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Theory & Methods: Cross‐over Designs in the Presence of Higher Order Carry‐overs
Author(s) -
Bose Mausumi,
Mukherjee Bhramar
Publication year - 2000
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00121
Subject(s) - carry (investment) , mathematics , order (exchange) , class (philosophy) , optimal design , mathematical optimization , econometrics , statistics , computer science , artificial intelligence , finance , economics
In cross‐over experiments, where different treatments are applied successively to the same experimental unit over a number of time periods, it is often expected that a treatment has a carry‐over effect in one or more periods following its period of application. The effect of interaction between the treatments in the successive periods may also affect the response. However, it seems that all systematic studies of the optimality properties of cross‐over designs have been done under models where carry‐over effects are assumed to persist for only one subsequent period. This paper proposes a model which allows for the possible presence of carry‐over effects up to k subsequent periods, together with all the interactions between treatments applied atk + 1 successive periods. This model allows the practitioner to choosek for any experiment according to the requirements of that particular experiment. Under this model, the cross‐over designs are studied and the class of optimal designs is obtained. A method of constructing these optimal designs is also given.