Rasch model based analysis of the Force Concept Inventory

Abstract

The Force Concept Inventory (FCI) is an important diagnostic instrument which is widely used in the field of physics education research. It is therefore very important to evaluate and monitor its functioning using different tools for statistical analysis. One of such tools is the stochastic Rasch model, which enables construction of linear measures for persons and items from raw test scores and which can provide important insight in the structure and functioning of the test (how item difficulties are distributed within the test, how well the items fit the model, and how well the items work together to define the underlying construct). The data for the Rasch analysis come from the large-scale research conducted in 2006-07, which investigated Croatian high school students' conceptual understanding of mechanics on a representative sample of 1676 students (age 17--18 years). The instrument used in research was the FCI. The average FCI score for the whole sample was found to be $(27.7\ifmmode\pm\else\textpm\fi{}0.4)\mathrm{%}$, indicating that most of the students were still non-Newtonians at the end of high school, despite the fact that physics is a compulsory subject in Croatian schools. The large set of obtained data was analyzed with the Rasch measurement computer software WINSTEPS 3.66. Since the FCI is routinely used as pretest and post-test on two very different types of population (non-Newtonian and predominantly Newtonian), an additional predominantly Newtonian sample ($N=141$, average FCI score of 64.5%) of first year students enrolled in introductory physics course at University of Zagreb was also analyzed. The Rasch model based analysis suggests that the FCI has succeeded in defining a sufficiently unidimensional construct for each population. The analysis of fit of data to the model found no grossly misfitting items which would degrade measurement. Some items with larger misfit and items with significantly different difficulties in the two samples of students do require further examination. The analysis revealed some problems with item distribution in the FCI and suggested that the FCI may function differently in non-Newtonian and predominantly Newtonian population. Some possible improvements of the test are suggested.