Three-Factor Additive Designs More General Than the Latin Square
TL;DR: In this paper, a class of designs for the case of three factors at levels m, n and p were described for which the total number of experiments required is a fraction of mnp.
Abstract: A class of designs are described for the case of three factors at levels m, n and p respectively for which the total number of experiments required is a fraction of mnp.
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01 May 1963
77 citations
01 Jan 1963
TL;DR: In this paper, the authors introduce a class of multidimensional designs under the model of additivity of factorial effects which involve partial balance, and apply the theory so developed to the problem of analysing irregular fractions of oertain kinds.
Abstract: The purpose of this paper is three fold. The first one is to introduce a class of multidimensional designs (under the model of additivity of factorial effects) which involve partial balance. The next purpose is to examine closely the pattern in the matrices which one has to invert in order to carry out the analysis. The third aim is to apply the theory so developed to the problem of analysing irregular fractions of oertain kinds.
48 citations
01 Jan 1969
44 citations
TL;DR: In this article, a simple 0: OT: OTT (0: OP: OPP) is proposed for the simultaneous estimation of the effects of two noninteracting sets of treatments, with two-way elimination of heterogeneity.
Abstract: This paper provides some new, simple designs for the simultaneous estimation of the effects of two non-interacting sets of treatments, with two-way elimination of heterogeneity. The designs are suitable for use when a new set of treatments is to be applied to experimental material which may still be affected by an eailier set of treatments. One type of design, obtained by omitting a row or rows from a GraecoLatin square of order t, has each set arranged in a t X k Youden square design, t > k; this type is 0: OT: OTT, in the notation of Pearce [1963], and includes series of designs for which t is a prime of the form (4n + 3) and k = l(t 1 1). Closely related X L(t zL 1) 0: OP: OPP designs, for which t is a prime of the form (4n + 1), are also described and discussed. A further type of design, first discussed by Clarke [1963], is for one set of t treatments arranged in a t X k Youden square design, and one set of k treatments; 7 X 3 and 11 X 5 designs of this 0: OT: TOO type are given for the first time.
43 citations
TL;DR: In this article, the authors describe and list block designs for two non-interacting sets of treatments, where each set of treatments is arranged relative to blocks in a non-symmetrical balanced incomplete block design.
Abstract: 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 balanced 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.
27 citations
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