Series4 {Tri.Hierarchical.IBDs}

Tri-Hierarchical IBDs using Initial Block Solution

Description

This function gives Tri-Hierarchical IBDs using initial sequences. Here, v = 4t+1 or 4t+3, where t is an integer and v should be a prime number, using primitive element of Galois field designs are generated. We find balanced incomplete block designs (BIBD) at block level and PBIB designs at sub-block level as well as sub-sub block level with circular association scheme. 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

Series4(
  v,
  D1 = FALSE,
  D2 = FALSE,
  D3 = FALSE,
  D4 = FALSE,
  D5 = FALSE,
  D6 = FALSE,
  Randomization = FALSE
)

Arguments

v

Number of treatments, (11 <= v < 200) a prime number

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)
Series4(13,D1=FALSE,D2=FALSE,D3=TRUE,D4=TRUE,D5=FALSE,D6=TRUE,Randomization=TRUE)