https://rss.onlinelibrary.wiley.com/doi/pdf/10.2307/2982800

The Non-Orthogonal Design of Experiments

In this paper, we have proposed a type of arrangement that we call Youden-m square and is similar to the usual Youden square but generates PBIB designs instead of BIB designs when its columns are t...

m-Associate PBIB designs using Youden-m squares

J. N. Srivastava and experimental design

A class of multidimensional designs is presented for factorial experiments with two treatment factors and two or more orthogonal blocking factors. We assume that interactions between all factors, except for the two treatment factors, are negligible. A table of efficient three-dimensional designs is given together with tables of component designs that can be used to construct two-, three-, or higher-dimensional designs. All the multidimensional designs considered in this article have d > 2 crossed orthogonal blocking factors and exactly one treatment combination observed at each combination of levels of the blocking factors. They are constructed by amalgamating one-dimensional generalized cyclic designs with known properties. The purpose of this article is to increase the availability of multidimensional designs, three-dimensional designs in particular. Our main objective is to achieve efficient estimation of the factorial effects via least squares estimators that are uncorrelated after adjustment...

Multidimensional designs for two-factor experiments

Often several other factors potentially contribute to the variability of the observed response in addition to the treatments or factors under investigation. For example, gender, age, and center may also affect the blood pressure of patients in a placebo-controlled hypertensive clinical trial. The technique of blocking is used to control the experimental error variation due to these types of extraneous sources. Two sources can be controlled using a Youden square or a row–column design, the rows and columns comprising two different systems of blocking. This article provides the details for the least squares analysis of these designs. Designs having variance balance, supplemented balance, row-orthogonality, adjusted-orthogonality, designs for factorial experiments, and computer algorithms for constructing designs are also briefly discussed.


Keywords:

balanced incomplete block design;
block design;
complete block design;
incomplete block design;
Latin square design;
row–column design;
variance balance;
Youden square design

Youden Squares and Row–Column Designs

SUMMARY Balanced factorial designs which permit two-way elimination of heterogeneity are defined, and the combinatorial conditions for such designs are derived. Methods of constructing two-way balanced factorial designs are given. In particular, for s a prime power and > 3, a method is given to construct an s x s balanced factorial design with s(s -1) columns and s(s -1) rows such that none of the main effects is confounded with either row effects or column effects.

Chung-Yi Suen

Papers

Balanced factorial designs with two-way elimination of heterogeneity