
Experimental design  balanced incomplete block designs
Posted:
Nov 30, 1999 5:02 PM


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 telement subset of X is a subset of exactly lamda blocks, lamda>0, & such that k<v. Obviously, a 22(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(vj,tj)  C(kj,tj)
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

