On Monday, August 18, 2014 12:48:36 AM UTC-4, Rich Ulrich wrote: > 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. > > > > > > -- > > Rich Ulrich
Thank you for your response. Sorry for the confusion I added by mentioning pairs of boys. For the actual problem with which we're dealing the adult brothers might be a better analogy.
You mention that the total count should be total and should include partial matches. This is what I'm trying to get across to our group, unfortunately, the strongest opposition comes from our boss (who is a brilliant scientist as long as maths are not involved). Do you have a reference that I could use to back my case? I've been browsing over Phillip Good's books but have not found this restriction spelled out in a way someone with very little knowledge of maths in general.