Website and tutorials: https://yiqunchen.github.io/selectiveHotelling/
Selective inference for the difference in means between two estimated clusters, when the covariance matrix of the features is unknown.
Clustering and then testing the clusters with a textbook two-sample test uses the data twice, and the test rejects true null hypotheses far too often. selectiveHotelling computes selective p-values that control the selective Type I error for any clustering algorithm (k-means, hierarchical clustering, community detection, …) without estimating the covariance matrix.
Installation
# install.packages("remotes")
remotes::install_github("yiqunchen/selectiveHotelling")The package depends only on base R.
Quick start
library(selectiveHotelling)
set.seed(1)
X <- rbind(matrix(rnorm(40), 20, 2),
matrix(rnorm(40), 20, 2) + 5,
matrix(rnorm(40), 20, 2) - 5)
res <- selective_hotelling_test(X, k1 = 1, k2 = 2, K = 3) # k-means with K = 3
res$pval # selective p-value for clusters 1 and 2
res$cluster # the clusters that were tested
# hierarchical clustering
selective_hotelling_test(X, k1 = 1, k2 = 2, K = 3, clustering = "hclust")
# any clustering function that maps a data matrix to cluster labels
cl_fun <- function(x) cutree(hclust(dist(x), method = "complete"), k = 3)
selective_hotelling_bc(X, cl_fun, k1 = 1, k2 = 2)The package website has tutorials for k-means, hierarchical clustering, arbitrary clustering algorithms, and the one-dimensional test, a real data example, and the technical details. Its source is in vignettes/articles/.
Use with AI agents
The repository includes an MCP server, mcp/server.R, that lets an agent cluster a data set and compute the selective p-values (tools cluster_data, selective_test, onedim_test, package_help). It needs only R and jsonlite. Claude Code picks it up from .mcp.json when started in a clone of this repository. To add it elsewhere:
Agent skills in .claude/skills/ cover running the test correctly (selective-test-after-clustering) and developing the package (package-development). See mcp/README.md and .claude/skills/README.md.
Main functions
| Function | Purpose |
|---|---|
selective_hotelling_test() |
Selective test after k-means or hierarchical clustering |
selective_hotelling_bc() |
Selective test after any clustering function |
selective_truncated_F() |
One-dimensional selective test (faster, conditions on more) |
hotelling_T2() |
Two-sample Hotelling statistic for a pair of clusters |
Reference
Chen, Y. T. and Gao, L. L. Selective inference for clustering under unknown covariance. Code that reproduces the paper: https://github.com/yiqunchen/selectiveHotelling-paper.