A comparison between the hierarchical clustering of variables, implicative statistical analysis and confirmatory factor analysis

This study aims to gain insight about the distinct features and advantages of three statistical methods, namely the hierarchical clustering of variables, the implicative method and the Confirmatory Factor Analysis, by comparing the outcomes of their application in exploring the understanding of function. The investigation concentrates on the structure of students' abilities to carry out conversions of functions from one mode of representation to others. Data were obtained from 587 students in grades 9 and 11. Using Confirmatory Factor Analysis, a model, that provides information about the significant role of the initial representations of conversions in students' processes, is developed and validated. Using the hierarchical clustering and implicative analysis, evidence is provided to students' compartmentalized thinking among representations. These findings remain stable across grades. The outcomes of the three methods were found to coincide and to complement each other.