# Weighting & Combining Grading Components

Grades are typically based on a number of graded components (e.g., exams, papers, projects, quizzes). Instructors often wish to weight some components more heavily than others. For example, four combined quiz scores may be valued at the same weight as each of four hourly exam grades. When assigning weights the instructor should consider the extent to which:
• each grading component measures important goals.
• achievement can be accurately measured with each grading component.
• each grading component measures a different area of course content or objectives compared to other components.

Once it has been decided what weight each grading component should have, the instructor should insure that the desired weights are actually used. This task is not as simple as it first appears. An extreme example of weighting will illustrate the problem. Suppose that a 40-item exam and an 80-item exam are to be combined so they have equal weight (50 percent-50 percent in the total). We must know something about the spread of scores or variability (e.g., standard deviation) on each exam before adding the scores together. For example, assume that scores on the shorter exam are quite evenly spread throughout the range 10-40, and the scores on the other are in the range 75-80. Because there is so little variability on the 80-item exam, if we merely add each student's scores together, the spread of scores in the total will be very much like the spread of scores observed on the first exam. The second exam will have very little weight in the total score. The net effect is like adding a constant value to each student's score on the 40-item exam; the students maintain essentially the same relative standing.

The information appearing in this table will be used to demonstrate how scores can be adjusted to achieve the desired weighting before combining them. Exam No. 2 is twice as long as the first, but there is twice as much variability in Exam No. 1 scores. (This is the "observed weight.") The standard deviation tells us, conceptually, the average amount by which scores deviate from the mean of test scores. The larger the value, the more the scores are spread throughout the possible range of test scores. The variability of scores (standard deviation) is the key to proper weighting. If we merely add these scores together, Exam No. 1 will carry 66 percent of the weight and Exam No. 2 will carry 33 percent weight. We must adjust the scores on the second exam so that the standard deviation of the scores will be similar to that for Exam No. 1. This can be accomplished by multiplying each score on the 80-item exam by two; the adjusted scores will become more varied (standard deviation = 7.0). The score from Exam No. 1 can then be added to the adjusted score from Exam No. 2 to yield a total in which the components are equally weighted. (A practical solution to combining several weighted components is to first transform raw scores to standard scores, z or T, before applying relative weights and adding.) (Additional reading can be found in Ebel & Frisbie, (1991); Linn & Gronlund, (1995); and Ory & Ryan, (1993).

After grading weights have been assigned and combined scores are calculated for each student, the instructor must change the numbered scores into one of five letter grades. There are several ways of doing this; some are more appropriate than others.

 Exam No. 1 Exam No. 2 Total Number of items 40 80 120 Standard deviation 7.0 3.5 Desired weight 1 1 Observed weight 2 1 Multiplying factor 1 2 New standard deviation 7.0 7.0 Actual weight 1 1