I have two lots of data that have been independently, arbitrarily transformed from the same original data source using the same permutation algorithm. I would like to know what kind of statements I can make about the original data source or the transformation process by comparing these two data sets. All the data are non-negative integers.
To express this in R code:
# These true values and permutation function are unknown/unobservable
set.seed(1904)
true.xs <- round(rnorm(1000, mean=100, sd=15), 0)
unknown.trans <- function(orig)orig + round(rnorm(length(orig), sd=3),0)
# These observations have been made
xs.1 <- unknown.trans(true.xs)
xs.2 <- unknown.trans(true.xs)
I would like to know what I can say about true.xs or unknown.trans given xs.1 and xs.2. I'm willing to make some fairly strong assumptions if that will help (i.e. that the transformation function is symetrical around zero, etc.).
