Experimental Validation of an Axiomatically Derived Scoring Rule for the Assessment of Partial Knowledge

Multiple-choice (MC) tests are widely used in educational contexts for knowledge assessment. Traditional number-right scoring (NR) awards points only for the single correct answer, making the test vulnerable to random guessing and insensitive to partial knowledge. This study investigated a new response format, ZAXS, in which test-takers may select any number k out of n possible options, and receive 1/k points if the correct answer is included. To compare the two competing formats, we established a strong validation criterion by experimentally inducing different levels of knowledge in an unknown domain. ZAXS scores were found to be more reliable and more valid than NR scores when attempting to classify participants to their known knowledge level based on their obtained scores (Study 1). Furthermore, manipulating risk-taking behavior under uncertainty regarding the correct option showed no adverse effects on ZAXS’s reliability or validity (Study 2). These findings suggest that ZAXS is a promising alternative response format and scoring method for MC tests.