Factorial experimental designs. Construction and properties of fractions of designs
This monograph is dedicated to the construction and to the properties of (fractional) experimental designs for factorial experiments, i.e. for experimental situations with several factors of influence each of which can be adjusted to a few different levels. According to the preface the book aims at making precise which statistical arguments permit to justify the use of certain designs compared to others. Consequently, the approach chosen is directed towards algebraic and combinatorial methods and it is motivated by identifiability (estimability) considerations and statistical optimality criteria. Each of the six chapters on 1. Linear models and orthogonal designs, 2. Models for factorial experiments, 3. Fractional factorial designs of resolution \(R\), 4. Construction of orthogonal fractions of resolution \(III\), 5. Regular fractions, and 6. Optimal fractions, is augmented by a bibliography, separately, which makes them to self-contained units. The interrelations are indicated by a common subject index and a list of symbols. To take full advantage of the results presented some additional familiarity is required with the notions used. In view of the amount of material included the book is a valuable source for solving design problems in high-dimensional (factorial) experiments. Special emphasis is laid on orthogonal designs (proportional designs) which are characterized by having joint frequencies, for level combinations up to an appropriate order, proportional to the marginal frequencies for the levels of the single factors of influence. This concept covers, in particular, the narrow definition of orthogonal arrays and allows an extension of their favourable properties to model situations with varying numbers of levels and more general (hierarchical) interaction structures.
scientific article; zbMATH DE number 837319