# R/cPage.R In NSM3: Functions and Datasets to Accompany Hollander, Wolfe, and Chicken - Nonparametric Statistical Methods, Third Edition

#### Documented in cPage

```cPage<-function(alpha, k, n, method=NA, n.mc=10000){
outp<-list()
outp\$stat.name<-"Page L"
outp\$n.mc<-n.mc

if(alpha>1||alpha<0||!is.numeric(alpha)){
cat('Error: Check alpha value! \n')
return(alpha)
}

outp\$alpha<-alpha
outp\$n<-n
outp\$k<-k
outp\$n.mc<-n.mc

##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)))))
}

possible.ranks<-matrix(rep(1:outp\$k,outp\$n),ncol=outp\$k,byrow=T)

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])
}

L.vals<-sort(unique(exact.dist))
L.probs<-as.numeric(table(exact.dist))/(factorial(outp\$k)^outp\$n)
L.dist<-cbind(L.vals,L.probs)
upper.tails<-cbind(rev(L.dist[,1]),cumsum(rev(L.dist[,2])))
outp\$cutoff.U<-upper.tails[max(which(upper.tails[,2]<=alpha)),1]
outp\$true.alpha.U<-upper.tails[max(which(upper.tails[,2]<=alpha)),2]
}

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

upper.tails<-cbind(rev(mc.vals),cumsum(rev(mc.dist)))
outp\$cutoff.U<-upper.tails[max(which(upper.tails[,2]<=alpha)),1]
outp\$true.alpha.U<-upper.tails[max(which(upper.tails[,2]<=alpha)),2]

}

if(outp\$method=="Asymptotic"){
outp\$stat.name<-"Page L*"
outp\$cutoff.U<-qnorm(1-alpha)
}

class(outp)<-"NSM3Ch7c"
return(outp)
}
```

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NSM3 documentation built on Sept. 8, 2023, 5:52 p.m.