NSM3 (version 1.18)

pUmbrPK: 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)

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

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.

Author

Grant Schneider

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))

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")