On a Problem of Repeated Measurement Design with Treatment Additivity
Laycock, P. J. ; Seiden, E.
Ann. Statist., Tome 8 (1980) no. 1, p. 1284-1292 / Harvested from Project Euclid
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.
Publié le : 1980-11-14
Classification:  Design,  isomorphisms,  equivalence classes,  treatment additivity,  correlation,  optimality,  62K05,  05B05
@article{1176345201,
     author = {Laycock, P. J. and Seiden, E.},
     title = {On a Problem of Repeated Measurement Design with Treatment Additivity},
     journal = {Ann. Statist.},
     volume = {8},
     number = {1},
     year = {1980},
     pages = { 1284-1292},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176345201}
}
Laycock, P. J.; Seiden, E. On a Problem of Repeated Measurement Design with Treatment Additivity. Ann. Statist., Tome 8 (1980) no. 1, pp.  1284-1292. http://gdmltest.u-ga.fr/item/1176345201/