Series2: Tri-Hierarchical IBDs using Latin Square Association Scheme

In Tri.Hierarchical.IBDs: Tri-Hierarchical IBDs (Tri- Hierarchical Incomplete Block Designs)

Tri-Hierarchical IBDs using Latin Square Association Scheme

Description

It generates the Tri-Hierarchical IBDs based on Latin Square association scheme. Here, number of treatments (v) should be a perfect square. We find balanced incomplete block designs (BIBD) at block level and latin square 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

Series2(
  v,
  D1 = FALSE,
  D2 = FALSE,
  D3 = FALSE,
  D4 = FALSE,
  D5 = FALSE,
  D6 = FALSE,
  Randomization = FALSE
)

Arguments

v	Number of treatments, v (>=16) should be a square 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)
Series2(16,D1=TRUE,D2=TRUE,D3=FALSE,D4=FALSE,D5=FALSE,D6=FALSE,Randomization=FALSE)

Tri.Hierarchical.IBDs documentation built on Aug. 10, 2023, 5:06 p.m.