The earliest important papers on planned experiments in Biometrika appeared within a year of each other in 1917 and 1918. Roughly speaking, one was concerned with design optimality and industrial experiments, the other with agricultural trials and blocking. We find this approximate division of the subject into two parts helpful in describing its development and growth. As a result of the hostility between Fisher and Karl Pearson, much of the development of designs for agriculture in the 1920s and 1930s occurred off the pages of Biometrika. Despite this, we are able to trace a coherent history of the development of the subject from field trials and response surface methods to clinical trials and Bayesian versions of design optimality.

One hundred years of the design of experiments on and off the pages of Biometrika

https://digitalcommons.odu.edu/cgi/viewcontent.cgi?article=1088&context=mathstat_fac_pubs

Nested balanced incomplete block designs

SUMMARY A general method for constructing balanced incomplete-block designs with nested rows and columns is presented. Many designs are obtained in which none of the treatmentblock, treatment-row and treatment-column incidence matrices is the incidence matrix of a balanced incomplete-block design. If the method of construction is applied to a generally balanced design, then the resulting design is also generally balanced.

A method for constructing balanced incomplete-block designs with nested rows and columns

Optimality and construction of nested row and column designs

SUMMARY A method of construction of balanced incomplete block designs with nested rows and columns is developed using difference techniques, from which many infinite series of designs are obtained.

Some constructions for balanced incomplete block designs with nested rows and columns

SUMMARY A number of methods of construction of balanced incomplete block designs with nested rows and columns are developed using the method of differences.

Some methods of construction of balanced incomplete block designs with nested rows and columns

Summary

A number of methods of construction of GD-RC and RectanguIar-RC designs, based upon the series A of BIB-RC designs, using the method of Kronecker product, are developed.

Some Methods of Construction of Gd‐Rc and Rectangular‐rc Designs

A number of methods of construction of PBIB-RC designs, based upon the method of differences, are developed.

On Nested Row-Column Partially Balanced Incomplete Block Designs

Designs for two-way elimination of heterogeneity are of fundamental importance. Any tlu·ee factor additive design is defined to be a design for two-way elimination of heterogeneity. Methods of construction of these designs have been considered by Shrikhande [1951], Youden [1937], Potthoff [1962], Shrivastava and Anderson [1971], Agrawal [1966(a),(b),(c),(d),(e)], Agrawal and Sharma [1975]. In this paper methods of construction of two-way designs based upon the series of BIB design v = 4t+ 1, b = 2v, 1' = 4t, k = 2t, A = 2t-1 are given, analyses of the designs are included as well. The notation followed are that of AgTawal [1966(a)]. In section 2 some theorems based on the BIB design v = 4t+1 (prime power), b = 2v, 1' = -4t, k = 2t, A= 2t-1 are proved. In section 3 various methods of construction of two-way designs along with their analyses based on these theorems are given. The basic advantage of these methods is that the designs so obtv,ined are either balanced or partially balanced and require lesser number of observations.

On Construction of a Series of Two-Way Designs:

INTRODUCTION AND SuMMARY. Four diamentional incomplete block design (4 DIB) is a four factor additive design in which the four factors are at m, n, p, and q levels respectively and the total number of observations his some fractional part of mnpq, where h=~ ~ ~ ~ hcJkl and hcJtzis the number of I j k I observation taken on factorcombination(i,j, k, I); i,j = 1,2, ... , m; k = 1, 2, ... p; I= 1, 2, ... , q. The assumption of additivity means that there are no interections among any of the four factors; all interections are absent. The analysis of these designs have been censidered by Potthoff (1962 & 1963). Some methods of construction of these designs are considered in Potthoff (1963), Agrawal and Mishra (1971) and Agrawal and Sharma (1973). In this paper a general class of 4 DIB designs is constructed and it is further shown that these designs are balanced or partially balanced for at least three of the four factors. The notation followed are taken from Potthoff (1962 & 1963) e.g. H1, denotes marginal matrix; H 2, (n x q) contains the h.j.!'s where h.J-1 = ~hf1t1 ; '· k H 18(m x p) contains hc.t.'s; H 84 (p x q) contains the h .. t,'s and so forth. H 4z (q X n) is the transpose of H 24• 2. METHOD OF CONSTRUCTION

H. L. Agrawal

Papers

Some methods of construction of balanced incomplete block designs with nested rows and columns

Some Methods of Construction of Gd‐Rc and Rectangular‐rc Designs

On Nested Row-Column Partially Balanced Incomplete Block Designs

On Construction of a Series of Two-Way Designs:

A Method of Construction of 4 DIB Designs