Measuring Student Knowledge, Ignorance and Risk Aversion with Objective Examination Questions

Abstract

This paper applies deductive logic to the structure and outcomes of objective questions. When all terms are clearly defined and deductive logic is correctly used, then the results must be true, even if they are surprising or counter-intuitive. The defined premises are 1) student’s true knowledge, 2) student’s false knowledge, 3) student’s admitted ignorance and 4) student’s level of risk aversion. Definitions for 5) correct answer, 6) wrong answer, and 7) abstain are also needed. Some logical processes are numerical and involve simple equations. The main outcomes include: i) the standard scoring of correct answers, the number of wrong answers and the number of abstain can result from varying levels of true knowledge, false knowledge and admitted ignorance; ii) the level of risk aversion is measured by the proportion of answers where the student abstains from answering. High risk aversion lowers standard score, but this effect can be easily corrected.