The Annals of Statistics

On a Problem of Repeated Measurement Design with Treatment Additivity

P. J. Laycock and E. Seiden

Full-text: Open access


We consider an experimental design problem in which $n$ treatments are applied successively to each experimental unit, and once applied their effects are permanent. To examine all $2^n - 1$ treatments combinations, a minimum of $\binom{n}{\big\lbrack \frac{n}{2} \big\rbrack}$ experimental units is both required and sufficient. A linear model is described and the first nontrivial case, $n = 4$, is examined in detail. It is shown that there are 24 nonisomorphic designs which reduce to 13 under the assumption of no interaction between the treatments. A serial correlation model is considered and the D, A and E, optimality criteria evaluated for $\rho = 0, 0.5$ and 0.75. Possible uses for the design automorphisms are then considered.

Article information

Ann. Statist., Volume 8, Number 6 (1980), 1284-1292.

First available in Project Euclid: 12 April 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62K05: Optimal designs
Secondary: 05B05: Block designs [See also 51E05, 62K10]

Design isomorphisms equivalence classes treatment additivity correlation optimality


Laycock, P. J.; Seiden, E. On a Problem of Repeated Measurement Design with Treatment Additivity. Ann. Statist. 8 (1980), no. 6, 1284--1292. doi:10.1214/aos/1176345201.

Export citation