?Or maybe analyze at each individual length (interval-width = 1)??
As you pointed out early on in this effort, danger inheres in ?cleaving nature? by ANY choice of length interval when the empirical situation is still murky (even though some cleavages can be more/less defensible than others on purely technical grounds.) But in our case I think a special danger lurks in ANY length interval cleavage we make because even though we haven?t studied how long important structural subunits actually are in different folds (length = number of amino acids = number of codons), our length interval cleavages (equi-width OR equi-ratio) not only imply that we do have this privileged knowledge, but also imply that any u,e-based ?profiles? relevant to evolution of important structural subunits should be defined on a particular set of length intervals rather than another.
So in the case of some folds, we might get lucky with our choice of length intervals (as the good Aug two-ways for certain length intervals within folds a1,b1,c1,c2 seem to indicate), while with other folds such as a3 and b47, our luck may not hold up (as the absence of any good Auq two-ways for any length intervals within folds a3 and b47 seems to indicate.
And the only way to stop playing this kind of russian roulette with the data is to take your suggestion and drop back to singleton length intervals.
This will, of course, lead to some Bonferroni issues later on because given the fact that our singleton lengths range roughly from 25 to 125, we?ve multiplied Bonferroni entries by a factor of 8.5 (= 100/12). But it is to be hoped that if the move to singletons is correct, the data will show us natural groupings for Bonferroni tables that we can?t see now.
Anyway, I?ve completed the code additions for the second new regression, and desk-checked them.
So now I?ll rerun the analysis for the first and second regressions using singleton length intervals and post back when complete.
Thanks again for your continued consideration of these matters, and please feel free to again interject ?unilaterally? if any other changes occur to you that might increase our chances of success, or at least decrease our chances of arrogant methodological error.