Partners meet halfway: a simple correlation study of an undergrad lab class

Last semester I taught two classes of an Introductory Physics (Electrodynamics) for Engineers lab course at the University of Texas at Austin. The first day that my students came in, most of them did not know each other. They just came in and sat at tables of two, and this pretty much became their permanent seats in the room for the rest of the course (that’s human habit). They were supposed to work with their partner on the experiments in the first part of the class, but individually on their worksheets in the second part. So choosing their seats also fixed the partners. Thus, it is a good assumption to say that the pairing had been pretty random, at least as far as academic ability of the students was concerned.

I noticed though that both partners in a group tended to move towards a common average in their performance over the course. If one partner was diligent, it would motivate (and sometimes force) the other to work harder, while the sloppiness and uncaring attitude of a partner would also negatively affect the performance of the other. I was happy to notice though that the ‘uplifting’ effect was usually more dominant than the ‘down-dragging’. In any case, this caused the performance of partners to pull closer, irrespective of their starting academic ability.

At the end of the semester, after I had the final scores that I handed out to them, I decided to do a simple correlation test. The following are two scatter plots of pairs of student scores for each of my classes, each pair ordered as (better score, worse score) (which is why all points are below the bottom-left to top-right diagonal of the plot). The linear fits through them have also been shown. Although I had suspected that there would be a significant correlation between partners’ scores, I was surprised at how high the correlation coefficients turned out to be. (Note that if you pair an even number of numbers randomly, on the average you should expect a linear correlation coefficient of zero.)

I had felt this trend even by the middle of the semester, and I had this crazy idea of using this to try and pull up the performance of the students who were not doing too good. I thought of sorting the students by their score so far into the course, and re-assigning partners so as to pair the best student with the worst, the second-best to the second-worst and so on. However, I know that habit is a deadly force, and if I suggest my students in the middle of the course that they have to say goodbye to their partner with whom they already have some steady chemistry going and have new partners again, ones that I have chosen for them, all hell would break loose. So I had to rest it in my head as a theoretical result with possible practical applications, to be taken up by a braver soul than me. But hey, here’s the data, so you can quote it if you want to try it and someone doesn’t take the idea too well.