Indicators

[R A Bailey]

> 
> The Wilson usage is good to learn. I don't have Puri and Nigam on hand, but 
> isn't their defn of PEB same as Kageyama and Calinski, *not* requiring an 
> association scheme?

Their definition (see my encyclopedia article) was merely that the
weighted information matrix be diagonalizable, which it always is.

C&K talk about a (5;3,4;7)-EB design to mean one in which the
multiplicities of the canonical efficiency factors, in descending
order of cef, are 5,3,4,7, with 5 being the multiplicity of cef 1 
and 7 being the multiplicity of cef 0.
> 
> >
> >``Forget about any
> >concept of partial efficiency balance, which will not be of interest
> >in our lifetime (efficiency balance in itself is a marginal concept)''
> >
> >If you think this then read Volume II of Cali\'nski and Kageyama.
> >
> 
> My usage of the term here was as I had defined it 
(with an association scheme), 
> not as C&K defined. So I do not think the criticism is on target, but on the 
> other hand I should know better than to cavalierly anticipate the future. 

Misunderstanding.  I meant that C& K think that `efficiency balance' 
is important. So do John & Williams.

> 
> 
> >I think that each concept (concurrence matriz in the BMA,
> >information matrix in the BMA, weighted concurrence matrix
> >in the BMA) is valuable to some people.
> >
> >RAB
> >
> 
> RAB's post with a Sunday time stamp did not arrive at my mailer until Monday 
> 19:53 - clearly my mailer and the list do not play well together, which can 
> muddy discussions. 

JP, your email address is not working.



> RAB above suggests something that may be different: the 
weighted concurrence  matrix is in BMA. I take this to mean 
weighting by replication, having not first 
> weighted blockwise-concurrences by blocksize; is that correct? 

No, I mean take the information matrix and pre and post multiply it by
the square root of the inverse of the diagonal matrix of replications.

RAB


-- 
R. A. Bailey
       
Snail:  School of Mathematical Sciences    Tel:  (+44) 20 7882 5517
        Queen Mary, University of London
        Mile End Road                      Email: r.a.bailey at qmul.ac.uk
        London E1 4NS
        U.K.