balance

[J. P. Morgan]

Peter said:
> 
> Just a brief note to clarify what I didn't make clear before.
> 
> JP said:
> 
[...]> 
> I wasn't claiming any implications between the three types of balance
> (pairwise, variance, and efficienccy balance); only that the concepts
> of pairwise/variance/efficiency partial balance with the trivial
> association scheme reduce precisely to the previously-defined concepts
> of pairwise/variance/efficiency balance (if I have understood the
> definitions correctly).
> 

No, I didn't think any such claim was made. But I believe the defn of
efficiency balance is that the matrix R^{-1/2}NR^{-1/2} has v-1 nonzero,
identical eigenvalues (that's what we wrote in the external rep). I was
pointing out that R^{-1/2}NR^{-1/2} can have this property without being
constant on-diagonal and off-diagonal. That would mean t-balance of
R^{-1/2}NR^{-1/2} would not necessarily be equivalent to efficiency balance
(also if I have understood defns correctly). JP