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Globally orthogonal regular fractions of the \(s^ n\) factorial. (English) Zbl 0594.62089

Summary: Dependence of the global orthogonality of a regular fraction of the \(s^ n\) factorial, as introduced by W. T. Federer and the last two authors [Can. J. Stat. 8, 65-77 (1980; Zbl 0445.62089)], on the basic matrix of contrasts used is brought out and studied in this paper. Some basic matrices for \(s=3,4,5,8\), and a series of other higher values are presented for which any subspace-type regular design is globally orthogonal.
For \(s=4\), under suitable basic matrices of contrasts, all regular fractions of the \(4^ n\) factorial are shown to be globally orthogonal. A similar result for \(s=2\) is obtained in the quoted paper. Finally subspace-type fractions that are globally orthogonal under any basic matrix of contrasts are also identified.

MSC:

62K15 Factorial statistical designs
05B15 Orthogonal arrays, Latin squares, Room squares

Citations:

Zbl 0445.62089
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References:

[1] Kiefer, J. 1975.Construction and optimality of generalized Youden designs. A Survey of Statistical Design and Linear Models, 333–353. Amsterdam: North-Holland.
[2] Raghavarao D., Constructions and Combinatorial Problems in Design of Experiments (1971) · Zbl 0222.62036
[3] Raktoe B.L., To appear in Canadian Journal of Statistics 8 (1980)
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