JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARYIn this paper we consider the problem of sequentially applying v treatments to n experimental units over time or space where there may be an unknown trend effect which can be expressed as a polynomial function of the order in which the observations are taken. A method is given for constructing ordered applications of treatments to experimental units which produce easily computed and optimal estimates for treatment differences that are orthogonal to the unknown trend effect.Some key words: A-optimal; Run order; Treatment; Trend free.

Row-column design, block design, incidence matrix, balanced unequal block design,

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