  Clustering is part of unsupervised analysis methods that consist in grouping
samples into homogeneous and separate subgroups of observations also called
clusters. To interpret the clusters, statistical hypothesis testing is often
used to infer the variables that significantly separate the estimated clusters
from each other. However, data-driven hypotheses are considered for the
inference process, since the hypotheses are derived from the clustering
results. This double use of the data leads traditional hypothesis test to fail
to control the Type I error rate particularly because of uncertainty in the
clustering process and the potential artificial differences it could create. We
propose three novel statistical hypothesis tests which account for the
clustering process. Our tests efficiently control the Type I error rate by
identifying only variables that contain a true signal separating groups of
observations.
