# Computer Adaptive Testing Using Upper-Confidence Bound Algorithm for Formative Assessment
## 4 Discussion  
UCB algorithm has a potential to significantly reduce assessment length without the loss of accuracy. Even for very short tests with few topics the algorithm offers significant reduction of test length (Table 2). However, there is no advantage for quizzes in which each topic contains only one question, at which point the notion of topic loses its pedagogical meaning. There is evidence that time allocated to study positively affects student performance [41], thus reducing the time spend on assessment is desired. The experiments with real students support the conclusions drawn from the simulations (Figure 3). Such strong change in quiz length has the potential to change the dynamics in the classroom, because the instructor would not need to spend an entire lesson just for formative assessment. This in turn, may increase opportunities to provide personalized feedback to students linked to better performance [14; 42]. This advantage comes at no cost in quiz creation complexity, unlike IRT and Elo rating based systems where quiz creation can be prohibitively complex in some situations due to item calibration problem [22; 27]. Because of this fundamental difference we do not compare performance of UCB to IRT and Elo based algorithms. Such comparison would not discredit either approach: If UCB performs worse (as is safe to assume), its simplicity of use and independence from question item calibration makes it an interesting alternative to traditional assessment. It is clear that exploration component of the algorithm becomes more important with the increase in number of items within a topic. This can be observed in bad performance of algorithm in 4 topic quiz when \(C\) was set to 0 in Figure 2. It took 45 questions to reach \(>\)95% assessment accuracy. Figure 6: Distribution of assessment accuracies for students, where dark blue \(<\)1%, blue 1–50%, cyan 50–99%, and green \(>\)99% accuracy. Also, unintuitively, it takes less questions to identify weakest topics of students' when there are more topics when the size of the item pool is kept constant. Compared to IRT and Elo algorithms UCB will obtain less information about the student in a mathematical sense [27; 43], and this can be seen as a disadvantage. However, not all information is equally pedagogically valuable [12; 16]. For example, assume we are assessing student's knowledge on two topics. We are nearing the end of the quiz and have determined that knowledge on first topic is adequate, but lacking on the second topic. Because of the nature of UCB algorithm topic two is more explored than topic one, therefore we expect to gain less information by exploring second topic. However, from pedagogical point of view the information on topic two can be more valuable to address the assessment needs according to the three question feedback model [15]. According to the assessment, topic two is in need of instruction. If we are going to proceed to teach it, we can use the extra diagnostic data to save time and effort by not teaching what the student already knows. Meanwhile we have no immediate use for the more precise data about first topic. Simulation data presented in Figure 4 and empirical results (Figures 3 and 5) suggest that the UCB assessment approach can offer significant reduction in quiz length for any practical item pool size and inter-topic variance of answers. This is an important result because it indicates suitability of the method for any grouping of questions regardless of how correlated the answers are within one topic. Method effectiveness stays almost constant for any observed answer variance, which makes it easy to predict quiz length. This allows a teacher to group questions on each topic as they see fit according with syllabus and the learning material at hand, regardless of existence or lack of a common latent trait underlying the items within a topic. This separates UCB method from IRT and Elo based alternatives which depend on the assumption of common latent trait [22; 28].