Attendance in Introductory Physics Courses
 
–M.M. Jarrio

The one who does not remember history is bound to live through it again.
–George Santayana

The following information is based on attendance data for over 2500 students who have taken PHYS 2212 between 2005 and 2008. It includes every section since Fall 2005 for which reliable attendance records were kept. Note, too, that statistics prior to 2005, as well as after 2008, show the same general trends—as do the statistics for PHYS 2211.

Students taking either of the introductory physics courses are strongly advised to pay heed to the conclusions reached below–they directly contradict some of the common student misconceptions about the impact of attending class.

Preliminaries

To begin, attendance records can be divided into one of three categories: Good, Fair, or Poor:

• Good - maintain 90% or better attendance over the course of the term
• Fair - maintain 60% to 89% attendance over the course of the term
• Poor - maintain less than 60% attendance over the course of the term

These breakpoints were were chosen for two reasons:

1. Historically, we find that about one third of all students fall into each category.
    
2. 2212 GPAs plotted as a function of attendance rate show three distinct tiers, illustrated quite nicely by the cumulative data going all the way back to 2002:

Attendance & Final Grades

Let's begin by considering the distribution of letter grades within each category, for our our database of recent students:

A few points worth emphasis:

• Only 6% of students with Good attendance earn D's or F's, while three fourths of them earn A's or B's. In other words: students maintaining Good attendance are twelve times likelier to earn a good grade (A or B) than a bad grade (D or F).
   
• Among students with Fair attendance, 55% earn A's or B's, while only 13% earn D's or F's. The good-to-bad grade ratio is thus four to one–still a very good ratio, but note that the likelihood of a getting a D has doubled, while the likelihood of getting an A has been halved.
   
• Among students with Poor attendance, more students earn bad grades than good grades. Note that these students, although they make up only one third of all students, earn 68% of all D's and F's awarded in 2212–meaning that the other two-thirds of all students only earn 32% of all D's and F's. The upshot of all this is that students with Poor attendance are four times likelier to earn D's or F's than everone else!
   
• If you combine both the Fair and Good categories to get a Not Bad attendance group (60% attendance or better), you will find an overall 2.89 GPA, and two thirds of these students will earn A's or B's. Over 80% of all good grades go to the students with at least Fair attendance.

It is worth noting that the grade distribution for students maintaining a Not Bad attendance record is virtually identical to the distribution of grades for students who make a Not Bad effort to do extra assigned homework. This suggests that the cutoffs selected for both attendance and extra homework are not as arbitrary as one might suspect.

Attendance, PRS Scores, & Letter Grades

In the terms used for this study, attendance (via the PRS) actually counted for points (typically 5%) toward each student's final grade. A student with Good attendance might be expected to earn 90% or better on the PRS, for about 4.5 Class Participation points, while a student with Poor attendance might only earn 35% on the PRS, for 1.75 Class Participation points–ending roughly 3 points lower than those with Good attendance, at term's end. All other things being equal, and assuming a standard grade scale of ten points per letter grade, the expected GPA difference between the two groups would be just 0.3 grade points. But if you review the figures above, you'll see that the actual GPA difference between Good and Poor attendance is 1.34 grade points (3.13 vs. 1.79). The true value of going to class is about five times greater than that the nominal points awarded through the PRS.

Attendance & Test Scores

Hopefully, by this point you're asking the question, Why is the actual GPA difference so much bigger than the PRS point values for attendance? The answer lies in the the assumption above about ...all other things being equal.... The truth is—contrary to what every student might wish to believe—students who don't go to class do not perform equally well with their peers that do attend. This can be clearly demonstrated by looking at the test scores of the two populations. Before we do, let's review the two common student rebuttals to required attendance policies:

1. Why should I have to go to class, if I can get A's on all my quizzes without attending?
    
2. Why should I have to go to class, if I can do just as well on the quizzes without attending?

As for Argument 1: yes, there is a small number of people who can routinely skip class and still get A's on their tests, but in reality the number who actually do so is exceedingly small—only about half of one percent of students with Poor attendance end up with all A's on quizzes. Contrast that with the almost 5% of students with Good attendance who end up with A's on all their quizzes, and it's easy to see that Argument 1 applies only to the best of the best (a tiny fraction of the student body), and is nothing more than a straw man argument for anyone else.

