Conceptual Representation of the Homogeneity of Variance Test in Educational Statistics Textbooks and Its Potential to Cause Misconceptions

Abstract

Textbooks play an important role in shaping students' understanding of statistical concepts. However, when conceptual representations emphasize procedural aspects rather than conceptual understanding, they may contribute to misconceptions. This study aims to analyze how the concept of the homogeneity of variance test is represented in educational statistics textbooks and to identify the potential misconceptions arising from these representations. The study employed a descriptive qualitative approach using document analysis. The data consisted of ten educational statistics and statistics-for-educational-research textbooks that are widely used in teacher education programs in Indonesia. Data were collected through document review and analyzed using qualitative content analysis, focusing on definitional, procedural, and conceptual representations, as well as potential misconceptions. The findings indicate that all textbooks present the F-test procedure by dividing the larger variance by the smaller variance. However, only a few textbooks explain the underlying concept of the F distribution, the rationale for placing the larger variance in the numerator, and the relationship between the F distribution and statistical decision-making. The dominance of procedural representations may lead students to the misconception that the larger variance must always be placed in the numerator and that the F statistic can never be less than one. These findings suggest that the current representation of the homogeneity of variance test in educational statistics textbooks does not adequately support the development of students' conceptual understanding. Therefore, a more balanced presentation integrating both procedural and conceptual aspects is needed to minimize potential misconceptions in statistics education.