P-value function: Cauchy Combined Indepence Test

Usage

pCombCauchyDist(
  dat,
  fmla = YcontNorm ~ trtF | blockF,
  simthresh = 20,
  sims = 1000,
  parallel = "no",
  ncpu = NULL,
  distfn = fast_dists_and_trans_nomax_hybrid
)

Arguments

dat: An object inheriting from class data.frame
fmla: A formula appropriate to the function. Here it should be something like outcome~treatment|block
simthresh: is the size of the data below which we use direct permutations for p-values
sims: Either NULL (meaning use an asymptotic reference dist) or a number (meaning sampling from the randomization distribution implied by the formula)
parallel: is "no" then parallelization is not required, otherwise it is "multicore" or "snow" in the call to coin::independence_test() (see help for coin::approximate()). Also, if parallel is not "no" and adaptive_dist_function is TRUE, then an openmp version of the distance creation function is called using ncpu threads (or parallel::detectCores(logical=FALSE) cores).
ncpu: is number of cpus to be used for parallel operation.
distfn: is a function that produces one or more vectors (a data frame or matrix) of the same number of rows as the dat. Here until further notice users should leave it at mean_dist_raw_rank_tanh since that function is purpose built for this function.

Value

A p-value

Details

This function combines the p-values from univariate tests using using (1) the raw outcome, (2) the rank-transformed outcome, (3) the tanh transformed raw outcome (another test statistic that is more sensitive when there is skew), (4) the mean difference in raw outcome Euclidean distances bwtween treated and control observations within block; (5) the mean difference in ranked outcome Euclidean distances bwtween treated and control observations; (6) a Hotelling-T style quadratic combination of the preceding test statistics. Inspired by Rizzo and Székely's work on Euclidean distance based testing and by Liu and Xie (2020) on the Cauchy Combination Test and Hansen and Bowers (2008) on omnibus tests. Distance and ranks and other transformations are all calculated by block when block is supplied in the formula.