Hints that partial attendance is better than none

Students arriving late for class, especially early morning classes, is not uncommon at the college where I teach. There are a variety of factors that contribute to this, all of which are discussed perpetually by faculty. Each new faculty member discovers anew the issue of late arrivals. Some faculty in the past have gone as far as locking the class room doors. Others, intentionally or unintentionally, may embarrass the late arriving student.

Late arrivals can be disruptive to a class, especially if group work is the plan for the day. How one handles late arrivals also determines the impact those late arrivals may or may not have.

While rummaging through attendance and late arrival data looking for signals, a practice strongly discouraged by the statistical test community, I noticed that absences appeared to be correlated to weaker performance in class while late arrival - partial attendances if you will - were not correlated to performance.

The course examined was MS 150 Statistics course. There were 45 students in the course with 46 attendance days in the term. The sample size for each correlation varies as some students missed presentations, others did not take the final. The table is a table of correlation coefficients r.

	Overall	Presentations	Final	Abs	Late
Overall	1.00	0.72	0.74	-0.72	0.13
Presentations	0.72	1.00	0.36	-0.63	0.05
Final	0.74	0.36	1.00	-0.39	-0.05
Abs	-0.72	-0.63	-0.39	1.00	0.03
Late	0.13	0.05	-0.05	0.03	1.00

The variables in the table are:
Overall: The student's overall course percentage for all work in the course including homework, quizzes, tests, presentations, and the comprehensive final examination.
Presentations: The student's average performance on three open data exploration presentations that capped the course at the end of the term.
Final: The student's performance on the final examination.
Abs: The number of absences.
Late: The number of late arrivals to class.

Of note is that there is moderate to strong negative correlation for absences to the overall mark in the course (-0.72) and to the open data exploration presentations (-0.63). The negative correlation indicates that performance decreased for the overall course percentage and performance on presentations as absences increased.

Performance on the comprehensive final was also negatively correlated to absences but only weakly at best (-0.39) given the sample size.

Of more interest is that the number of late arrivals was not correlated to a student's overall mark (0.13), their performance on the open data exploration presentations (0.05), nor to their performance on the final examination (-0.05). The correlation values are too small, there is no relationship. Being late had a random effect on overall mark, presentations scores, and final examination performance.

Thus being absent appears to negatively impact a student's ability to succeed in the course, but being late has a random impact on their ability to succeed in the course. That random impact suggests being late has no functional impact on student performance. The take away is "best to be present, better to be late than absent."

I choose to permit late arrivals. Whether my students tend to take advantage of this, I have not sought to determine. The correlations above suggest that even partial attendance is better than being absent.

As an internal statistical note for the course, there is the somewhat curious statistic that the presentations and the final are well correlated to the overall mark, but not to each other. Of course the correlation to the overall mark is in large part because both contribute to that overall score. The lack of correlation between them, or a weak positive correlation at best (0.36), suggests the two are measuring quite different skill sets. This is useful information for the instructor: the presentations and the final are not generating redundant information. One could not be dropped in favor of the other.