The mere possibility of Argument 1—regardless of its implausibility&mdahs;leads students to the postulate Argument 2 as a sort of necessary corollary, applicable to the less-exceptional students taking 2212. Anecdotal claims notwithstanding, Argument 2 is nothing more than wishful thinking, and is directly contradicted by the actual evidence that is avaliable. In the plots below, you will see a breakdown of final quiz averages for students in each of the three attendance categories. (These plots exclude data for any student who did not take all the required quizzes–those who dropped the class, or just gave up and quit trying are NOT part of this analysis.) For both the Good and Poor attendance categories, test scores form an obvious Bell Curve (also known as a normal, or Gaussian, distribution), and each plot consequently shows a best Gaussian fit to the data.

Note well the differences between the Good and Poor plots: the typical student with Poor attendance averages out to be more than ten points lower on the quizzes than an average student with Good attendance, at the end of the term. Even at the high end, the difference is clear: the very best students with Poor attendance score five points lower than the very best students with Good attendance. (So much for Argument 2, eh? Nobody does better–or even as good–by NOT going to class as they could by going to class. If there were any validity to such a claim, the plots would match at the high end, in the scores of exceptional students for whom attendance doesn't matter.)

Just to drive this point home, let's look at the Gaussian fits for each of the three categories:

Attendance Mean Std. Deviation Mean + 1 SD Good 67.9 14.6 82.4 Fair 60.0 13.8 73.7 Poor 54.6 13.1 67.8

You may not be familiar with Gaussian distributions, so let's quickly point out some standard results. In a Gaussian, 68% of the populations will fall within one standard deviation of the mean (above or below). Of the remainder, 16% will be one SD or more above the mean and 16% will be one SD or more below the mean. With that in mind, note:

• An average student with Poor attendance, scoring the mean value of 54.6%, would only rank among the bottom 18% of students with Good attendance.
   
• Students with Poor attendance who are one SD above their mean (score = 67.8) are still below the mean score of students with Good attendance (score = 67.9). This means that only 16% of students with Poor attendance will exceed the mean score of students with Good attendance. If we were to define a good student as someone whose test scores are merely above average, then 84% of students with Poor attendance are not good students, when compared to those with Good attendance.
   
• Students with Good attendance who are one standard deviation above the mean have quiz averages of 82.4 or better. Students with Poor attendance would have to be 2.1 standard deviations above their mean to earn that same score. Statistically only 1.7% of a Gaussian population will exceed the mean by that much. If we were to define a very good student as someone whose test scores are in the top 16% of the class, then 98.3% of students with Poor attendance are not very good, when compared to those with Good attendance.
   
• Consider a score of 61, which looks to be roughly the place where the Good attendance and Poor attendance distributions cross one another. Note that this particular score is also roughly at the dividing line between having a C and a D at the end of the term (assuming typical values for homework, lab, and Lab Breakout, and a final exam score that is equal to the quiz average). The majority of students with Good attendance will have test averages above the C/D line (roughly, two-thirds of them), while the majority of students with Poor attendance will have test averages below the C/D line (again, roughly two-thirds of them).

Conclusions

• If you are an exceptional student:
  If you don't go to class, you can expect that your quiz average–although probably high–is likely to be about 5 points lower than it might otherwise be. Since quizzes are typically half your grade, that's a loss of 2.5 points from your final score; add in the 2.5 PRS points you'll be missing as well, and you end up roughly 5 points lower overall. The good news is that you can still earn an A; the bad news is that your effective window is now only half as large (90–95, instead of 90–100). If you can accept those odds, fine–but don't forget the letter grade plots, above: although the window will only be halved in size, the success rate in reaching that window has historically been six times smaller (7% A's versus 45% A's).
   
• If you are a typical student:
  If you maintain a Poor attendance rate, you can expect your quiz average to be about ten to twelve points lower than it might otherwise be–a loss of 5 to 6 points from your overall final score. When you factor in the missed PRS points as well, you are down something like 7 to 9 points. Odds are, you are going to lose a letter grade in the course, compared to what you might otherwise earn.
   
• If you are a struggling student:
  You need every point you can get. Don't listen to anyone who tries to throw Argument 2 at you—they do not really know what they are talking about. Go to class.
   

A Final Caveat

It goes without saying that go to class really means Prepare for class by reading ahead, Pay attention to what is being discussed, and Participate actively in the PRS activities. If you are sitting in the back and reading a paper, doing you homework, or goofing off on your laptop, you're not going to get any real benefit, and of course you will reach the conclusion that going to class is worthless–but that will be your fault, not that of the instructor. You will get out of class attendance only as much as you put into the three Ps above.