Series3 {Tri.Hierarchical.IBDs}

Tri-Hierarchical IBDs using Rectangular Association Scheme

Description

This function provides the Tri-Hierarchical IBDs based on Rectangular association scheme. Here, v= m*n, v should be composite number and (m,n)>=3. We find balanced incomplete block designs (BIBD) at block level and rectangular PBIB designs at sub-block level as well as sub-sub block level. Information matrix pertaining to the estimation of treatments effects, canonical efficiency factor in comparison to an orthogonal design and six component designs are provided.

Usage

Series3(
  m,
  n,
  D1 = FALSE,
  D2 = FALSE,
  D3 = FALSE,
  D4 = FALSE,
  D5 = FALSE,
  D6 = FALSE,
  Randomization = FALSE
)

Arguments

m

Any integer >=3

n

Any integer >=3

D1

Bi-Hierarchical IBD by ignoring blocks

D2

Bi-Hierarchical IBD by ignoring sub-blocks

D3

Bi-Hierarchical IBD by ignoring sub-sub blocks

D4

IBD at block level

D5

IBD at sub block level

D6

IBD at sub-sub block level

Randomization

Randomization of layout of the designs if needed enter TRUE; by default it is FALSE.

Value

It gives Tri-HIB design and six component designs with canonical efficiency factor in comparison to an orthogonal design.

Note

Numbers in the outer most parentheses represents as block elements, second level parentheses as sub block elements and inner most parentheses as sub-sub block elements.

References

Preece, D.A. (1967) <https://doi.org/10.1093/biomet/54.3-4.479>."Nested balanced incomplete block designs".

Examples

library(Tri.Hierarchical.IBDs)
Series3(4,3,D1=TRUE,D2=TRUE, D3=TRUE, D4=TRUE,D5=FALSE,D6=TRUE,Randomization=TRUE)