for info.

[John P. Morgan]

>On Thu, 7 Aug 2003 12:39:56 +0100
> Peter Cameron <p.j.cameron at qmul.ac.uk> wrote

>
>On Thu, Aug 07, 2003 at 10:36:37AM +0100, Leonard Soicher wrote:
>> 
>> Dear All,
>> 
>> Following our discussions, I have changed the rnc to move 
>> <partial_balance_properties> to the top level under <block_design>.
>> 
>> Also for your info, I consider both <variance_balanced> and 
>> <efficiency_balanced> to be "not_applicable" if the design is 
>> not connected or only has one point. OK?
>> 
>> Regards,  Leonard
>>
>Both changes fine by me. The alternative for variance balance would be
>false except in the trivial case where each block has one element (and
>all pairwise variances infinite) - I prefer "not_applicable" to any
>question which has an answer infinity.
>
>Peter.
> 

The definitions for both variance_balanced and efficiency_balanced say that the 
answer is "false" for disconnected designs. For any v>1 this includes the case 
mentioned by Peter where each block has only one element (I am assuming the 
value of "connected" is taken as "true" for v=1). The only remaining case is for 
designs with v=1 treatment, in which case the information matrix is the 1x1 
matrix 0, there are NO canonical variances, and NO efficiency factors. In this 
case it is also correct to say "false" (which, by the way, is in accord with the 
current rnc, which does not allow "not_applicable" as a value of these two 
indicators). Why? Since there are no contrasts to estimate, there can be no list 
of variances which are all identical, and consequently no "balance" in the ways 
that term is used in the statistical framework. 

Recommendation: assign the values of <variance_balanced> and 
 <efficiency_balanced> as "false" if the design is 
 not connected or only has one point. 

A somewhat tangential observation: since currently only binary designs are 
allowed, for v=1 there is only one design for given b with nonempty blocks.

JP