DOE- BIBD Flashcards
(10 cards)
IBD
Incomplete Block Design
The number of experimental units or plots in a block is smaller than the number of treatments
it is one having
‘v’ treatments
‘b’ blocks
‘k’ size of block
‘r’ number of replication of treatments
each pair of treatments occurs once and only once in each block
k<t
BIBD
Balanced Incomplete Block Design
An arrangement of
‘v’ treatments in
‘b’ blocks where
‘k’ size of block and
‘r’ number of replication of treatments
k<v
i) each treatment occurs once and only once in each block
ii) each treatment pair occurs together in lambda blocks
when is BIBD used?
when all treatment comparisons are equally important as it ensures equal precision of the estimate of all pairs of treatment effects
3 necessary conditions for BIBD
vr = bk
λ(v-1) = r(k-1)
b >= v (Fishers inequality)
Incidence matrix
BIBD is sometimes also called
Binary design
because nij can only take values 0 or 1 in incidence matrix
Different types of BIBD
- Symmetric BIBD b=v and r=k
- Resolvable BIBD - sets b/r
- Affine Resolvable BIBD - sets b=v+r-1 k^2/v
- Complimentary BIBD
- Residual Design - symmetric first
- Derived Design - symmetric first
Defining Contrast
a contrast which is used to split a replicate into a divisible fraction
Alias
Aliases are the generalised interactions of an effect with the defining contrasts.
idea of fractional factorial through an example
consider 2^3 factorial exp
conduct the exp with 1/2 replicate
having the treatment combinations of positive signs in the contrast for the interaction ABC
From the exp results, the main effects and the interactions can be delineated as given below
table
treatment combinations | main effects and interactions
above set of contrasts, we reveal the following points
1) defining contrasts definition - ABC is the one in table
2) aliases definition - show from table
