THE STUDY OF DIFFICULTY AND DIFFERENTIAL ABILITY OF COMPETITIVE ITEMS

摘要

This article is devoted to the method of assessing both the relative difficulty and differentiating ability of any items offered within the one test, competition or thematic Olympiad. The main object of research, which all the conclusions are based on, is the empirical function of the success of the solution. The adequacy with the theoretical function accepted in the Item Response Theory (IRT) gives as a quantative measure of the differentiating ability of the particular problem. The parameter in the model characterizes the difficulty of the task and indicates the level of preparation relatively which the division is made. A numerical measure of the likelihood theoretical and empirical functions is the sum of squares of deviations of their values on a uniform grid. The adequacy test is carried out with the help of some consent criterion. For obtaining the criteria distributions we apply the numerical simulations according to the Monte Carlo approach. The level of significance is interpreted as an indicator of the reliability of the obtained results. The study is motivated by the need for accurately assessing the difficulty of the Olympiad problems in order to determine the winners more reasonably. Finally, an example of practical analysis of the math problems from the school Olympiad organized by USPTU is given as concluding remarks.