Self-Adjusting Weighted Averages in Standard Scoring

Herewith a methods paper for the benefit of law professors and other university instructors who seek a sensible alternative to all-or-nothing final exams:

James Ming Chen, Self-Adjusting Weighted Averages in Standard Scoring, available at http://ssrn.com/abstract=2397637.

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.

The secret underlying this methods paper, such as it is, involves the application of the standard logistic curve to the computation of weighted arithmetic means.

Cnidarians and academic life

O cnidarians! Cnidaria are the phylum of invertebrates including jellyfish, coral, and hydroids. They lack spine, but they sting. Their name is derived from the Greek word κνίδη, which means nettle. Many cnidarians — namely, those in subphylum Anthozoa — are sessile. Even the free-swimming Medusozoa, which subphylum includes jellyfishes, are rather limited in their locomotive power. The relevance of cnidarians to university life is left as an exercise for the reader.

Although this post arguably belongs in Biolaw rather than MoneyLaw, a wonderful New York Times video prompted me to post it here. Glaucus atlanticus, a nudibranch, enthusiastically and safely feeds off the infamous Portuguese man o' war. This little sea slug's ingenuity is well worth the three minutes needed to watch the video. May all of us who toil in acadème be inspired by the example of Glaucus atlanticus. Though cnidarians prevail throughout this vast ocean, there are ways to leverage their venom into defenses of our own and, indeed, to thrive on a diet of stinging nematocysts. Bon appetit!