Measuring academic educational quality presents three major difficulties, typical of all customer satisfaction and service quality studies: the use of subjective scales; the ordinal nature of the data; and the multifold structure of satisfaction. In order to solve these problems, principal component analysis (PCA) of compositional data is proposed in this work. The core idea behind this methodology is to analyze by PCA the relative information within the data rather than focusing on absolute scores. This approach is discussed in comparison with a widely used Item Response Theory method (the Partial Credit Model) in order to assess its merits, e.g. always identifying a coherent preference structure. Both procedures were, thus, carried out on a real dataset collected with the 2013/14 ANVUR questionnaire by L’Universitá di Napoli-L’Orientale.