The results of a typical simulation are shown in the graph, "Change in GPA under plus/minus system vs. Old GPA." This graph displays the change students can expect in their GPA from the switch from the current system to the new system.

The source code used in this simulation is in the accompanying document, gradeval.f90.

- Nearly all students (those with grade point averages between 1.0 to 3.6), will see a change in GPA of less than +/- 0.06. The change is small because the benefit of the "plus" grades almost exactly balances the penalty of the "minus" grades.

- Students with GPA's around 0.6, well below our standards for continuation, will see their grades hurt by about 0.12. These poorly performing students receive more grades of D- than D+.

- Students with a very high GPA of around 3.9 will see a decrease of as much as 0.08. They will on occasion receive an A-, whereas now they receive almost all A's. Fewer students will achieve a 4.0 under the proposed system.

This computer simulation assumes the same grading system as the previous study (100 point scale, 10 point spacing between letter grades). It also assumes that the errors in the instructor's assessments of student performance are normally distributed with a standard deviation of 3 points on the 100 point scale. Thus, the raw score the instructor determines on a 100 point scale is assumed to be within 6 points of the student's true performance, 95% of the time. If the student deserves a score of 85, the instructor is assumed to award the student a score between 79 and 91, 95% of the time. This assumed accuracy is close to that claimed by many faculty.

The results of this simulation are displayed in the second graph, "RMS
error in assigned grade points vs. raw grade". This graph summarizes
a computer simulation of the __consequences__ of the errors that instructors
make in evaluating student performance. Displayed is the root mean square
(RMS) difference between the grade points assigned by the instructor and
the grade points the student should have received had the instructor been
perfectly discerning of student performance. The RMS error is calculated
for a group of students whose performances warranted grades ranging from
50 to 100.

The graph illustrates that, under the current system, the RMS error in the assigned grades is typically between about 0.3 and 0.7. The largest errors occur for students close to the cutoff between letter grades, as expected. Students who should have earned an 81 (and therefore a B) are assigned a C almost half the time under the current system. Similarly, students who should have earned a 79 and a C are assigned a B almost half the time. For borderline students, the reported grade is wrong almost half the time. When the wrong grade is assigned, the awarded grade is in error by a full grade point.

Under the new system, the RMS error in assigned grade points is between 0.3 and 0.33 for most students. For students who earn raw grades above 68, the largest RMS error under the plus/minus system is less than half of what is seen under the current system. While instructors will be just as inaccurate in their assessment of students under the proposed system, the effects of their errors on student grade points are much smaller. A student who should have earned an 81 and therefore a B- may instead receive a C+ or B; however, these grades carry only small differences (0.333) in grade points assigned from the proper grade of B-.

**Thus, reported grades will be more accurate reflections of student
performance under the proposed plus/minus system, even if faculty can grade
with only an accuracy of one letter grade. Rounding inaccurate grades to
the nearest letter grade increases inaccuracy.**

There is little basis for the assumption that student performance in courses is normally distributed with a standard deviation of three points. To assess the importance of this assumption, other simulations were conducted with distributions of differing shape and width. The findings reported here are rather insensitive to both the detailed shape and width of the distribution.

Similarly, little basis exists for the assumed distribution of errors in assessment of student performance. However, the findings regarding errors in student assessment are even less sensitive to the shape and width of the distribution of errors. In particular, the maximum predicted RMS error in assigned grade points is consistently much higher under the current system than under the proposed plus/minus system.

The results of such a simulation are shown in the graph, "Effects on student grades, with and without A+". This simulation shows that including A+ in the grading system would cause the decrease in A- GPA's to be even smaller ( a change of 0.05 instead of 0.08). GPA's above 3.93 would increase in a plus/minus system including A+. An old 3.99 is boosted 4.14 with the A+ system, instead of dropping to 3.96 under a plus/minus system without A+.

(Editorial comment: The principal argument against inclusion of
A+ is that many employers and graduate schools scale all grades to the
4.0 scale with which they are most familiar. These organizations
would thus multiply all WFU GPA's by (4.0/4.333), reducing all GPA's by
nearly 8%. Under such a scaling, **all** of our students would
fair more poorly under a system including the A+.)