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P-value function: combined Stephenson rank test of the sharp null

pStephensonQuad.Rd

Tests the sharp null of no effect with several Stephenson rank statistics at once. For each tuning parameter in zeta the function scores every unit by stephenson_scores within its block, forms the treated sum of scores summed over blocks, and combines the resulting statistics by the quadratic form of Strasser and Weber (1999) in coin::independence_test(), referred to a chi-square distribution with one degree of freedom per tuning parameter. This is the test the block_test_power paper calls the combined Stephenson test, and it lets an analyst use several values of \(\zeta\) without choosing among them.

Usage

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

Arguments

dat

A data.table with the outcome, treatment, and block columns.

fmla

A formula, outcome ~ treatment | block or outcome ~ treatment when the scores are to be computed over the whole sample.

zeta

Integer tuning parameters, one statistic each. The paper uses c(2, 6, 10).

simthresh

The number of rows at or below which the permutation reference replaces the chi-square reference.

sims

The number of resampled assignments for the permutation reference.

parallel

Passed to coin::approximate(): "no", "multicore", or "snow".

ncpu

Number of cpus for the permutation reference when parallel is not "no".

Value

A p-value.

Details

The scores are signed, so block-level contributions of opposite sign cancel in the sum: the test has power when effects push the same way in every block and little when they reverse sign across blocks. The distance-based tests pIndepDist and pCombCauchyDist are the ones for that case.

This is not pCombStephenson, which wraps the CMRSS quantile-of-effects procedure with polynomial scores and an optimizer.

References

Stephenson, W. R. (1981). A general class of one-sample nonparametric test statistics based on subsamples. Journal of the American Statistical Association 76(374), 450–456.

Strasser, H. and Weber, C. (1999). On the asymptotic theory of permutation statistics. Mathematical Methods of Statistics 8(2), 220–250.

Examples

data(example_dat, package = "manytestsr")
library(data.table)
idat <- as.data.table(example_dat)
pStephensonQuad(idat, Y1 ~ trtF | blockF)
#> [1] 0.1059222
pStephensonQuad(idat, Y1 ~ trtF | blockF, zeta = 2)
#> [1] 0.03662658