# cLepage: Computes a critical value for the Lepage D distribution. In NSM3: Functions and Datasets to Accompany Hollander, Wolfe, and Chicken - Nonparametric Statistical Methods, Third Edition

## Description

This function computes the critical value for the Lepage D distriburion at (or typically in the "Exact" and "Monte Carlo" cases, close to) the given alpha level.

## Usage

 `1` ```cLepage(alpha, m, n, method=NA, n.mc=10000) ```

## Arguments

 `alpha` A numeric value between 0 and 1. `m` A numeric value indicating the size of the first data group (X). `n` A numeric value indicating the size of the second data group (Y). `method` Either "Exact", "Monte Carlo" or "Asymptotic", indicating the desired distribution. When method=NA, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. `n.mc` If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used.

## Value

Returns a list with "NSM3Ch5c" class containing the following components:

 `m` number of observations in the first data group (X) `n` number of observations in the second data group (Y) `cutoff.U` upper tail cutoff at or below user-specified alpha `true.alpha.U` true alpha level corresponding to cutoff.U (if method="Exact" or "Monte Carlo")

Grant Schneider

## Examples

 ```1 2 3 4``` ```##Hollander-Wolfe-Chicken Example 5.3 Platelet Counts of Newborn Infants cLepage(0.02,10,6,"Exact") cLepage(0.02,10,6,"Monte Carlo") cLepage(0.02,10,6,"Asymptotic") ```

### Example output

```Loading required package: combinat

Attaching package: ‘combinat’

The following object is masked from ‘package:utils’:

combn

Loading required package: MASS
Loading required package: partitions
Loading required package: survival
Number of X values: 10 Number of Y values: 6
For the given alpha=0.02, the upper cutoff value is Lepage D=6.90252100840336,
with true alpha level=0.02

Monte Carlo  Approximation (with  10000  Iterations) used:

Number of X values: 10 Number of Y values: 6
For the given alpha=0.02, the upper cutoff value is Lepage D=6.90252100840336,
with true alpha level=0.0199

Asymptotic  Approximation used:

Number of X values: 10 Number of Y values: 6
For the given alpha =0.02, the approximate upper cutoff value is Lepage D=7.82404601085629,
```

NSM3 documentation built on April 6, 2021, 5:05 p.m.