Like many teachers, I get a little annoyed when my students don't do their homework, since I've always been pretty sure their overall grades would be better if they did. I recently decided to do a little statistical analysis to find out if there was in fact any correlation between my students' homework grades and their overall course grade.
I sat down with my TI-84 calculator and the mid-semester grades for my 3 classes this semester. For each class I entered each student's mid-semester homework grade into one list, and their overall mid-semester grade into another list, and I had the TI-84 calculate the correlation coefficient for these two variables.
[If that sounds super complicated, it's really not. A correlation coefficient is just a number that tells you how strong is the relationship between two variables. If the number is close to zero, the two variables aren't related at all, and if it's close to 1, they're strongly related.]
Here are the numbers I got for my 3 classes:
- Honors Geometry A (23 students): y = .36x + 59.5, r = .84
- Honors Geometry B (21 students): y = .47x + 45.5, r = .61
- Advanced Functions and Modeling (25 students): y = .76x + 8.2, r = .79
The r-values are the correlation coefficients. The equations are the least-squares regression equations (i.e., prediction equations) that allow you to predict (though not with 100% accuracy) a student's overall mid-semester grade (the y-variable) just by knowing their homework grade (the x-variable).
A standard rule of thumb for correlation coefficients is that values between .8 and 1 indicate a very strong correlation between the the variables, and values between .6 and .8 indicate a strong correlation. So the correlation coefficients for my classes indicate fairly strong correlation between homework grades and overall grades, which is to say that the students who have higher homework grades tend to have higher overall grades, and vice versa.
Something else that statisticians are interested in when talking about correlation is statistical significance. If a correlation coefficient is statistically significant, that means that statisticians are sure that the indicated correlation actually exists in the larger population of students, and not just in that particular sample. According to my stats book, all of these correlations are statistically significant.
I also notice that in the prediction equations, the weight associated with the predictor variable (homework) is noticeably higher for my (non-honors) AFM class than for my Honors Geometry classes (.79 vs. .36 and .47). This leads me to think that, to the degree that overall grades can be predicted by homework grades, an AFM student's overall grade is more heavily influenced by their homework grade than an Honors Geometry student.
Have other teachers looked at the correlation between homework grades and overall grades for their classes? I did a quick google search but didn't find anything similar to this posted by individual teachers so if you're out there I'd love to hear from you. Also, I know there's a bunch of research on the value of homework on student achievement, and I also know there are a lot of things to take into account; if any researchers or statisticians out there can provide additional insights on any of these numbers, I'd love to hear from you as well.