  We consider the problem of testing for a difference in means between clusters
of observations identified via k-means clustering. In this setting, classical
hypothesis tests lead to an inflated Type I error rate. To overcome this
problem, we take a selective inference approach. We propose a finite-sample
p-value that controls the selective Type I error for a test of the difference
in means between a pair of clusters obtained using k-means clustering, and show
that it can be efficiently computed. We apply our proposal in simulation, and
on hand-written digits data and single-cell RNA-sequencing data.
