How to implement Aly's permutation test for comparison of variances in R?

Question

The excerpt below is from "Permutation, Parametric and Bootstrap Tests of Hypotheses", Third Ed. by Phillip Good (pages 58-61), section 3.7.2..

I am trying to implement this permutation test in R (see further below) to compare two variances. I am thinking now about how to calculate the p-value, and whether the test allows for different alternative hypothesis (greater, less, two-sided) and I am not sure on how to proceed.

Could you shed some light on this and perhaps give me some criticism about the code? Many thanks!

# Aly's non-parametric, permutation test of equality of variances
# From "Permutation, Parametric and Bootstrap Tests of Hypotheses", Third Ed. 
# by Phillip Good (pages 58-61), section 3.7.2.

# Implementation of delta statistic as defined by formula in page 60
# x_{i}, order statistics
# z = x_{i+1} - x_{i}, differences between successive order statistics
aly_delta_statistic <- function(z) {
  z_length <- length(z)
  m <- z_length + 1
  i <- 1:z_length
  sum(i*(m-i)*z)
}

aly_test_statistic <- function(sample1, sample2 = NULL, nperm = 1) {

  # compute statistic based on one sample only: sample1
  if(is.null(sample2)) {
    sample1 <- sort(sample1)
    z <- diff(sample1)
    return(aly_delta_statistic(z))
  }

  # statistic based on randomization of the two samples
  else {
    m1 <- length(sample1)
    m2 <- length(sample2)
    # allocate a vector to save the statistic delta
    statistic <- vector(mode = "numeric", length = nperm)
    for(j in 1:nperm) {
      # 1st stage resampling (performed only if samples sizes are different)
      # larger sample is resized to the size of the smaller
      if(m2 > m1) {
         sample2 <- sort(sample(sample2, m1))
         m <- m1
      } else {
         sample1 <- sort(sample(sample1, m2))
         m <- m2
      }
      # z-values: z1 in column 1 and z2 in column 2.
      z_two_samples <- matrix(c(diff(sample1), diff(sample2)), ncol = 2)
      # 2nd stage resampling
      z <- apply(z_two_samples, 1, sample, 1)
      statistic[j] <- aly_delta_statistic(z)
    }
    return(statistic)
  }
}