Compute p-Value for the Quantile Test

Compute the p-value associated with a specified combination of \(m\), \(n\), \(r\), and \(k\) for the quantile test (useful for determining \(r\) and \(k\) for a given significance level \(\alpha\)).

quantileTestPValue(m, n, r, k, exact.p = TRUE)

Arguments

m

numeric vector of integers indicating the number of observations from the “treatment” group. Missing (NA), undefined (NaN), and infinite (Inf, -Inf) values are allowed but will be removed.

n

numeric vector of integers indicating the number of observations from the “reference” group. Missing (NA), undefined (NaN), and infinite (Inf, -Inf) values are allowed but will be removed.

r

numeric vector of integers indicating the ranks of the observations to use as the lower cut off for the quantile test. All values of r must be greater than or equal to 2 and less than or equal to the corresponding elements of m+n (the total number of observations from both groups). Missing (NA), undefined (NaN), and infinite (Inf, -Inf) values are allowed but will be removed.

k

numeric vector of integers indicating the number of observations from the “treatment” group contained in the \(r\) largest observations. This is the critical value used to decide whether to reject the null hypothesis. All values of k must be greater than or equal to 0 and less than or equal to the corresponding elements of r. Missing (NA), undefined (NaN), and infinite (Inf, -Inf) values are allowed but will be removed.

exact.p

logical scalar indicating whether to compute the p-value based on the exact distribution of the test statistic (exact.p=TRUE; the default) or based on the normal approximation (exact.p=FALSE).

Details

If the arguments m, n, r, and k are not all the same length, they are replicated to be the same length as the length of the longest argument.

For details on how the p-value is computed, see the help file for quantileTest.

The function quantileTestPValue is useful for determining what values to use for r and k, given the values of m, n, and a specified significance level \(\alpha\). The function quantileTestPValue can be used to reproduce Tables A.6-A.9 in USEPA (1994, pp.A.22-A.25).

Value

numeric vector of p-values.

References

See the help file for quantileTest.

Author

Steven P. Millard (EnvStats@ProbStatInfo.com)

Note

See the help file for quantileTest.

Examples

  # Reproduce the first column of Table A.9 in USEPA (1994, p.A.25):
  #-----------------------------------------------------------------

  p.vals <- quantileTestPValue(m = 5, n = seq(15, 45, by = 5), 
    r = c(9, 3, 4, 4, 5, 5, 6), k = c(4, 2, 2, 2, 2, 2, 2)) 

  round(p.vals, 3) 
#> [1] 0.098 0.091 0.119 0.089 0.109 0.087 0.103
  #[1] 0.098 0.091 0.119 0.089 0.109 0.087 0.103 

  #==========

  # Clean up
  #---------

  rm(p.vals)