Finding Dependent Test Items: An Information Theory Based Approach

In this paper, we propose a new approach to find the most dependent test items in students’ response data by adopting the concept of entropy from information theory. We define a distance metric to measures the amount of mutual independency between two items, and it is used to quantify how independent two items are in a test. Based on the proposed measurement, we present a simple yet efficient algorithm to find the best dependency tree from the students’ response data, which shows the hierarchical relationship between test items. The extensive experimental study has been performed on synthetic datasets, and results show that the proposed algorithm for finding the best dependency tree is fast and scalable, and the comparison with item correlations has been made to confirm the effectiveness of the approach. Finally, we discuss the possible extension of the method to find dependent item sets and to determine dimensions and sub-dimensions from the data.