ym1 | R Documentation |
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
, for i = 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)
for i = 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
, for i = 0, 1, \ldots, t - 1
\lambda_{m - (t - 1) - i} = \lambda_{m - (t - 1)} - i
, for i = 0, 1, \ldots, t - 1
\lambda_2 = \lambda_3 = \ldots = \lambda_{m - 2t + 1} = \lambda_{m - 2t + 2}
ym1(n, t)
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. |
The function returns the Youden-m square design and the parameters of the PBIB design formed by taking its incomplete columns as blocks.
Kush Sharma, Davinder Kumar Garg
ym1(6, 1)
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