Cox D.R., Solomon P.J. Components of Variance

New York: Chapman and Hall/CRC, 2002. — 181 p.The notion that haphazard variation may arise from a number of sources and that it may be valuable to identify these sources and measure their impact has a long history and many applications and implications. Indeed. it is only in very simple situations that it is likely to be satisfactory to represent haphazard variation by independent identically distributed random variables or by the essentially equivalent notion of random sampling from a hypothetical infinite population.
The statistical ideas. models and methods associated with structured haphazard variability arose in industrial applications especially in the textile industries via the work in the 1930s in the cotton industry by L.H.C.Tippett and in the wool industries by H.E. Daniels. In those industries producing very uniform output from very variable input is a key issue. It was in this setting that one of the authors (DRC) first encountered components of variance. The other author (PJS) met them in the context of the variation of blood pressure and other features in large clinical trials. There are. of course, many other applications, of which biometrical genetics. animal and plant breeding and psychometric testing are important examples.Key Models and Concepts
One-Way Balanced Case
More General Balanced Arrangements
Unbalanced Situations
Discrete Data
Non-Normal Data
Model extensions and Criticism
Appendix
References.