New Approach for Test Quality Evaluation Based on Shannon Information Measures
Keywords:
Test quality, IRT models, Test information function, Shannon entropy, Average mutual informationAbstract
There are two currently popular statistical frameworks for addressing test data analyzing: Classical Test Theory (CTT) and Item Response Theory (IRT). Each of these approaches has its advantages and disadvantages. The detailed description of CTT was given in the previous paper of V. K. Avetisyan [1]. In this paper the description of IRT models are provided to show the complex mathematical apparatus used. In this investigation we suggest a new model of test quality evaluation based on information measures such as Shannon entropy, conditional entropy and average mutual information.We show that this approach is easier and more informative.
References
V. Avetisyan, “Investigation of knowledge control tests quality characteristics”, Proceedings of Engineering Academy of Armenia, vol.11, no. 1, pp. 156-163, 2015.
L. Crocker and J. Algina, Introduction to Classical and Modern Test Theory, New York, NY: Holt, Rinehart and Winston. 1986.
M. B. Chelishkova, Theory and Practice of Pedagogical Tests Constructing, Moscow: Logos, 2002.
C.DeMars, Item Response Theory, Oxford University Press, 1 edition, 2010.
R. K. Hambleton and R. W. Jones, Comparison of classical test theory and item response theory and their applications to test development , Educational Measurement: Issues and Practice, vol. 12, no.3, pp. 3847, 1993.
C. Spearman, The proof and measurement of association between two things, American Journal of Psychology, vol. 15, pp. 72–101. 1904.
M. R. Novick, The axioms and principal results of classical test theory, Journal of mathematical psychology, vol. 3, pp. 1 18. 1966.
V. S. Kim, Testing of Educational Achievements, Ussuriysk: USPI Publishing, 2007.
V. S. Avanesov, “The bases of the scientific organization of pedagogical control in the higher school”, M, 1987.
R. K. Hambelton, Emergence of item response modeling in instrument development and data analysis, Medical Care, vol. 38, pp. 60-65. 2000.
R. M. Kaplan and D. P. Saccuzo , Psychological testing: Principles, applications and issues, Pacific Grove: Brooks Cole Pub. Company. 1997.
Wim J. van der Linden and R. K. Hambleton, Handbook of Modern Item Response Theory, New York: S pringer-Verlag. 1997.
R. K. Hambleton, H. Swaminathan and H. J. Rogers, Fundamentals of item response theory, Newbury Park, CA: Sage. 1991.
E. Muraki, RESGEN: Item response generator [computer program]. Princeton, NJ: Educational Testing Service. 1992.
F. M. Lord, The relation of the reliability of multiple-choice tests to the distribution of item difficulties, Psychometrika, vol. 17, pp. 181-194. 1952.
T. M. Cover and J. A. Thomas, Elements of Information Theory, New York: Wiley, 2nd Edition, 2006.
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