Balanced Incomplete Block Designs (BIBD)

Experimental Design in R

Joanne Xiong

Data Scientist

Balanced Incomplete Block Designs

  • Balanced - each pair of treatments occur together in a block an equal number of times

  • Incomplete - not every treatment will appear in every block

  • Block - experimental groups are blocked to be similar (e.g. by sex)

  • Design - this is your experiment!

Experimental Design in R

Is there a BIBD? - Part 1

  • Let:

    • t = # of treatments
    • k = # of treatments per block

    • r = # replications

    • $\lambda = r \times \dfrac{(k-1)}{t-1}$

  • $\lambda$ is whole number? There is a BIBD!

Experimental Design in R

Is there a BIBD? - Part 2

library(agricolae)
trt <- c("A","B","C","D")
k <- 3
my_design <- design.bib(trt,k,seed = 42)

Parameters BIB
==============
Lambda     : 2
treatmeans : 4
Block size : 3
Blocks     : 4
Replication: 3
Experimental Design in R

BIBD examples (1)

$\lambda = r \times \dfrac{(k-1)}{t-1}$

lambda = 2 * (2-1) / 4-1
lambda = 2/3 # = 0.667
Experimental Design in R

Invalid BIBD

alt text

Experimental Design in R

BIBD examples (2)

$\lambda = r \times \dfrac{(k-1)}{t-1}$

lambda = 3 * (3-1) / 4-1

lambda = 6/3 # = 2
Experimental Design in R

Valid BIBD

alt text

Experimental Design in R

Let's practice!

Experimental Design in R

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