Three-Way and Higher-Order Crossed Classifications
In the preceding two chapters, we considered random models involving two factors. In many fields of research, an investigator often works with experiments or surveys involving more than two factors; which entails simultaneous data collection under conditions determined by several factors. This type of design is usually more economical and can provide more information than separate one-way or two-way layouts. The analysis of variance of the two-way crossed model can be readily extended to situations involving three or more factors. In this chapter, we study random effects models involving three factors in somewhat greater detail. The extension of the model to experiments involving four or more factors is also indicated briefly.
KeywordsVariance Component Exact Confidence Interval Approximate Confidence Interval Closed Form Analytic Expression Uncorrelated Random Variable
Unable to display preview. Download preview PDF.
- C. A. Bennett and N. L. Franklin (1954), Statistical Analysis in Chemistry and the Chemical Industry, Wiley, New York.Google Scholar
- R. K. Burdick (1994), Using confidence intervals to test variance components, J. Qual. Tech., 26, 30–38.Google Scholar
- C. R. Hicks and K. V. Turner (1999), Fundamental Concepts in Design of Experiments, 5th ed., Oxford University Press, Oxford, UK.Google Scholar
- J. D. Hudson and R. G. Krutchkoff (1968), A Monte Carlo investigation of the size and power of test employing Satterthwaite’s synthetic mean squares, Biometrika, 55, 431–433.Google Scholar
- T. J. Lorenzen (1978), A Comparison of Approximate F Tests Under Pooling Rules, Research Publication GMR-5928, Mathematics Department, General Motors Research Laboratories, Warren, MI.Google Scholar
- S. Moriguti (1954), Confidence limits for a variance component, Rep. Statist. Appl. Res. (JUSE), 3, 7–19.Google Scholar