Group work seems quite important to the learning process, and yet, at least in my sample size of 1, it is unfortunately rare during schooling. A reason for this seems to be that grading group work is difficult and often unfair: it is difficult for a grader to see into the group mechanics to discern who is contributing, and yet giving all group members the same grade does not capture that few students do a substantial portion of the work, while the others free-ride.

It should be possible to solve this problem if enough group assignments were done over a period of time, and students were randomly assigned to their groups. The idea would be to evaluate a student’s contribution to a groups grade by looking at performance across multiple groups.

Here’s sketch of how this might be possible:

Each group assignment is graded, say from 1-100.

A student’s grade would then be calculated by looking at the average grades of the projects for that student’s groupmates, and seeing whether this project does better or worse.

So, if the average of a students’ groupmates’ project grades is 85, and this group’s project grade is 90, we attribute the overperformance to a student’s influence.

The question is, what do the groupmates tend to earn without a student in their group, and what do they tend to learn with that student in their group.

Perhaps it will be easiest to work through with some sample data. Let’s say there are four students, and groups of two.

Students: A, B, C, D

Project 1:

AB - 95%

CD - 75%

Project 2:

AC - 90%

BD - 80%

Project 3:

AD - 85%

BC - 85%

For student A, we could average together all projects that she worked on, (.95+.9+.85)/3 = 90%

And we could average together all projects that she didn’t: (.75+.8+.85)/3 = 80%

The number I’m interested is, I think, the difference between those averages. It may not matter here, and it may not be more meaningful than the raw average, but in a larger class, with larger groups, where not every combination of groups can be tried, can’t we approximate the influence of an individual on a group by comparing this difference? Unfortunately, my knowledge of statistics is thin, but I’m looking to measure a difference across several projects that better captures A’s contribution to them.

Any insight would be helpful.

I’ll work on writing a script to generate some more interesting sample data – including an explicit ‘contribution amount’, so that we can test how well an algorithm approximates it.

Also, I should say that I am interested in reinventing the wheel a bit here. I’m sure this problem is solved, but solving it is more fun than just reading the answer.