Comparing partitions is one of the open-ended questions in data analysis. The need to compare two partitions occurs during the study of two surveys of different units based on the same questionnaires but with the same structure. The goal of our work is to study this approach and to find formal procedures based on probabilistic models that are realistic under the null hypothesis that “the two partitions are close”. We propose a method of projection partitions using linear discriminant analysis. For this purpose, for only two data sets we considered the partition from the first one as a reference; then, the individuals of the second data set are allocated according to both such a reference partition by projection and by the classical k-means algorithm. These two partitions are compared by well-known measures of association to evaluate the significance of their difference. The empirical distributions of the association measures are derived by simulation and on a real data set.