box1way <-
function(x,tr=.2,grp=c(1:length(x))){
#
# A heteroscedastic one-way ANOVA for trimmed means
# using a generalization of Box's method.
#
# The data are assumed to be stored in $x$ in list mode.
# Length(x) is assumed to correspond to the total number of groups.
# By default, the null hypothesis is that all groups have a common mean.
# To compare a subset of the groups, use grp to indicate which
# groups are to be compared. For example, if you type the
# command grp<-c(1,3,4), and then execute this function, groups
# 1, 3, and 4 will be compared with the remaining groups ignored.
#
# Missing values are automatically removed.
#
J<-length(grp) # The number of groups to be compared
print("The number of groups to be compared is")
print(J)
h<-vector("numeric",J)
w<-vector("numeric",J)
xbar<-vector("numeric",J)
svec<-vector("numeric",J)
for(j in 1:J){
xx<-!is.na(x[[j]])
val<-x[[j]]
x[[j]]<-val[xx] # Remove missing values
h[j]<-length(x[[grp[j]]])-2*floor(tr*length(x[[grp[j]]]))
# h is the number of observations in the jth group after trimming.
svec[j]<-((length(x[[grp[j]]])-1)*winvar(x[[grp[j]]],tr))/(h[j]-1)
xbar[j]<-mean(x[[grp[j]]],tr)
}
xtil<-sum(h*xbar)/sum(h)
fval<-h/sum(h)
TEST<-sum(h*(xbar-xtil)^2)/sum((1-fval)*svec)
nu1<-sum((1-fval)*svec)
nu1<-nu1^2/((sum(svec*fval))^2+sum(svec^2*(1-2*fval)))
nu2<-(sum((1-fval)*svec))^2/sum(svec^2*(1-fval)^2/(h-1))
sig<-1-pf(TEST,nu1,nu2)
list(TEST=TEST,nu1=nu1,nu2=nu2,p.value=sig)
}
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