Randomization for a Balance Superimposition of one Youden Square on Another

Bailey, R.A. and Preece, D.A. and Rowley, C.A. (1995) Randomization for a Balance Superimposition of one Youden Square on Another. Journal of the Royal Statistical Society Series B-Methodological, 57 (2). pp. 459-469. ISSN 0035-9246. (The full text of this publication is not available from this repository)

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Abstract

Some experimentation, particularly on trees in orchards, requires the superimposition Of a new set of treatments on an existing experiment, on the assumption that the effects of the new treatments do not interact with those of the old. Different approaches to the randomization of such new treatments were considered by Preece, Bailey and Patterson, who investigated in detail the case when one Latin square is superimposed on another to produce a Graeco-Latin square. For non-orthogonal superimpositions the theory is in general much more complicated. However, this paper shows that fairly simple randomization results are obtainable for certain balanced superimpositions of one Youden square on another (i) when each Youden square is of size (t - 1) x t and (ii) when each Youden square is of size k x t, where t is a prime power of the form 4s - 1 and k = 2s - 1 or k = 2s. In each case, t is the number of treatments in each Youden square. The valid randomization procedure obtained for the second case is unlike any previously known randomization procedure and is unlikely to be acceptable in practice; it is, however, an excellent indication of the difficulties that arise when randomization is attempted in unusual circumstances.

Item Type: Article
Uncontrolled keywords: BALANCED INCOMPLETE-BLOCK DESIGNS; CYCLIC DESIGNS; DESIGNS FOR 2 NONINTERACTING SETS OF TREATMENTS; EFFICIENCY; RANDOMIZATION; SUCCESSIVE EXPERIMENTS ON SAME MATERIAL; VALIDITY
Subjects: H Social Sciences > HA Statistics
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Statistics
Depositing User: P. Ogbuji
Date Deposited: 08 Jun 2009 17:05
Last Modified: 08 May 2012 13:03
Resource URI: http://kar.kent.ac.uk/id/eprint/19682 (The current URI for this page, for reference purposes)
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