pJCK {NSM3}

Function to compute the P-value for the observed Jonckheere-Terpstra J statistic.

Description

This function computes the observed J statistic for the given data and corresponding P-value. When there are no ties in the data, the function takes advantage of Harding's (1984) algorithm to quickly generate the exact distribution of J.

Usage

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

Arguments

x

Either a list or a vector containing the data.

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 ties are not present, "Exact" will be used. When method=NA and ties are present, "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.

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:

pJCK(x=list(c(1,2),c(3,4,5))) pJCK(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 J statistic

p.val

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 6.2 Motivational Effect of Knowledge of Performance
motivational.effect<-list(no.Info=c(40,35,38,43,44,41),rough.Info=c(38,40,47,44,40,42),
                          accurate.Info=c(48,40,45,43,46,44))
#pJCK(motivational.effect,method="Monte Carlo")
pJCK(motivational.effect,method="Asymptotic")