ym1 {PBIBD} | R Documentation |
Constructs Youden-m square designs and provides parameters of the corresponding PBIB design
Description
If the same number of rows, say t
, are omitted from the top and bottom of a Circulant matrix such that at least two rows remain, the resulting arrangement forms a Youden-m square.
(A) For even-ordered Circulant matrices (order v \geq 4
and even), the columns of the resulting Youden-m square constitute a PBIB design with parameters:
-
b = v
,r = k = v - 2t
-
\lambda_1 = v - 2(t + 1)
-
\lambda_{m - i} = v - 2t - 1 - 2i
, fori = 0, 1, \ldots, t - 1
-
\lambda_t = \lambda_{t+1} = \ldots = \lambda_{m - t} = v - 4t
If
t \geq 3
, then\lambda_i = v - 2(t + i)
fori = 2, 3, \ldots, t - 1
(B) For odd-ordered Circulant matrices (order v \geq 5
and odd), the columns of the resulting Youden-m square constitute a PBIB design with parameters:
-
b = v
,r = k = v - 2t
-
\lambda_1 = v - 2t - 1
-
\lambda_{m - i} = v - 2(t + 1) - i
, fori = 0, 1, \ldots, t - 1
-
\lambda_{m - (t - 1) - i} = \lambda_{m - (t - 1)} - i
, fori = 0, 1, \ldots, t - 1
-
\lambda_2 = \lambda_3 = \ldots = \lambda_{m - 2t + 1} = \lambda_{m - 2t + 2}
Usage
ym1(n, t)
Arguments
n |
Order of the circulant matrix, which is also the number of treatments. |
t |
Number of rows to omit from both the top and bottom of the circulant matrix. |
Value
The function returns the Youden-m square design and the parameters of the PBIB design formed by taking its incomplete columns as blocks.
Author(s)
Kush Sharma, Davinder Kumar Garg
Examples
ym1(6, 1)