#' Find the critical test statistic for a given number of objects and type-I
#' error.
#'
#' @param n A positive integer.
#' @param alpha A vector of probabilities (preferably below .5).
#' @param stat A character string; the name of the desired element returned by
#' [tau_a_p()].
#' @param ... Additional parameters passed to [tau_a_p()].
#' @return For each entry of alpha, the least extreme test statistic whose
#' p-value is smaller.
#' @export
#' @examples
#' tau_a_crit(5, 10 ^ (-1:-3), stat = "k")
tau_a_crit <- function(n, alpha, stat = "tau", ...) {
tab <- tau_a_p(n, ...)
i <- which(names(tab) == stat)
mat <- sapply(alpha, function(a) {
tab[which(tab$p < a)[1], i]
})
return(mat)
}
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