[R] non-parametric permutation and signed paired-difference distributions

[Michael Friendly]

On 10/14/2011 4:10 PM, Bert Gunter wrote:
> If I understand what you want to do, it's simple. 2^15 is small (only 
> about 33000), so you can generate all the possible means (sums, 
> actually) and and find the population quantile for your result. If 
> avals is the vector of 15 absolute values, the complete distribution is:
>
> allsums <- as.matrix(expand.grid(as.data.frame(matrix(rep(c(-1,1),15), 
> nr =2)))) %*% avals
>
> This was instantaneous on my machine.
That's beautiful, Bert.  Thanks!  Here is my fleshed-out example

mean(ZeaMays$diff)
# complete permutation distribution of diff, for all 2^15 ways of assigning
# one value to cross and the other to self
allmeans <- as.matrix(expand.grid(as.data.frame(matrix(rep(c(-1,1),15), 
nr =2)))) %*% abs(ZeaMays$diff) / 15

# upper-tail p-value
sum(allmeans > mean(ZeaMays$diff)) / 2^15
# two-tailed p-value
sum(abs(allmeans) > mean(ZeaMays$diff)) / 2^15

hist(allmeans, breaks=64, xlab="Mean difference, cross-self",
     main="Histogram of all mean differences")
abline(v=mean(ZeaMays$diff), col="red", lwd=2)
abline(v=-mean(ZeaMays$diff), col="red", lwd=2, lty=2)


-- 
Michael Friendly     Email: friendly AT yorku DOT ca
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