Mid-p permutation p-values

Given a statistic evaluated across the observed assignment and its re-randomizations (a single vector v, length 1 + number of draws), returns the mid-p permutation p-value of each entry relative to the whole set: two-sided by default, or one-sided with alternative = "greater" (large values are extreme) or "less" (small values are extreme). The most extreme value (largest |v|) gets 0.5 / n; the least extreme gets (n - 0.5) / n. Every value is strictly inside (0, 1), so the Cauchy transform never reaches a pole.

Usage

riposte_midp(v, alternative = c("two.sided", "greater", "less"))

Arguments

v

numeric vector of a statistic across assignments (observed plus draws). Two-sidedness is by abs(v).

alternative

"two.sided" (default), "greater", or "less".

Value

numeric vector of mid-p values, the same length as v, all in (0, 1). Without ties, the "greater" and "less" values add to one.

Details

The mid-p value is the ordinary upper-tail count minus half the mass at the observed value: (# strictly more extreme) + 0.5 * (# tied, including self), divided by n. Values within about 1.5e-8 of each other, relative to their size when it exceeds one, count as tied, because rank scores make many re-randomizations tie exactly, and floating-point summation in a different order can separate such ties in their last bits.