Indicators

[Peter Cameron]

Briefly, on the subject of partial balance:

I take JP's point that there is already some literature on "partial variance
balance". However, there is also some literature on "partial pairwise balance",
at least in the case of group-divisible designs (which are definitely not
required to have constant block size). For this reason I would not like
to see the unadorned term "partial balance" pre-empted for one of these
concepts.

There are two choices. One is to use, as JP suggests, terms like
"information_matrix_association_scheme" and 
"concurrence_matrix_association_scheme". Such terms would never pass 
into popular usage, but would be completely unambiguous.

The other is to try to influence popular usage. Rosemary tells me (I think
I have this right) that "partial variance balance" has already been used
to mean "the information matrix is diagonalisable", that is, an empty
concept. Clearly this usage should be discouraged. But the two terms
"variance partial balance" and "pairwise partial balance" seem to me
to be clear enough (though not as transparent as the ones in the preceding
paragraph) and also attractive enough that people may begin to use them.

Good terminology does matter! How many people would study nilpotent groups
if they were still called, as Burnside had it, "groups with properties
analogous to the properties of groups whose order is a power of a prime"?

Peter.