We study the question: What is the cost (to a student's course grade) of missing a class? ---------------------------------------------------------------------- In Spring 2013, in 22 lectures and 11 recitations, a single quiz was given. In one lecture, 2 quizzes were given. For that lecture, we are excluding the second of the 2 quizzes. Based on those 22 + 11 + 1 = 34 quizzes in 34 classes, we wish to evaluate the effect of attendance on the student's course grade. In the 34 classes in question we consider a student to have "attended" that quiz if his/her quiz score was nonzero. In Spring 2013, there were 178 students who took the final exam. We will only look at the course grades for those 178 students. For each of them, an "A" or "A-" in the course counts 4.0 points, a "B+", "B" or "B-" in the course counts 3.0 points, a "C+", "C" or "C-" in the course counts 2.0 points, a "D" in the course counts 1.0 points, an "F" in the course counts 0 points. ---------------------------------------------------------------------- Summary of data: 69 students attended 33-34 quizzes with average points 196 / 69 = 2.84 out of 4.0 31 students attended 31-32 quizzes with average points 85 / 31 = 2.74 out of 4.0 30 students attended 29-30 quizzes with average points 64 / 30 = 2.13 out of 4.0 18 students attended 27-28 quizzes with average points 35 / 18 = 1.94 out of 4.0 20 students attended 21-26 quizzes with average points 23 / 20 = 1.15 out of 4.0 10 students attended 0-20 quizzes with average points 8 / 10 = 0.80 out of 4.0 Note that students who attended only 0-28 quizzes (out of 34) had a very hard time getting a "C-" grade (2.0 points) for the class. We calculate 28 / 34 = 82.35%. So students whose attendance drops below 82% are at risk of receiving a grade lower than "C-". ---------------------------------------------------------------------- Regression analysis For each of the 178 students who took the final exam, we created a point in the plane whose x-coordinate is the number of quizzes they attended (between 0 and 34) and whose y-coordinate is the points corresponding to their course grade (between 0 and 4.0). All this data appears under "Raw data for all 34 quizzes" below. A least squares regression analysis gives the line of best fit to be y = (0.126536) * x - 1.45227 . With this model, missing one quiz reduces grade points by 0.126536; missing eight quizzes reduces grade points by more than one full grade point (8 * 0.126536 = 1.012288), which pulls the student's grade down from "A" to "B", or from "B" to "C", or etc. There were 34 quizzes and 74 days of class. To some extent, students knew which days there were quizzes (e.g., recitation quizzes were always on Thursdays, never on Tuesdays), and their attendance on non-quiz days may have been worse than on quiz days. However, if we ignore that, and assume the same attendance rate on quiz days and non-quiz days, then missing one class reduces grade points by (0.126536) * 34 / 74 = 0.0581381 . ---------------------------------------------------------------------- Does missing early classes have more of an effect on course grade than missing late classes? There were 8 lecture quizzes and 6 recitation quizzes before Spring Break, totaling 8 + 6 = 14 quizzes. Let's call these the "early quizzes". For