Preliminary development of a simple statistical tool for estimating mental model states from a diagnostic test

Science knowledge is reflected in mental models that students tend to form when dealing with science phenomena. One way to identify students' mental models about scientific concepts is the use of diagnostic tests (inventories). Even though several statistical approaches and tools intended for the analysis of such inventories' results exist in the literature, there are certain inventories for which analysis might require the development of more convenient tools. Thus, there seems to be no simple way to handle the results of inventories whose items include different numbers of statements, the number of statements relating to the same mental model within an item is not fixed, and neutral distractors are possible. This exploratory study aims at meeting this challenge and suggests a relatively simple statistic F2m for estimating the mental model state of a subject or a group of subjects in the case of two mental models under consideration, providing a preliminary estimation of F2m consistency using the results of the sound concept inventory instrument.