Showing papers on "Orthogonal array published in 1984"
TL;DR: In this paper, the authors present an approach to analysis of variance modeling in designs where all factors are orthogonal, based on formal mathematical definitions of concepts related to factors and experimental designs.
Abstract: Summary This paper presents an approach to analysis of variance modelling in designs where all factors are orthogonal, based on formal mathematical definitions of concepts related to factors and experimental designs. The structure of an orthogonal design is described by a factor structure diagram containing the information about nestedness relations between the factors. An orthogonal design determines a unique decomposition of the observation space as a direct sum of orthogonal subspaces, one for each factor of the design. A class of well-behaved variance component models, stated in terms of fixed and random effects of factors from a given design, is characterized, and the solutions to problems of estimation and hypothesis testing within this class are given in terms of the factor structure diagram and the analysis of variance table induced by the decomposition.
104 citations
TL;DR: In this paper, a general method for constructing quasi-complete Latin squares based on groups is given, and an explicit construction for valid randomization sets of quasicomplete Latin squares whose side is an odd prime power is given.
Abstract: SUMMARY A general method for constructing quasi-complete Latin squares based on groups is given. This method leads to a relatively straightforward way of counting the number of inequivalent quasi-complete Latin squares of side at most 9. Randomization of such designs is discussed, and an explicit construction for valid randomization sets of quasicomplete Latin squares whose side is an odd prime power is given. It is shown that, contrary to common belief, randomization using a subset of all possible quasicomplete Latin squares may be valid while that using the whole set is not.
83 citations
TL;DR: This work gives a short, self-contained noncomputer proof which requires a minimum of casework of the nonexistence of a pair of orthogonal Latin squares of order six.
60 citations
TL;DR: In this paper, it was shown that ODLS(n) exist for all n except n = 2, 3, 6, 10, 14, 15, 18 and 26, in which the first three are impossible.
Abstract: Orthogonal diagonal latin squares of order n, ODLS(n) , are orthogonal latin squares of order n with transversals on both the main diagonal and the back diagonal of each square. It has been proven that ODLS(n) exist for all n except n = 2, 3, 6, 10, 14, 15, 18 and 26, in which the first three are impossible. In this note an example of ODLS (14) is given.
4 citations
TL;DR: In this paper, a cyclic Latin square of order 2n, which has no orthogonal Latin square mate, was shown to have (2n−1) mutually orthogonality F(2n; 2n− 1,2n − 1)-squares.
3 citations
TL;DR: In this paper, six statistical analyses are presented for a pair of mutually orthogonal latin square experiment designs and a set of mutually balanced Youden experiment designs, and the results are generalized for t mutually Orthogonal Latin Square experiment designs.
Abstract: Suppose that t experiments are conducted simultaneously on the same set of experimental units. For example, suppose that t mutually orthogonal latin square experiment designs are used for the t experiments on n2 experimental units. Statistical literature is voluminous on construction of such designs, but contains relatively little and incomplete results on statistical analyses for such designs. Six statistical analyses are presented for a pair of orthogonal latin square experiment designs. Then, the methods are generalized for t mutually orthogonal experiment designs. The results are also extended to a set of t mutually balanced Youden experiment designs.
1 citations
TL;DR: In this article, a Bose-Chakravarti-Knuth method for constructing sets of mutually kn-orthogonal n×m latin rectangles was proposed.
Abstract: Generalizing a Bose-Chakravarti-Knuth’s method of constructing sets of mutually orthogonal latin squares [3], we give a method of constructing sets of mutually kn-orthogonal latin squares of order n with 1