P-value function: Polynomial Rank Score Test

Tests Fisher's sharp null of no treatment effects using multiple polynomial rank score functions simultaneously via coin::independence_test(). This provides adaptive sensitivity to effects at different parts of the outcome distribution without pre-committing to a single scoring.

Usage

pPolyRank(
  dat,
  fmla = Y ~ trtF | blockF,
  r_vec = c(2, 6, 10),
  teststat = "quadratic",
  simthresh = 20,
  sims = 1000,
  parallel = "no",
  ncpu = NULL
)

Arguments

dat

An object inheriting from class data.frame (will be coerced to data.table internally if needed).

fmla

A formula: outcome ~ treatment | block.

r_vec

Numeric vector. Polynomial rank score parameters. Default c(2, 6, 10). r = 2 gives Wilcoxon-like scores; larger r emphasizes extreme ranks.

teststat

Character. Type of test statistic passed to coin::independence_test(). "quadratic" (default) gives an omnibus chi-squared statistic that pools across score functions; "maximum" takes the max of the standardized statistics across score functions.

simthresh

Integer. Below this number of observations, use permutation-based inference instead of asymptotic approximation.

sims

Integer. Number of permutations when using simulation-based inference.

parallel

Character. "no" (default), "snow", or "multicore", passed to coin::approximate().

ncpu

Integer. Number of CPUs for parallel operation.

Value

A p-value (numeric scalar).

Details

For each value of r in r_vec, the function computes within-block polynomial rank scores: (rank(Y) / (n_b + 1))^(r-1) where n_b is the block size. These scores are passed as a multivariate response to coin::independence_test(), which computes a joint test statistic that accounts for the correlation structure among the score functions.

With r = 2 the scores are nearly linear in rank (Wilcoxon-like). Larger r values place increasing weight on observations with high ranks, providing sensitivity to treatment effects concentrated in the upper tail of the outcome distribution.

This function tests the same sharp null as pOneway and pIndepDist but uses polynomial rank scores from the combined Stephenson rank test framework (Kim, Li, and Bowers). For quantile-of-effects hypotheses (whether the k-th largest individual effect exceeds a threshold), see pCombStephenson.

Examples

# Example using built-in data
data(example_dat, package = "manytestsr")
library(data.table)

# Test for treatment effect using polynomial rank scores
single_block <- as.data.table(subset(example_dat, blockF == "B080"))
p_val <- pPolyRank(single_block, Y1 ~ trtF | blockF)
print(p_val)
#> [1] 0.627839