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Bayesian Networks in Educational Testing Jiˇr´ı Vomlel http://utia.cas.cz/vomlel/ Abstract In this paper we discuss applications of Bayesian networks to educa- tional testing. Namely, we deal with the diagnosis of person’s skills. We show that when modeling dependence between skills we can get better diagnosis faster. We present results of experiments with basic operations that use fractions. The experiments suggest that the test design can ben- efit from a Bayesian network that models relations between skills, not only in the case of an adaptive test but also when designing a fixed (non- adaptive) test. 1 Introduction One task in educational testing is diagnosis of the presence or the absence of person’s skills. A possible scenario is that an institution provides a certain course and wishes to test the applicants for gaps in their prerequisites for attending the course. This task is more difficult than giving grades to students or the classification of examinees according to their overall level since the goal is not only to say whether an examinee is good or not but to pinpoint each examinee’s abilities and weak points. Typically, a test designer specifies a set of tested skills, abilities, misconcep- tions, etc. and a bank of questions, tasks, etc. Let S = {S , . . . , S } denote the 1 k set of tested skills, abilities, misconceptions, etc. and let X = {X1 , . . . , Xm } de- note the bank of questions, tasks, etc.1 The designer should also specify which skills are directly related to each question. These relations are often probabilis- tic, especially if a multiple choice test is u