each of the 178 students who took the final exam, we created a point in the plane whose x-coordinate is the number of early quizzes they attended (between 0 and 14) and whose y-coordinate is the points corresponding to their course grade (between 0 and 4.0). All this data appears under "Raw data for early quizzes" below. A least squares regression analysis gives the line of best fit to be y = (0.24165) * x - 0.67769 . With this model, missing one quiz reduces grade points by 0.24165; missing four early quizzes reduced grade points by almost one full grade point (4 * 0.24165 = 0.9666), which pulls the student's grade down from "A" to "B", or from "B" to "C", or etc. Let's say that a class is an "early class" if it came before Spring Break. There were 14 early quizzes and 39 early classes. To some extent, students knew which days there were quizzes (e.g., recitation quizzes were always on Thursdays, never on Tuesdays), and their attendance on non-quiz days may have been worse than on quiz days. However, if we ignore that, and assume the same attendance rate on quiz days and non-quiz days, then missing one early class reduces grade points by (0.24165) * 14 / 39 = 0.0867461 . The comparable figure for all classes (not just early classes) from above was 0.0581381. This indicates that missing an early class has significantly more of an effect on course grade than does missing a class *after* Spring Break. ---------------------------------------------------------------------- Slightly processed data: 35 students attended 34 quizzes with average points 103 / 35 = 2.94 out of 4.0 34 students attended 33 quizzes with average points 93 / 34 = 2.74 out of 4.0 13 students attended 32 quizzes with average points 42 / 13 = 3.23 out of 4.0 18 students attended 31 quizzes with average points 43 / 18 = 2.39 out of 4.0 15 students attended 30 quizzes with average points 36 / 15 = 2.40 out of 4.0 15 students attended 29 quizzes with average points 28 / 15 = 1.86 out of 4.0 9 students attended 28 quizzes with average points 17 / 9 = 1.89 out of 4.0 9 students attended 27 quizzes with average points 18 / 9 = 2.00 out of 4.0 6 students attended 26 quizzes with average points 9 / 6 = 1.50 out of 4.0 4 students attended 25 quizzes with average points 6 / 4 = 1.50 out of 4.0 4 students attended 24 quizzes with average points 3 / 4 = 0.75 out of 4.0 2 students attended 23 quizzes with average points 2 / 2 = 1.00 out of 4.0 1 student attended 22 quizzes with average points 0 / 1 = 0.00 out of 4.0 3 students attended 21 quizzes with average points 3 / 3 = 1.00 out of 4.0 3 students attended 20 quizzes with average points 5 / 3 = 1.67 out of 4.0 2 students attended 19 quizzes with average points 0 / 2 = 0.00 out of 4.0 no students attended 18 quizzes 1 student attended 17 quizzes with average points 2 / 1 = 2.00 out of 4.0 no students attended 10-16 quizzes 1 student attended 9 quizzes with average points 1 / 1 = 1.00 out of 4.0 1 student attended 8 quizzes with average points 0 / 1 = 0.00 out of 4.0 no students attended 7 quizzes 1 student attended 6 quizzes with average points 0 / 1 = 0.00 out of 4.0 no students attended 5 quizzes 1 student attended 4 quizzes with average points 0 / 1 = 0.00 out of 4.0 no students attended 0- 3 quizzes ---------------------------------------------------------------------- Raw data for all 34 quizzes: In the data below, each row corresponds to one of the 178 students who took the final exam. The first column gives the number of quizzes that that student attended (between 0 and 34). The second column gives their grade points (between 0 and 4.0) based on their course grade. 