Selective Inference for Hierarchical Clustering.

Testing for a difference in means between two groups is fundamental to answering research questions across virtually every scientific area. Classical tests control the Type I error rate when the groups are defined a priori. However, when the groups are instead defined via a clustering algorithm, then applying a classical test for a difference in means between the groups yields an extremely inflated Type I error rate. Notably, this problem persists even if two separate and independent data sets are used to define the groups and to test for a difference in their means. To address this problem, in this paper, we propose a selective inference approach to test for a difference in means between two clusters obtained from any clustering method. Our procedure controls the selective Type I error rate by accounting for the fact that the null hypothesis was generated from 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-seq data.