Efficient Scoring of Multiple-Choice Tests

This paper studies the optimal scoring of multiple choice tests by using standard estimation theory where obtained scores are efficient estimators of examinees' ability. The marks for wrong selections and omissions jointly minimize the mean square difference between obtained score and ability. Examinees are loss averse, ie. disproportionately weight the penalty for wrong selection in their utility function, which entails a preference for omission. With a limited number of items, it is efficient to incentivize the lowest able to omit as their answers essentially reflect noise. The shorter the test, the stronger the incentives to omit. Loss aversion improves estimators efficiency by inducing more omission, which reduces the need to bias the marks to foster omission. The model also sheds new lights on the statistical properties of two widely used scoring methods: number right and formula scoring