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Biometrika 1966 53(3-4):497-506; doi:10.1093/biomet/53.3-4.497
© 1966 by Biometrika Trust
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Some balanced incomplete block designs for two sets of treatments

D. A. PREECE

Rothamsted Experimental Station

This paper describes and lists certain block designs for two non-interacting sets of treatments. The designs have the following properties: (a) each set of treatments is arranged relative to blocks in a non-symmetrical balanced incomplete block design, the same blanaced incomplete block solution being used for both sets of treatments; (b) each set of treatments is totally balanced with respect to the other, i.e. each is disposed relative to the other in the same way that treatments are disposed relative to blocks in a balanced incomplete block design; (c) the number of replications of each treatment of each set is either one more than or one fewer than the number of treatments in the set; and (d) the designs are balanced, in the sense that the variance of an estimated difference in effect between two treatments from the same set is independent of the treatments compared.


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