Performance in Pass-Fail Assessments

Trading the cost of better performance off the probability that an imprecise test’s performance estimate falls short of the pass threshold, an assessee may perform above the threshold (and fear failure because of negative errors) or below it (and hope to pass because of positive errors). This paper characterizes in general and in a parameterized model how that choice depends on the test’s precision and threshold, which the assessor may choose to elicit high performance, and on other features of the assessee’s problem, which the assessor must take as given and may not know exactly. When it is costly for the assessor to increase precision and assessees are heterogeneous it is optimal for some to fear failing, for others to hope to pass. This is empirically true in the results of exams that conform to the model's assumptions. The model is also applicable to editorial and research funding processes.