https://stats.stackexchange.com/questions/18887/how-to-calculate-a-confidence-interval-for-spearmans-rank-correlation/506367#506367

spearman-ci.R

spearman_ci <- function(x, y, alpha = 0.95, method = c("norm", "t")) {
  # modified from https://stats.stackexchange.com/questions/18887/how-to-calculate-a-confidence-interval-for-spearmans-rank-correlation/506367#506367
  method <- mark::match_param(method)
  ok <- stats::complete.cases(x, y)
  x <- x[ok]
  y <- y[ok]
  r <- cor(x, y, method = "spearman")
  n <- sum(ok)
  q <- switch(
    method,
    norm = stats::qnorm(p = (1 - alpha) / 2),
    t =  stats::qt(p = (1 - alpha) / 2, df = n - 3)
  )
  
  ones <- c(-1L, 1L)
  ci <- tanh(atanh(r) + ones * sqrt((1 + r^2/2) / (n - 3)) * q) 
  ci <- sort(ci)
  attr(ci, "conf.level") <- alpha
  attr(ci, "conf.method") <- method
  ci
}