support the idea

[John P. Morgan]

>Date: Thu, 4 Sep 2003 22:30:46 -0700 (PDT)
>From: Nam-Ky Nguyen <nkn at designcomputing.net>

>
>Collin has raised a very interesting question. My view
>is that  we only need a small database of BIBD. Among
>non-BIBD I wonder whether it makes much difference if
>the experimenter who need a 2-resolvable IBD of size
>(v,k,r)=(21,6,10) uses an RGD in
>http://www.designcomputing.net/gendex/bib/b10.html
>with E=0.8733 (99.97% of the upper bound) or another
>one she generates with with E=0.8735 or E=0.8730).
>

Hi Nam-Ky,

Does it make much difference? In some cases yes, in others no. A-efficiency is a 
1-dimensional measure of design worthiness that can miss many pertinent aspects 
of design behaviour. Might the collection of contrast variances for one of the 
competing designs be more disperse than that of another? Might one enjoy a clear 
advantage over another in terms of minimizing its worst variance (usually called 
the E-criterion)? Might one be more robust to loss of plots or blocks? Might one 
possess a variance/covariance matrix for treatment effects that better aligns 
with underlying treatment structure than another? These are just some of the 
questions that can be addressed if one has a collection of designs and 
associated criteria values available. 

Putting these questions aside, any one or all three of the designs you mention 
can be in the database, accessible via a few mouse clicks. This seems very smart 
to me. Why ever search more than once? Get the design and store it. If someone 
else wants to come up with a better (in some sense) design, then they can store 
that in the database, too. They will all be there, online, accessible, and free.

Also, let us not forget that this database is about much more than statistical 
aspects of design. It will contain *many* block designs for reasons ranging from 
direct combinatorial interest to the need for a design in the construction of 
other designs to much more. The current external representation lays out the 
basic idea set, which will surely grow and change in the weeks to come.

JP



J P Morgan
Department of Statistics
Virginia Tech