An intelligent tutoring system for learning basic statistics, called Stat-Knowlab, is presented and analyzed. The algorithms implemented in the system are based on the competence-based knowledge space theory, a mathematical theory developed for the formative assessment of knowledge and learning. The system’s architecture consists of the two assessment and learning modules that interact with each other in a continuous exchange of information about the current knowledge state of a student. This allows the system to personalize the student’s learning, providing only with the learning objects that she is ready to learn. During the browsing of the system, several types of navigation data are recorded. In this work, we analyzed data from two studies that were aimed at examining the learning processes induced by the navigation of the system. The results of both studies highlighted that the system is useful for monitoring the student learning processes during a university course of basic statistics.

Missing data are a well known issue in statistical inference, because some responses may be missing, even when data are collected carefully. The problem that arises in these cases is how to deal with missing data. In this article, the missingness is analyzed in knowledge space theory, and in particular when the basic local independence model (BLIM) is applied to the data. Two extensions of the BLIM to missing data are proposed: The former, called ignorable missing BLIM (IMBLIM), assumes that missing data are missing completely at random; the latter, called missing BLIM (MissBLIM), introduces specific dependencies of the missing data on the knowledge states, thus assuming that the missing data are missing not at random. The IMBLIM and the MissBLIM modeled the missingness in a satisfactory way, in both a simulation study and an empirical application, depending on the process that generates the missingness: If the missing data-generating process is of type missing completely at random, then either IMBLIM or MissBLIM provide adequate fit to the data. However, if the pattern of missingness is functionally dependent upon unobservable features of the data (e.g., missing answers are more likely to be wrong), then only a correctly specified model of the missingness distribution provides an adequate fit to the data.

Assessing executive functions in individuals with disorders or clinical conditions can be challenging, as they may lack the abilities needed for conventional test formats. The use of more personalized test versions, such as adaptive assessments, might be helpful in evaluating individuals with specific needs. This paper introduces PsycAssist, a web-based artificial intelligence system designed for neuropsychological adaptive assessment and training. PsycAssist is a highly flexible and scalable system based on procedural knowledge space theory and may be used potentially with many types of tests. We present the architecture and adaptive assessment engine of PsycAssist and the two currently available tests: Adap-ToL, an adaptive version of the Tower of London-like test to assess planning skills, and MatriKS, a Raven-like test to evaluate fluid intelligence. Finally, we describe the results of an investigation of the usability of Adap-ToL and MatriKS: the evaluators perceived these tools as appropriate and well-suited for their intended purposes, and the test-takers perceived the assessment as a positive experience. To sum up, PsycAssist represents an innovative and promising tool to tailor evaluation and training to the specific characteristics of the individual, useful for clinical practice.