ТОЧНОСТь ОЦЕНОК ЕГЭ в зависимости от количества и трудности заданий группы «С»

The article presents three methods for estimates of levels of entrants’ proficiency at the United State Examination. The first of them is currently used at the exam, the second was proposed by the author in his previous works, the third method is a method of primary points, which is known enough in testing theory; it was proved by the author in his works. In the article the author investigates the dependence of the accuracy the methods mentioned above on the number and complexity of test tasks of С group. On the basis of the obtained graphs and tables, the author gives specific recommendations to improve the accuracy of ratings at the exam. The article describes the three main methods for obtaining estimates of levels of entrants’ proficiency at the Unified State Exam. Among them there are two direct methods: a method of scaling used at present at the exam, and a modified scaling method proposed by the author in his previous works. These methods make it possible to translate the primary points obtained by entrants to the scale of percentage logits, characterizing the levels of entrants’ proficiency. The third method, being investigated in this work, was proved by the author in his previous works, i.e. the method of initial points. This method is an indirect method that makes it possible to assess levels of entrants’ proficiency by means of two steps. The first step consists in obtaining estimates of the latent parameters of proficiency levels, which are measured in logits. In the second step the logits are translated into percentage logits. Then, the article describes the main stages of the simulation of testing process followed by description of methods of estimates of levels of entrants’ proficiency. The simulation uses a well-known mathematical model of testing suggested by famous Danish mathematician G. Rasch. Some elements of a computer program performing simulation of testing are discussed. The results of the program are diagrams and tables that show the character of dependence of accuracy of the three methods on the number and complexity of tasks of C group. On the basis of the obtained material the author makes specific findings and gives recommendations aimed at improving estimates accuracy at the exam. 1) For estimating at the exam it is recommended to use the method of initial points; its accuracy in a fixed set of tasks of B group is 2.25 - 2.5 times higher than the scaling method, which is currently used at the exam. 2) When using the scaling method, it is recommended to use the smallest possible number of the tasks of C group, because the error grows to 0.5 % when the number of tasks increases to a unit. When using the method of the primary points, it is recommended to use 6 tasks of C group, because stabilization of errors takes place since n_С = 6 and further increase of n_С does not lead to a significant accuracy. 3) When using the scaling method, it is more profitable to use the sets of tasks of C group starting from (2...2) and ending with (3...3). When using method of the primary points, it is more advantageous to use the sets of tasks of C group starting from (1...1) and ending with (1...3).

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