R/R.test.R

In depthTools: Depth Tools Package

R.test <- function(x,y,n,m,seed=0)
{
#Input:
# x = matrix of data from group 1
# y = matrix of data from group 2
# n = size of test group 1
# m = size of test group 2

#Output:
# pvalue = the p-value for the test
# statistic = the value of the test statistic

set.seed(seed); #x<-as.matrix(x); y<-as.matrix(y)
p <- ncol(x); N <- nrow(x); M <- nrow(y)  #size of each data group 
u <- matrix( runif(N),1,N)
w <- matrix( runif(M),1,M)
I <- order(u); J<-order(w)
n0 <- max(N-n, M-m); 

if (n0<=max(n,m)) {stop("Incorrect sample sizes")}
g1 <- x[I[1:n],] #Randomly select n and m observations from each group to create the test groups
g2 <- y[J[1:m],] 

if ((N-n)>=(M-m)) {gref <- x[I[(n+1):N],]}     # Consider the remaining observations from group 1 as the reference group
else {gref <- y[J[(m+1):M],] }                 # Consider the remaining observations from group 2 as the reference group

r <- MBD(g1,gref, plotting=FALSE)$MBD; # calculate the modified band depth of test group 1 with respect to reference group
s <- MBD(g2,gref,plotting=FALSE)$MBD; # calculate the modified band depth of test group 2 with respect to reference group
z <- MBD(gref,plotting=FALSE)$MBD     # calculate the modified band depth of reference group

# we apply the two-sided rank sum test with null hypothesis that data in the vectors r and s are independent samples 
# from identical continuous distributions. The test is equivalent to a Mann-Whitney U-test.

n1 <-length(r); n2<-length(s);
g <- cbind(r,s); I <- order(g)
u <- which(I>n1)
w <- which(I<=n1)
p.value <- wilcox.test(u,w)$p.value

Rx<-c();Ry<-c();
for (i in 1:n) {Rx[i]<-sum(z<=r[i])/length(z)}
for (i in 1:m) {Ry[i]<-sum(z<=s[i])/length(z)}
#print(Rx);print(Ry)
R <- order(c(Rx,Ry))
W <- sum(R[(n+1):(n+m)])
#print(R)
#print(W)
#print(p.value)

return(list(p.value=p.value, statistic=W))
}