# quantileTestPValue: Compute p-Value for the Quantile Test In EnvStats: Package for Environmental Statistics, Including US EPA Guidance

## Description

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 α).

## Usage

 `1` ``` 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 α. 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.

## Note

See the help file for `quantileTest`.

## Author(s)

Steven P. Millard ([email protected])

## References

See the help file for `quantileTest`.

`quantileTest`, `wilcox.test`, `htest.object`, Hypothesis Tests.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ``` # 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 #========== # Clean up #--------- rm(p.vals) ```