Use of Roughness Analysis to Describe the Difficulty and Discrimination of Math Tests

Abstract

The assessment and evaluation of fractal dimensions is the subject of this exploratory study. In particular, the study sought to ascertain how the characteristics of the tests: The fractal dimensions of the tests can be used to measure test difficulty and discrimination. Through analyzing and evaluating the ruggedness and irregularities of students' performance, we may be able to identify which of the mathematics subjects (from first year to fourth year) is found to be the most challenging as a byproduct of the analysis. Fractal statistics and segmentation were used by the researcher to determine the students' mathematical ability and the difficulty of the test. According to the findings, test discrimination indices and difficulty indices can be derived from test fractal dimensions. With increasing or decreasing fractal dimensions, both traditional test characteristics increase and decrease monotonically. High fractal dimensions indicate significant performance differences among students, a telltale sign of a lack of comprehension of mathematical concepts.