Microaggregation is one of the most employed microdata protection methods. The idea is to build clusters of at least k original records, and then replace them with the centroid of the cluster. When the number of attributes of the dataset is large, a common practice is to split the dataset into smaller blocks of attributes. Microaggregation is successively and independently applied to each block. In this way, the effect of the noise introduced by microaggregation is reduced, but at the cost of losing the k-anonymity property. The goal of this work is to show that, besides of the specific microaggregation method employed, the value of the parameter k, and the number of blocks in which the dataset is split, there exists another factor which can influence the quality of the microaggregation: the way in which the attributes are grouped to form the blocks. When correlated attributes are grouped in the same block, the statistical utility of the protected dataset is higher. In contrast, when correlated attributes are dispersed into different blocks, the achieved anonymity is higher, and, so, the disclosure risk is lower. We present quantitative evaluations of such statements based on different experiments on real datasets.