Balanced Factorial Experiments
Shah, B. V.
Ann. Math. Statist., Tome 31 (1960) no. 4, p. 502-514 / Harvested from Project Euclid
Usually, in a factorial experiment, the block size of the experiments is not large enough to permit all possible treatment combinations to be included in a block. Hence we resort to the theory of confounding. With respect to symmetric factorial designs, the theory of confounding has been highly developed by Bose [1], Bose and Kishen [2] and Fisher [4], [5]. An excellent summary of the results of this research appears in Kempthorne [6]. Some examples of asymmetric factorial designs can be found in Yates [14], Cochran and Cox [3], Li [8], Kempthorne [6] and Nair and Rao [9], [10]. Nair and Rao [11] have given the statistical analysis of a class of asymmetrical two-factor designs in considerable detail. The author [13] has considered the problem of achieving "complete balance" over various interactions in factorial experiments. In the present paper a class of factorial experiments, balanced factorial experiments (BFE) (Definition 4.2) is considered. The theorems proved in Section 4 outline a detailed analysis of BFE's, including estimates of various interactions at different levels. Finally, a method of constructing BFE's is given in Section 6. It should be noted that Theorems 5.2 to 5.5 are generalisations of the corresponding theorems by Zelen [15], and the method of construction in Section 6 is a general form of the one indicated by Yates [14], Nair and Rao [9], [10] and Kempthorne [6] (Section 18.7).
Publié le : 1960-06-14
Classification: 
@article{1177705917,
     author = {Shah, B. V.},
     title = {Balanced Factorial Experiments},
     journal = {Ann. Math. Statist.},
     volume = {31},
     number = {4},
     year = {1960},
     pages = { 502-514},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177705917}
}
Shah, B. V. Balanced Factorial Experiments. Ann. Math. Statist., Tome 31 (1960) no. 4, pp.  502-514. http://gdmltest.u-ga.fr/item/1177705917/