# cKW: Computes a critical value for the Kruskal-Wallis H... 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 Kruskal-Wallis H distribution at (or typically in the "Exact" and "Monte Carlo" cases, close to) the given alpha level.

## Usage

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

## Arguments

 `alpha` A numeric value between 0 and 1. `n` A vector of numeric values indicating the size of each of the k data groups. `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 "NSM3Ch6c" class containing the following components:

 `n` number of observations in the k data groups `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 6.1 Half-Time of Mucociliary Clearance #cKW(0.0503,c(5,4,5),"Exact") cKW(0.7147,c(5,4,5),"Asymptotic") cKW(0.7147,c(5,4,5),"Monte Carlo",n.mc=20000) ```

### Example output

```Loading required package: combinat

Attaching package: ‘combinat’

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

combn

Asymptotic Approximation used:

Group sizes: 5 4 5
For the given alpha=0.7147, the approximate upper cutoff value is Kruskal-Wallis H=0.671784809512408,

Monte Carlo Approximation (with 20000 Iterations) used:

Group sizes: 5 4 5
For the given alpha=0.7147, the upper cutoff value is Kruskal-Wallis H=0.77142857,
with true alpha level=0.7126
```

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