balance

[J. P. Morgan]

Peter Cameron wrote
Wednesday, October 08, 2003 11:42 AM


> On Wed, Oct 08, 2003 at 11:36:01AM -0400, J. P. Morgan wrote:
> > 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
> >
> You are right.
> 
> Peter.

Having first brought up the idea of an association scheme on
F=R^{-1/2}NR^{-1/2), which would seem to imply that the trivial assoc scheme
should correspond to "balance", I did not realize the difficulty with
unequal replication until thinking about your post on the different forms of
balance. Balancing of F may need more thought, but I am still not convinced
it is worthwhile. JP