Shift error detection in standardized exams

Hundreds of millions of multiple choice exams are given every year in the United States. These exams permit form-filling shift errors, where an absent-minded mismarking displaces a long run of correct answers. A shift error can substantially alter the exam's score, and thus invalidate it. In this paper, we develop algorithms to accurately detect and correct shift errors, while guaranteeing few false detections. We propose a shift error model, and probabilistic methods to identify shifted exam regions. We describe the results of our search for shift errors in undergraduate Stony Brook exam sets, and in over 100,000 Scholastic Amplitude Tests. These results suggest that approximately 2% of all tests contain shift errors. Extrapolating these results over all multiple choice exams and forms leads us to conclude that exam takers make millions of undetected shift errors each year. Employing probabilistic shift correcting systems is inherently dangerous. Such systems may be taken advantage of by clever examinees, who seek to increase the probability of correct guessing. We conclude our paper with a short study of optimal guessing strategies when faced with a generous shift error correcting system.