Dear R-list,

I am sorry for my shortage of stat knowlege. I want know how to conduct a
hypothesis test : Ho:|E(X)|=|E(Y)|<->H1:otherwise.

Actually, in my study, X and Y is two observations of bias,
where bias=u^hat-u, u is a parameter I concerned. Given X=(u^hat_xi - u) and
Y=(u^hat_yi - u), I want to know which bias is smaller, or the absolute
expection of which is smaller. Due to limit of sample size, I think we
cannot make a conclusion by comparing the absolute mean value of each
sample. So I turn to a means of  hypothesis testing as I post in the title.

Now my strategy is using permutation test. Like this:

permutation.test.bias=function(x,y,mc=1000){
 n1=length(x)
 n2=length(y)
 n=n1+n2
 xy=c(x,y)
 dbar=abs(abs(mean(x))-abs(mean(y)))
 z=c()
 for(i in 1:mc){
  mn=sample(1:n,n1)
  z[i]=abs(mean(xy[mn]))-abs(mean(xy[-mn]))
 }
 p.value=sum(abs(z)>dbar)/mc
 p.value
}

Although it seems plausible, this function doesn't work
> n=1000
> x=rnorm(n)+10
> y=rnorm(n)-10
> permutation.test.bias(x,y)
[1] 0

I think there should be other test methods for this problem.

Thanks for any suggestion/solution.




-- 
Junjie Li,                  klijunjie@gmail.com
Undergranduate in DEP of Tsinghua University,

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