34 4.0 34 4.0 34 4.0 34 4.0 34 4.0 34 4.0 34 4.0 34 4.0 34 4.0 34 4.0 34 4.0 34 3.0 34 3.0 34 3.0 34 3.0 34 3.0 34 3.0 34 3.0 34 3.0 34 3.0 34 3.0 34 3.0 34 3.0 34 3.0 34 2.0 34 2.0 34 2.0 34 2.0 34 2.0 34 2.0 34 2.0 34 2.0 34 2.0 34 1.0 34 1.0 33 4.0 33 4.0 33 4.0 33 4.0 33 4.0 33 4.0 33 4.0 33 4.0 33 3.0 33 3.0 33 3.0 33 3.0 33 3.0 33 3.0 33 3.0 33 3.0 33 3.0 33 3.0 33 3.0 33 3.0 33 3.0 33 2.0 33 2.0 33 2.0 33 2.0 33 2.0 33 2.0 33 2.0 33 2.0 33 2.0 33 1.0 33 1.0 33 1.0 33 1.0 32 4.0 32 4.0 32 4.0 32 4.0 32 4.0 32 4.0 32 3.0 32 3.0 32 3.0 32 3.0 32 2.0 32 2.0 32 2.0 31 4.0 31 4.0 31 4.0 31 3.0 31 3.0 31 3.0 31 3.0 31 3.0 31 2.0 31 2.0 31 2.0 31 2.0 31 2.0 31 2.0 31 1.0 31 1.0 31 1.0 31 1.0 30 4.0 30 4.0 30 3.0 30 3.0 30 3.0 30 3.0 30 3.0 30 2.0 30 2.0 30 2.0 30 2.0 30 2.0 30 1.0 30 1.0 30 1.0 29 4.0 29 3.0 29 3.0 29 3.0 29 2.0 29 2.0 29 2.0 29 2.0 29 1.0 29 1.0 29 1.0 29 1.0 29 1.0 29 1.0 29 1.0 28 4.0 28 3.0 28 3.0 28 2.0 28 1.0 28 1.0 28 1.0 28 1.0 28 1.0 27 4.0 27 2.0 27 2.0 27 2.0 27 2.0 27 2.0 27 2.0 27 1.0 27 1.0 26 3.0 26 2.0 26 2.0 26 1.0 26 1.0 26 0.0 25 2.0 25 2.0 25 2.0 25 0.0 24 2.0 24 1.0 24 0.0 24 0.0 23 2.0 23 0.0 22 0.0 21 2.0 21 1.0 21 0.0 20 3.0 20 1.0 20 1.0 19 0.0 19 0.0 17 2.0 9 1.0 8 0.0 6 0.0 4 0.0 ---------------------------------------------------------------------- Raw data for early quizzes: In the data below, each row corresponds to one of the 178 students who took the final exam. The first column gives the number of early quizzes (quizzes before Spring Break) that that student attended (between 0 and 14). The second column gives their grade points (between 0 and 4.0) based on their course grade. 14 4.0 14 4.0 14 4.0 14 4.0 14 4.0 14 4.0 14 4.0 14 4.0 14 4.0 14 4.0 14 4.0 14 4.0 14 4.0 14 4.0 14 4.0 14 4.0 14 4.0 14 4.0 14 4.0 14 4.0 14 4.0 14 4.0 14 3.0 14 3.0 14 3.0 14 3.0 14 3.0 14 3.0 14 3.0 14 3.0 14 3.0 14 3.0 14 3.0 14 3.0 14 3.0 14 3.0 14 3.0 14 3.0 14 3.0 14 3.0 14 3.0 14 3.0 14 3.0 14 3.0 14 2.0 14 2.0 14 2.0 14 2.0 14 2.0 14 2.0 14 2.0 14 2.0 14 2.0 14 2.0 14 2.0 14 2.0 14 2.0 14 2.0 14 2.0 14 2.0 14 1.0 14 1.0 14 1.0 14 1.0 14 1.0 14 1.0 14 1.0 14 1.0 13 4.0 13 4.0 13 4.0 13 4.0 13 4.0 13 3.0 13 3.0 13 3.0 13 3.0 13 3.0 13 3.0 13 3.0 13 3.0 13 3.0 13 3.0 13 3.0 13 3.0 13 3.0 13 3.0 13 3.0 13 3.0 13 3.0 13 3.0 13 2.0 13 2.0 13 2.0 13 2.0 13 2.0 13 2.0 13 2.0 13 2.0 13 2.0 13 2.0 13 2.0 13 2.0 13 2.0 13 1.0 13 1.0 13 1.0 13 1.0 13 1.0 13 1.0 13 0.0 12 4.0 12 4.0 12 4.0 12 4.0 12 3.0 12 3.0 12 3.0 12 2.0 12 2.0 12 2.0 12 2.0 12 2.0 12 2.0 12 2.0 12 1.0 12 1.0 12 1.0 12 1.0 12 1.0 12 0.0 12 0.0 11 4.0 11 3.0 11 3.0 11 3.0 11 2.0 11 2.0 11 2.0 11 2.0 11 2.0 11 2.0 11 2.0 11 1.0 11 1.0 11 1.0 11 1.0 11 1.0 11 1.0 11 1.0 11 0.0 11 0.0 11 0.0 11 0.0 10 4.0 10 2.0 10 2.0 10 2.0 10 2.0 10 2.0 10 2.0 10 2.0 10 1.0 10 1.0 10 1.0 10 0.0 9 2.0 9 1.0 9 0.0 8 1.0 8 0.0 7 1.0 7 1.0 6 2.0 5 3.0 4 0.0 2 0.0 1 1.0 ----------------------------------------------------------------------