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pDurSkiMa<-function(x,b=NA,trt=NA,method=NA,n.mc=10000){
outp<-list()
outp$stat.name<-"Durbin, Skillings-Mack D"
outp$n.mc<-n.mc
ties<-!length(unique(as.numeric(x)))==length(x)
if(is.matrix(x)){
outp$n<-n<-nrow(x)
outp$k<-k<-ncol(x)
}
##Turn x into a matrix if it's given as a vector
if(!is.matrix(x)){
if ((length(x) != length(b))||(length(x) != length(trt)))
stop("'x', 'b', and 'trt' must have the same length")
outp$n<-n<-length(unique(b))
outp$k<-k<-length(unique(trt))
x.vec<-x
num.obs<-length(x.vec)
##In case the user gives some kind of labels other than 1,2,3...
b.ind<-as.numeric(as.factor(b))
trt.ind<-as.numeric(as.factor(trt))
##Turn x into a matrix;
x<-matrix(ncol=outp$k,nrow=outp$n)
for(i in 1:num.obs){
x[b.ind[i],trt.ind[i]]<-x.vec[i]
}
}
###########################################
###Check Data structure
if(length(unique(rowSums(!is.na(x))))!=1){
stop("Must be same number of observations per block")
}
if(length(unique(colSums(!is.na(x))))!=1){
stop("Must be same number of observations per treatment")
}
###
outp$ss<-s<-sum(!is.na(x[1,]))
outp$pp<-p<-sum(!is.na(x[,1]))
outp$lambda<-outp$pp*(outp$ss-1)/(outp$k-1)
outp$obs.mat<-matrix(0,ncol=outp$k,nrow=outp$n)
outp$obs.mat[!is.na(x)]<-1
outp$x<-x
##When the user doesn't give us any indication of which method to use, try to pick one.
if(is.na(method)){
if(factorial(outp$ss)^outp$n<=10000){
method<-"Exact"
}
if(factorial(outp$ss)^outp$n>10000){
method<-"Monte Carlo"
}
}
#####################################################################
outp$method<-method
possible.ranks<-t(apply(x,1,rank,na.last=NA))
DSK.stat<-function(obs.data){
tmp.mat<-outp$obs.mat
for(i in 1:outp$n){
tmp.mat[i,tmp.mat[i,]!=0]<-obs.data[i,]
}
Rj<-apply(tmp.mat,2,function(x) sum(x[!is.na(x)]))
D.stat<-12/(outp$lambda*outp$k*(outp$ss+1))*sum((Rj-outp$pp*(outp$ss+1)/2)^2)
return(D.stat)
}
outp$obs.stat<-DSK.stat(possible.ranks)
if(outp$method=="Exact"){
possible.perm<-multCh7(possible.ranks)
exact.dist<-apply(possible.perm,3,DSK.stat)
outp$p.val<-mean(exact.dist>=outp$obs.stat)
}
if(outp$method=="Monte Carlo"){
mc.perm<-matrix(ncol=outp$ss,nrow=outp$n)
mc.stats<-numeric(n.mc)
for(i in 1:n.mc){
for(j in 1:n){
mc.perm[j,]<-sample(possible.ranks[j,])
}
mc.stats[i]<-DSK.stat(mc.perm)
}
outp$p.val<-mean(mc.stats>=outp$obs.stat)
}
if(outp$method=="Asymptotic"){
outp$p.val<-1-pchisq(outp$obs.stat,outp$k-1)
}
class(outp)<-"NSM3Ch7p"
outp
}
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