ym3 {PBIBD} | R Documentation |
Constructs Youden-m square designs and provides parameters of the corresponding PBIB design
Description
This function constructs a Youden-m square by omitting the middle row and an equal number of rows t
from both ends of an odd-ordered Circulant matrix of order v \geq 7
. The rows retained lie between the middle omitted row and the omitted rows from the top or bottom. This arrangement yields a Youden-m square suitable for two-way elimination of heterogeneity.
The columns of this Youden-m square constitute a PBIB design with the following parameters:
-
v \geq 7
and odd -
b = v
,r = k = \left( \frac{v + 1}{2} \right) - 1 - t
-
\lambda_1 = v - 6 - (m - 4 + t)
-
\lambda_i = 0
fori = 2, 3, \ldots, t + 2
If
m > 3
, then\lambda_j = \lambda_{j - 1} + 1
forj = t + 3, t + 4, \ldots, m
Usage
ym3(n, t)
Arguments
n |
Order of the circulant matrix, which is also the number of treatments. |
t |
Number of rows to omit from both ends of the circulant matrix. |
Value
The function returns the constructed Youden-m square design and the parameters of the PBIB design obtained by treating the incomplete columns of the square as blocks.
Author(s)
Kush Sharma, Davinder Kumar Garg
Examples
ym3(7, 1)