Two-Way Crossed Classification without Interaction
The one-way classification discussed in Chapter 2 involved the levels of only a single factor. It is the simplest model in terms of experimental layout, assumptions, computations, and analyses. However, in many investigations, it is desirable to measure response at combinations of levels of two or more factors considered simultaneously. Two factors are said to be crossed if the data contain observations at each combination of a level of one factor with a level of the other factor. Consider two factors A and B, where a levels are sampled from a large population of levels of A and b levels are sampled from a large population of levels of B, and one observation is made on each of the ab cells. This type of layout is commonly known as the balanced two-way crossed random model with one observation per cell. It can also be viewed as a randomized complete block design where both blocks and treatments are regarded as random.
KeywordsMean Square Error Variance Component Computing Software Approximate Confidence Interval Simultaneous Confidence Interval
Unable to display preview. Download preview PDF.
- D. M. Andrews and A. Herzberg (1985), Data: A Collection of Problems from Many Fields for Students and Research Workers, Springer-Verlag, New York.Google Scholar
- O. L. Davies and P. L. Goldsmith, eds. (1972), Statistical Methods in Research and Production, 4th ed., Oliver and Boyd, Edinburgh.Google Scholar
- J. L. Hodges, Jr. and E. L. Lehmann (1951), Some applications of the Cramér-Rao inequality, in L. Lecam and J. Neyman, Proceedings Second Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, CA, 13–22.Google Scholar
- W. Y. Tan (1965), On the estimation of parameters in the analysis of variance I: Two-way simple random effects model, J. Agricultural Assoc China, 21, 9–18.Google Scholar
- A. J. Weeks (1983), A Genstat Primer, Arnold, London.Google Scholar