Great Performance !

Now it was time to construct an algorithm that could tease some conclusions from this mass of data. What might a cheating teacher’s classroom look like?

The first thing to search for would be unusual answer patterns in a given classroom: blocks of identical answers, for instance, especially among the harder questions. If ten very bright students (as indicated by  past and future test scores) gave correct answers to the exam’s first five questions (typically the easiest ones), such an identical block shouldn’t be considered suspicious. But if ten poor students gave correct
answers to the last five questions on the exam (the hardest ones), that’s worth looking into. Another red flag would be a strange pattern within any one student’s exam—such as getting the hard questions right while missing the easy ones—especially when measured against the thousands of students in other classrooms who scored similarly on the same test. Furthermore, the algorithm would seek out a classroom full of students who performed far better than their past scores would have predicted and who then went on to score significantly lower the following year. A dramatic one-year spike in test scores might initially be attributed to a good teacher; but with a dramatic fall to follow, there’s a strong likelihood that the spike was brought about by artificial means.

Consider now the answer strings from the students in two sixth-grade Chicago classrooms who took the identical math test. Each horizontal row represents one student’s answers. The letter a, b, c, or d indicates a correct answer; a number indicates a wrong answer, with 1 corresponding to a, 2 corresponding to b, and so on. A zero represents an answer that was left blank. One of these classrooms almost cer tainly had a cheating teacher and the other did not. Try to tell the dif- ference—although be forewarned that it’s not easy with the naked eye.

Taken From : FREAKONOMICS - A Rogue Economist Explores the Hidden Side of Everything