  For many applications, it is critical to interpret and validate groups of
observations obtained via clustering. A common validation approach involves
testing differences in feature means between observations in two estimated
clusters. In this setting, classical hypothesis tests lead to an inflated Type
I error rate. To overcome this problem, we propose a new test for the
difference in means in a single feature between a pair of clusters obtained
using hierarchical or $k$-means clustering. The test based on the proposed
$p$-value controls the selective Type I error rate in finite samples and can be
efficiently computed. We further illustrate the validity and power of our
proposal in simulation and demonstrate its use on single-cell RNA-sequencing
data.
