Do Country Stereotypes Exist in PISA? A Clustering Approach for Large, Sparse, and Weighted Data

Abstract

Certain stereotypes can be associated with people from different countries. For example, the Italians are expected to be emotional, the Germans functional, and the Chinese hard-working. In this study, we cluster all 15-year-old students representing the 68 different nations and territories that participated in the latest Programme for International Student Assessment (PISA 2012). The hypothesis is that the students will start to form their own country groups when clustered according to the scale indices that summarize many of the students’ characteristics. In order to meet PISA data analysis requirements, we use a novel combination of our previously published algorithmic components to realize a weighted sparse data clustering approach. This enables us to work with around half a million observations with large number of missing values, which represent the population of more than 24 million students globally. Three internal cluster indices suitable for sparse data are used to determine the number of clusters and the whole procedure is repeated recursively to end up with a set of clusters on three different refinement levels. The results show that our final clusters can indeed be explained by the actual student performance but only to a marginal degree by the country.