ym3: Constructs Youden-m square designs and provides parameters of...

In PBIBD: Partially Balanced Incomplete Block Designs

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 for i = 2, 3, \ldots, t + 2

• If m > 3, then \lambda_j = \lambda_{j - 1} + 1 for j = 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)

PBIBD documentation built on June 8, 2025, 10:10 a.m.