-nothing final examinations. But all-or-nothing final exams put enormous pressure on students, who often labor for months with no meaningful feedback on their mastery of the material.

One alternative to the all-or-nothing final exam consists of administering some sort of initial graded assignment. Assigning a relatively modest weight to the initial assignment maintains the primacy of the comprehensive final exam. To further minimize the pressure that accompanies the initial assignment, I propose an algorithm for adjusting the weight of the grade on the initial assignment so that students who boost their performance by the time of the final exam will benefit from their improvement. By the same token, students who do well on the initial assignment may wish to “lock in” some of the benefit of that performance as a hedge against declining performance on the final exam.

The method for self-adjusting weighted averages described in this paper achieves both of those objectives. It does so in strictly parametric terms, thereby removing guesswork and potential capriciousness in grading decisions. By using the standard logistic function to adjust the relative weight of z-scores, the method prescribed in this paper preserves the symmetry inherent in the presumptively elliptical distribution of grades.

Keywords: Standard score, weighted average, logistic function, normal distribution, university grading