On Sun, 17 Aug 2014 18:32:07 -0700 (PDT), firstname.lastname@example.org wrote:
[snip, previous] >Hi Rich, > >Thank you for your response. I'll try to be more clear with a very >similar example. We want to test whether the heights of pairs of >brothers are more similar than the heights of random pairs of boys of >similar age but with no relation to each other. Problem is that the
If your sample were adults who had completed their growth, this would be the basic hypothesis of a simple correlation.
The complexity that I see is what arises from "boys" displaying heights that are so strongly correlated with age that you should be measuring age in months, not years. I would probably stick with parametric procedures, where for (X1, X2), X1 is always the older sib; and I would covary for linear and quadratic effects of age, hoping that would be enough. (What is the age range?) - That would be the partial r between sibs, partialing for the dummy variables for age.
If you want to use a "non-parametric" sort of procedure on heights, you could transform each height into the percentiles estimated from growth charts across their ages.
>sample we have has only pairs of brothers but we think that the boys in the sample are representative of the population. Thus, to have an idea of how similar the heights of random pairs of brothers we randomly make pairs with the boys in the sample and calculate our similarity metric. This metric we compare with the metric we obtained from the brothers' pairs. We repeat the random pairing a large number of times and count the number of random pairings whose similarity metric is as extreme as or more extreme than that of the paired brothers. The ratio of this number to the total number of random pairings is our p-value. > >Our argument is whether or not to allow two brothers in the same random pair. Now, from the little I know about permutation test, the observed data must be one of the possible random permutations, otherwise we're comparing a possible outcome against an impossible one. > The total count of permutations should be the "Total", so the sampling includes partial matches. That does nothing to account for age, so I would not consider it.