Composite indicators are very useful in addressing complex variables that cannot be directly observed: they can be used to assess for example quality of life and customer satisfaction. In practice, it is very often of interest to reduce the dimension of a composite indicator by selecting among its components the most important ones. In this paper we propose a method for reducing the dimension of composite indicators based on the comparison of rank correlation coefficients and we compare it with another method. A practical application to university student satisfaction data is presented. Moreover, we evaluate how the choice of the rank correlation coefficient influences the results of the practical application.