Introduction

My annual retreat in the Adirondack Mountains of upstate New York was interrupted by a phone call from an old friend. It seemed that he was hired as a statistical consultant for an unfortunate young man who had been accused of cheating on a licensing exam. My friend, a fine statistician, felt that he could use a little help on the psychometric aspects of the case. After hearing the details, I agreed to participate. The situation that led to the young man's problem was directly due to fallacies associated with the unprincipled exploratory analyses of big data. The accusers had access to a huge data set from which they drew an unjustified conclusion because they did not consider the likelihood of false positives. As discussed in Chapter 5, we see again how a little thought should precede the rush to calculate.

Fishing for Cheaters

The young man had taken, and passed, a licensing test. It was the third time he took the exam – the first two times he failed by a small amount, but this time he passed, also by a small amount. The licensing agency, as part of their program to root out cheating, did a pro forma analysis in which they calculated the similarity between all pairs of examinees based on the number of incorrect item responses those examinees had in common. For the eleven thousand examinees they calculated this for all sixty million pairs. After completing this analysis, they concluded that forty-six examinees (twenty-three pairs) were much more similar than one would expect by chance. Of these twenty-three pairs, only one took the exam at the same time in the same room, and they sat but one row apart. At this point a more detailed investigation was done in which their actual test booklets were examined. The test booklets were the one place where examinees could do scratch work before deciding on the correct answer. The investigator concluded on the basis of this examination that there was not enough work in the test booklets to allow him to conclude that the examinee had actually done the work, and so reached the decision that the examinee had copied and his score was not earned. His passing score was then disallowed, and he was forbidden from applying to take this exam again for ten years.