mwwutestrss {RSSampling}

Mann-Whitney-Wilcoxon test with RSS

Description

In this function, we introduce the RSS version of the Mann-Whitney-Wilcoxon (MWW) test.

Usage

  mwwutestrss(X,Y,m,r,l,n,delta0=0,alpha=0.05,lambda=0.5,alternative="two.sided")

Arguments

X

First obtained ranked set sample

Y

Second obtained ranked set sample

m

Set size which was used while sampling X

r

Cycles size which was used while sampling X

l

Set size which was used while sampling Y

n

Cycles size which was used while sampling Y

delta0

The median value of difference in the null hypothesis. (By Default = 0)

alpha

The significance level (by default = 0.05).

lambda

constant in the variance formula of the test statistic, see Chen et. al.(2003)

alternative

Character string defining the alternative hypothesis, one of "two.sided", "less" or "greater" (by default = "two.sided")

Details

The test statistics and an approximate confidence intervals are constructed by using the normal approximation. Also note that, we assume that the ranking mechanism in the RSS is consistent. For more details please refer to Chen et. al.(2003, pg. 115-124).

There should be two datasets to compare as "X" and "Y", respectively.

Value

medianX

median value of the first sample

medianY

median value of the second sample

MWW.test.mwwUrss

The value of the Mann-Whitney-Wilcoxon test statistic

C.I.

the confidence interval of the Mann-Whitney-Wilcoxon test statistic

z.test

the z statistic for test

p.value

the p value for the test

References

Chen, Z., Bai Z., Sinha B. K. (2003). Ranked Set Sampling: Theory and Application. New York: Springer.

Examples

library("LearnBayes")
mu=c(1,1.2,2)
Sigma <- matrix(c(1,2,0,2,5,0.5,0,0.5,3), 3, 3)
x <- rmnorm(10000, mu, Sigma)
xx=as.numeric(x[,1])
xy=as.numeric(x[,2])
samplerss=con.rss(xx,xy,m=3,r=12,concomitant=TRUE)
sample.x=as.numeric(samplerss$sample.x)
sample.y=as.numeric(samplerss$sample.y)
mwwutestrss(sample.x,sample.y,m=3,r=12,l=3,n=12,delta0=0)