pUmbrPK: Function to compute the P-value for the observed Mack-Wolfe...

In NSM3: Functions and Datasets to Accompany Hollander, Wolfe, and Chicken - Nonparametric Statistical Methods, Third Edition

Function to compute the P-value for the observed Mack-Wolfe Peak Known A_p distribution.

Description

The function generalizes Harding's (1984) algorithm to quickly generate the distribution of A_p.

Usage

pUmbrPK(x,peak=NA,g=NA,method=NA, n.mc=10000)

Arguments

x	Either a list or a vector containing the data.
peak	An integer representing the known peak among the k data groups.
g	If x is a vector, g is a required vector of group labels. Otherwise, not used.
method	Either "Exact", "Monte Carlo", or "Asymptotic", indicating the desired distribution. When method=NA, and there are ties in the data, "Exact" will be used if the number of permutations is 10,000 or less. Otherwise, "Monte Carlo" will be used. When method=NA and there are no ties in the data, if sum(n)<=200, the "Exact" method will be used to compute the A_p distribution. Otherwise, the "Asymptotic" method will be used.
n.mc	If method="Monte Carlo", the number of Monte Carlo samples used to estimate the distribution. Otherwise, not used.

Details

The data entry is intended to be flexible, so that the groups of data can be entered in either of two ways. For data a=1,2 and b=3,4,5 the following are equivalent:

pUmbrPK(x=list(c(1,2),c(3,4,5))) pUmbrPK(x=c(1,2,3,4,5),g=c(1,1,2,2,2))

Value

Returns a list with "NSM3Ch6p" class containing the following components:

n	a vector containing the number of observations in each of the data groups
obs.stat	the observed A_p statistic
p.val	the upper tail P-value

Author(s)

Grant Schneider

References

Harding, E. F. "An efficient, minimal-storage procedure for calculating the Mann-Whitney U, generalized U and similar distributions." Applied statistics (1984): 1-6.

Examples

##Hollander-Wolfe-Chicken Example 6.3 Fasting Metabolic Rate of White-Tailed Deer
x<-c(36,33.6,26.9,35.8,30.1,31.2,35.3,39.9,29.1,43.4,44.6,54.4,48.2,55.7,50,53.8,53.9,62.5,46.6,
44.3,34.1,35.7,35.6,31.7,22.1,30.7)
g<-c(rep(1,7),rep(2,3),rep(3,5),rep(4,4),rep(5,4),rep(6,3))

pUmbrPK(x,4,g,"Exact")
pUmbrPK(x,4,g,"Asymptotic")

NSM3 documentation built on Sept. 8, 2023, 5:52 p.m.