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Biometrika 1970 57(3):537-549; doi:10.1093/biomet/57.3.537
© 1970 by Biometrika Trust
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Nonadditivity in change-over designs for a quantitative factor at four levels

H. D. PATTERSON

A.R.C. Unit of Statistics, University of Edinburgh

Some problems in the design of change-over trials when (i) the treatments are four equally spaced levels of a single treatment factor; (ii) estimates are required of linear direct x linear first residual interaction as well as direct effects and residual effects; and (iii) second, third, etc., residual effects are negligible are reviewed. Designs considered include (a) designs for eight periods and sixteen subjects constructed by the method described by Berenblut (1964), (b) additional designs for eight periods and sixteen subjects related to designs (a) but constructed by a different method, (c) designs as in (a) and (b) but with the subjects in blocks of four or eight, and (d) the design for four periods and eight subjects described by Berenblut (1967b). These designs are shown to vary widely in efficiency of estimation of linear direct x linear first residual interaction. The most efficient designs are listed.


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