A Network of Wrongs
"Wrong Answer. Try Again!"
I’ve been studying multiple-choice tests for the past several years, which led to the question, “Why do students choose wrong answers?” In a well-composed quiz or test, there is only one correct answer. You pick that answer when you know it is right (or randomly, assuming you are lucky). But what makes you choose one of the wrongs? The wrongs are all wrong, aren't they? Why prefer B over C, or C over D?
As it turns out, there is wrong, wrong, and wrong (and possibly wrong, too). We just need a simple network analysis exercise to uncover the difference.
Let's build a network of students and wrong answers. The network consists of two parts (it is bipartite and directed). A student node S1 is connected to an answer node A1 if the student S1 chooses B1. Presumably, two wrong answers A1 and A2 have something in common if they are consistently selected by the same students S1 and S2. We can project the bipartite network onto the set on answer nodes and get a weighted one-part network of the wrong answers, where two answer nodes are connected when (and to the extent) they are consistently marked by the same students. Note that the student nodes are…
