## The Annals of Statistics

### On a Problem of Repeated Measurement Design with Treatment Additivity

#### Abstract

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

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

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176345201

Digital Object Identifier
doi:10.1214/aos/1176345201

Mathematical Reviews number (MathSciNet)
MR594645

Zentralblatt MATH identifier
0481.62060

JSTOR