We propose a non parametric hypothesis test to compare two partitions of a same data set. It could be the result of two clustering approaches (different methods or similar approaches but using different hyperparameters). The test may be done using any index but we focus in particular on the Matching Error (ME) that is related to the misclassification error in supervised learning. Some properties of the ME and, especially, its distribution function for the case of two independent partitions are analyzed. Extensive simulations show the efficiency of the test.