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A Calculus for Factorial Arrangements (Paperback, Softcover reprint of the original 1st ed. 1989)
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A Calculus for Factorial Arrangements (Paperback, Softcover reprint of the original 1st ed. 1989)
Series: Lecture Notes in Statistics, 59
Expected to ship within 10 - 15 working days
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Factorial designs were introduced and popularized by Fisher (1935).
Among the early authors, Yates (1937) considered both symmetric and
asymmetric factorial designs. Bose and Kishen (1940) and Bose
(1947) developed a mathematical theory for symmetric
priIi't&-powered factorials while Nair and Roo (1941, 1942,
1948) introduced and explored balanced confounded designs for the
asymmetric case. Since then, over the last four decades, there has
been a rapid growth of research in factorial designs and a
considerable interest is still continuing. Kurkjian and Zelen
(1962, 1963) introduced a tensor calculus for factorial
arrangements which, as pointed out by Federer (1980), represents a
powerful statistical analytic tool in the context of factorial
designs. Kurkjian and Zelen (1963) gave the analysis of block
designs using the calculus and Zelen and Federer (1964) applied it
to the analysis of designs with two-way elimination of
heterogeneity. Zelen and Federer (1965) used the calculus for the
analysis of designs having several classifications with unequal
replications, no empty cells and with all the interactions present.
Federer and Zelen (1966) considered applications of the calculus
for factorial experiments when the treatments are not all equally
replicated, and Paik and Federer (1974) provided extensions to when
some of the treatment combinations are not included in the
experiment. The calculus, which involves the use of Kronecker
products of matrices, is extremely helpful in deriving
characterizations, in a compact form, for various important
features like balance and orthogonality in a general multifactor
setting.
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