Indicators

[R A Bailey]

JP said:

<begin>
I am going to argue that the suggestion is not at all a
recommendation for proceeding in ignorance. My proposal as made a few
days ago is that we implement a concept that is already used, and
that we use the terminology that is already given to that concept. We
could talk about "pairwise partial balance" and "efficiency partial
balance" (which can be defined as the weighted information matrix -
see the ext rep doc - as falling in the Bose-Mesner algebra) too, but
as far as I known this is truly striking into new territory. Is there
any mention anywhere in the literature of either of these concepts?
<end>


Yes.  Wilson (I believe) uses `group-divisible' to mean binary
block designs which may have unequal block sizes but whose
concurrence matrix is in the BMA of a group divisible association
scheme.  In the 1980s Puri and Nigam defined `partial efficiency
balance'.  Their definition makes it an empty concept, but it is not
true to say that

``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.

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