The Annals of Statistics

Some Contributions to the Theory of Multistage Youden Design

K. Afsarinejad and A. Hedayat

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It is shown that complete sets of $(\nu - 1)/2$ by $\nu$ and $(\nu + 1)/2$ by $\nu$ multistage balanced Youden designs of type I and II can be constructed if $\nu$, the number of treatments, is a prime power of the form $4\lambda + 3$. It is also proved that the existence of a difference set with certain properties implies the existence of a 2-stage balanced Youden design. The usefulness of this latter result is demonstrated for those experiments where the number of treatments is not a prime power.

Article information

Ann. Statist., Volume 3, Number 3 (1975), 707-711.

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62K05: Optimal designs
Secondary: 62K10: Block designs 62K15: Factorial designs 05B05: Block designs [See also 51E05, 62K10] 05B10: Difference sets (number-theoretic, group-theoretic, etc.) [See also 11B13] 05B30: Other designs, configurations [See also 51E30]

Multistage experimentation Youden design balanced Youden designs


Afsarinejad, K.; Hedayat, A. Some Contributions to the Theory of Multistage Youden Design. Ann. Statist. 3 (1975), no. 3, 707--711. doi:10.1214/aos/1176343133.

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