## The Annals of Statistics

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

### Some Contributions to the Theory of Multistage Youden Design

#### Abstract

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

**Source**

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

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176343133

**Digital Object Identifier**

doi:10.1214/aos/1176343133

**Mathematical Reviews number (MathSciNet)**

MR391424

**Zentralblatt MATH identifier**

0303.62061

**JSTOR**

links.jstor.org

**Subjects**

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]

**Keywords**

Multistage experimentation Youden design balanced Youden designs

#### Citation

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. https://projecteuclid.org/euclid.aos/1176343133