Testing Equality of Functions Across Multiple Experimental Conditions for Different Ability Levels in the IRT Context: The Case of the IPRASE TLT 2016 Survey
- 43 Downloads
In the educational field, it is common to analyze test data through item response theory models. In this context, a key role is played by item characteristic curves (ICCs) and item information curves (IICs). In many real cases, practitioners are interested in understanding if some factors have a significant influence on the probability of correctly answering items. In the literature, this problem has been addressed by applying the standard analysis of variance model, which is based on the total scores or the proportion of correct responses. However, this method needs to meet some strong assumptions and may present some limitations because it does not consider useful information typical of the IRT, such as the shapes of the ICCs and IICs, which provide interesting insights for different ability levels. To overcome these issues, this research suggests the use of the functional analysis of variance approach and a novel functional tool in the IRT context. The main advantages of this approach are that it is distribution-free and allows us to check the degree of consistency with the hypothesis of equality among mean curves for different ability levels. Specifically, the proposed method is applied on ICCs and IICs for improving the existing techniques in the educational studies. A real dataset drawn from the IPRASE Trentino Language Testing Survey 2016 is considered. The final purpose of this study is to provide additional tools for scholars and practitioners in defining specific educational plans.
KeywordsIRT ICC IIC FANOVA P-Statistic
- Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee’s ability. In F. Lord & M. Novick (Eds.), Statistical theories of mental test scores (pp. 397–479). Boston: Addison-Wesle.Google Scholar
- Carpita, M. (2017). L’analisi psicometrica dei test. In L. Covi & M. Dutto (Eds.), Rapporto TLT 2016 Trentino Language Testing Esito delle rilevazioni delle competenze linguistiche degli studenti trentini (pp. 71–86). Provincia Autonoma di Trento: IPRASE. (ISBN 978-88-7702-426-8).Google Scholar
- Council of Europe. (2011). Common European framework of reference for languages: Learning, teaching, assessment. Cambridge: Cambridge University Press.Google Scholar
- Covi, L., & Dutto, M. (2017). Rapporto TLT 2016 Trentino Language Testing. Esito delle rilevazioni delle competenze linguistiche degli studenti trentini. Provincia Autonoma di Trento: IPRASE. (ISBN 978-88-7702-426-8).Google Scholar
- de Ayala, R. (2009). The theory and practice of item response theory. New York: The Guilford Press.Google Scholar
- Di Battista, T., & Fortuna, F. (2016). Clustering dichotomously scored items through functional data analysis. Electronic Journal of Applied Statistical Analysis, 9, 433–450.Google Scholar
- Di Battista, T., Fortuna, F., & Maturo, F. (2014). Parametric functional analysis of variance for fish biodiversity. In International conference on marine and freshwater environments, iMFE 2014. www.scopus.com.
- Ferraty, F., & Vieu, P. (2006). Nonparametric functional data analysis. New York: Springer.Google Scholar
- Hambleton, R., & van der Linden, W. (1997). Handbook of modern item response theory. New York: Springer.Google Scholar
- Lord, F. (1980). Applications of item response theory to practical testing problems. Hillsdale: Lawrence Erlbaum.Google Scholar
- Lord, F., & Novick, M. (1968a). Statistical theories of mental test scores (with contributions by A. Birnbaum). Reading, MA: Addison-Wesley.Google Scholar
- Lord, F., & Novick, M. (1968b). Statistical theories of mental test scores. Reading, MA: Addison-Wesley.Google Scholar
- Manly, B. F. J. (1997). Randomization, Bootstrap and Monte Carlo Methods in Biology. Chapman and Hall, London. (ISBN 0412721309).Google Scholar
- Maturo, F. (2018). Unsupervised classification of ecological communities ranked according to their biodiversity patterns via a functional principal component decomposition of hill’s numbers integral functions. Ecological Indicators, 90, 305–315. https://doi.org/10.1016/j.ecolind.2018.03.013.CrossRefGoogle Scholar
- Maturo, F., Di Battista, T., & Fortuna, F. (2016). BioFTF: Biodiversity assessment using functional tools. https://cran.r-project.org/web/packages/BioFTF/index.html.
- Maturo, F., Migliori, S., & Paolone, F. (2018). Measuring and monitoring diversity in organizations through functional instruments with an application to ethnic workforce diversity of the U.S. federal agencies. Computational and Mathematical Organization. https://doi.org/10.1007/s10588-018-9267-7.Google Scholar
- Ramsay, J. O., & Silverman, B. W. (2005). Functional data analysis (2nd ed.). New York: Springer.Google Scholar
- Rasch, G. (1960). Probabilistic models for some intelligence and achievement tests. Copenhagen: Danish Institute for Educational Research.Google Scholar