A quantitative analysis of Educational Data through the Comparison between Hierarchical and Not-Hierarchical Clustering

Abstract

Many research papers have studied the problem of taking a set of data and separating it into subgroups through the methods of Cluster Analysis. However, the variables and parameters involved in Cluster Analysis have not always been outlined and criticized, especially in the field of Science Education. Moreover, in the field of Science Education, a comparison between two different Clustering methods is not discussed in the literature. In this paper two different Cluster Analysis methods are described and the variables and parameters involved are discussed in order to clarify the information that they can supply. The clustering results obtained by using the two methods are compared and showed a good coherence between them. The results are interpreted and compared with the literature. More detail about the relationship between different student conceptions of modeling in physics was obtained.

Unsupervised quantitative methods to analyze student reasoning lines: Theoretical aspects and examples

“…If cluster r was created by Other examples, based on real data, can be found in the literature. See, for example, the recent works of Di Paola et al [43] and Battaglia et al [44,45].…”

Profiles of Pre-Service Primary Teachers: Attitudes, Self-Efficacy, and Gender Stereotypes in Teaching Science and Mathematics

“…To answer the research question: What profiles can be established combining the gender stereotypes, attitudes and self-efficacy toward teaching science and mathematics in pre-service primary teachers?, a hierarchical cluster analysis was conducted. Cluster analysis is a multivariate exploratory technique with the purpose of grouping cases in larger groups with high degrees of internal homogeneity (intra-cluster) and external heterogeneity (inter-clusters) (Battaglia et al, 2017;Hair et al, 1999). As a grouping method, Ward's method was used and to define the number of conglomerates, the dendrogram graphic was examined, which represents how the hierarchical classification among individuals is formed.…”

“…As a grouping method, Ward's method was used and to define the number of conglomerates, the dendrogram graphic was examined, which represents how the hierarchical classification among individuals is formed. Given that the cluster analysis is not an inferential statistics technique, assumptions of normality and homoscedasticity have little importance; however, to conduct this kind of test, all variables must be in the same units (Battaglia et al, 2017). Hence, previous to the cluster analysis, the eight variables were transformed into Z-scores, given that not all of them use the same scale.…”

Exploring the impact of modeling in science education: A systematic review

“…According to Battaglia et al (2017), two different clustering analysis methods are described and related variables and parameters are discussed to clarify the information they can provide. The clustering results obtained using the two methods were compared and it was shown that there was a good agreement between them.…”