Dependence of the measurement results of students' abilities on the test complexity

Abstract

The analysis of results of Russian Unified State Examination in physics for 10472 pupils was done as well as modeling on the basis of Rush’s theory. The technique of revealing of the form of dependences by means of averaging of in special way sorted data is offered. It is shown that only results for part A of the examination can be explained by means of Rush’s theory. Results for the other types of tasks (parts B and C) agree qualitatively with the predictions of the Rush’s theory, but quantitatively deviate from the corresponding dependencies. Statistical scatter and non-linearity of dependences are very important factors in a comparison of results of tests of different difficulty. It is shown that ability to perform simple tasks corresponds to very wide range of ability to perform more difficult tasks, from low to the high. It is shown that ability to perform difficult tasks guarantees ability to perform more simple tasks.