Selective Inference for Hierarchical Clustering

Classical tests for a difference in means control the Type I error rate when the groups are defined a priori. However, when the groups are instead defined via clustering, then applying a classical test yields an extremely inflated Type I error rate. Notably, this problem persists even if two separate and independent datasets are used to define the groups and to test for a difference in their means. To address this problem, in this article, we propose a selective inference approach to test for a difference in means between two clusters. Our procedure controls the selective Type I error rate by accounting for the fact that the choice of null hypothesis was made based on the data. We describe how to efficiently compute exact p-values for clusters obtained using agglomerative hierarchical clustering with many commonly used linkages. We apply our method to simulated data and to single-cell RNA-sequencing data. Supplementary materials for this article are available online.