Journal
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume -, Issue -, Pages -Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/01621459.2022.2116331
Keywords
Difference in means; Hypothesis testing; Post-selection inference; Type I error
Categories
Funding
- NSERC Discovery Grants program
- NIH [R01-EB026908, R01-DA047869, R01-GM123993]
- NSF [DMS-1653017, DMS-1252624]
- Simons Investigator Award in Mathematical Modeling of Living Systems [560585]
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This article proposes a selective inference approach to test for a difference in means between two clusters, addressing the issue of inflated Type I error rate when using classical tests with clustering-defined groups.
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. for this article are available online.
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