ym1 {PBIBD}

The function constructs Youden-m square designs. The function provides the parameters of the PBIB design constituted when the incomplete columns of this Youden-m square are taken as blocks.

Description

If we omit the same number of rows, say t rows, from the top and the bottom of the Circulant matrix, such that we are left with atleast two rows, the resulting arrangement of rows is a Youden-m square.

(A) For even-ordered Circulant matrices with order v >= 4, the columns of the Youden-m squares so obtained constitute the PBIB designs with the following parameters:

v >= 4 and even, b = v, r = k = v-2t

lambda 1 = v - 2(t + 1), lambda m-i = v - 2t - 1 - 2i ; i = 0, 1, ..., t-1

lambda t = lambda t+1 = ... = lambda m-t = v - 4t. If t >=3 then, lambda i = v - 2(t + i); i = 2, 3, ..., t-1

(B)For odd-ordered Circulant matrices with order v >= 5, the columns of the Youden-m squares so obtained constitute the PBIB designs with the following parameters:

v >=5 and odd, b = v, r = k = v-2t

lambda 1 = v - 2t - 1, lambda m-i = v - 2(t + 1) - i; i = 0, 1, ..., t - 1, lambda m-(t-1)-i = lambda m-(t-1) - i ; i = 0, 1, 2, ..., t-1

and lambda 2 = lambda 3= ... = lambda (m-2t+1) = lambda (m-2t+2)

Usage

ym1(n, t)

Arguments

n

n is the order of the circulant matrix which is also the number of treatments

t

t is the number of rows you want to omit from both ends of the circulant matrix

Value

The function returns the required Youden-m square design. It also returns the parameters of the PBIB design constituted by taking the incomplete columns of the Youden-m square as blocks.

Author(s)

Kush Sharma, Davinder Kumar Garg

Examples

ym1(6,1)