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pPage<-function(x,b=NA,trt=NA,method=NA, n.mc=10000){
outp<-list()
outp$stat.name<-"Page L"
outp$n.mc<-n.mc
ties<-!length(unique(as.numeric(x)))==length(x)
#If given a list, try to convert to a matrix. Each item
#in the list represents a column in the matrix.
if(is.list(x)){x<-matrix(as.numeric(unlist(x)),ncol=length(x),byrow=F)}
if(is.matrix(x)){
outp$n<-n<-nrow(x)
outp$k<-k<-ncol(x)
}
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
##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:outp$n){
for(j in 1:outp$k){
x[i,j]<-x.vec[(b==i)&(trt==j)]
}
}
}
##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$k)^outp$n<=10000){
method<-"Exact"
}
if(factorial(outp$k)^outp$n>10000){
method<-"Monte Carlo"
}
}
#####################################################################
outp$method<-method
L.calc<-function(x){
return(sum((1:outp$k)*colSums(t(apply(x,1,rank)))))
}
outp$obs.stat<-L.calc(x)
possible.ranks<-t(apply(x,1,function(x) as.numeric(rank(x))))
if(outp$method=="Exact"){
possible.perm<-multCh7(possible.ranks)
exact.dist<-numeric(factorial(outp$k)^outp$n)
for(i in 1:factorial(outp$k)^outp$n){
exact.dist[i]<-L.calc(possible.perm[,,i])
}
outp$p.val<-mean(exact.dist>=outp$obs.stat)
}
if(outp$method=="Monte Carlo"){
mc.perm<-matrix(ncol=outp$k,nrow=outp$n)
mc.stats<-numeric(n.mc)
for(i in 1:n.mc){
for(j in 1:n){
mc.perm[j,]<-sample(possible.ranks[j,])
}
mc.stats[i]<-L.calc(mc.perm)
}
mc.vals<-sort(unique(mc.stats))
mc.dist<-as.numeric(table(mc.stats))/n.mc
outp$p.val<-mean(mc.dist>=outp$obs.stat)
}
if(outp$method=="Asymptotic"){
outp$stat.name<-"Page L*"
outp$obs.stat<-(outp$obs.stat-((outp$n*outp$k*(outp$k+1)^2)/4))/(sqrt(outp$n*outp$k^2*(outp$k+1)*(outp$k^2-1)/144))
}
outp$p.val<-1-pnorm(outp$obs.stat)
class(outp)<-"NSM3Ch7p"
outp
}
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