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Topic: Experimental design - balanced incomplete block designs
Replies: 1   Last Post: Dec 1, 1999 1:48 AM

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Kathleen

Posts: 58
Registered: 12/6/04
Experimental design - balanced incomplete block designs
Posted: Nov 30, 1999 5:02 PM
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I don't understand this material :( Could anyone help please? Or at
least recommend a good book on this sort of material so that I could
go and read it (& hope fore some quick enlightenment before my final)

For instance this is a exercise out of our text book that our prof
said we should be capable of doing ... I tried it and ended up with
something very wrong. As I said at the start of this post, I don't
understand this material ... I like the recurrence relations better.

In any event here is the qn:

It says if t >= 2, a t-(b,v,r,k,lamda) -design consists of a set X of
v >= 2 varieties, & a collection of b>0 subsets of X called blocks,
such that each block consists of exactly the same # k of varieties,
k>0, & each variety appears in exactly the same # r of blocks, r>0,
such that every t-element subset of X is a subset of exactly lamda
blocks, lamda>0, & such that k<v. Obviously, a 2-2-(b,v,r,k,lamda)
-design is a (b,v,r,k,lamda)-design.

Now the qn part asks us to suppose that x_(i_1), x_(i_2), ..., x_(i_t)
are t distinct varieties of a t-(b,v,r,k,lamda) -design. For 1=<j=<t
let lamda_j be the number of blocks containing x_(i_1), x_(i_2), ...,
x_(i_j). Let lamda_0 = b. Show that for 0=<j=<t,

lamda_j = lamda * C(v-j,t-j)
-----------------
C(k-j,t-j)

and conlude that lamda_j is independent of the choice of x_(i_1),
x_(i_2), ..., x_(i_j). Hence, conclude that for all 1=<j=<t, a
t-(b,v,r,k,lamda) -design is also a j-(b,v,r,k,lamda) -design.



Okay, way too much there .. I think I'm being completely overwhelmed
by all of this stuff. Any assistance would be a great help.

Thank you,
Kathleen





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