Analysis of Factorial Experiments Using Generalized Matrix Operations

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Analysis of Factorial Experiments Using Generalized Matrix Operations

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Journal of the ACM (JACM) archive
Volume 14 , Issue 3 (July 1967) table of contents

Pages: 508 - 519

Year of Publication: 1967

ISSN:0004-5411

Author

I. Oliver

Computer Center, Ohio State University, Columbus, Ohio and Computer Centre, University of Queensland, Queensland, Australia

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 2, Downloads (12 Months): 23, Citation Count: 1

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ABSTRACT

The computer analysis of factorial experiments is discussed in terms of a new generalized matrix notation which highlights the special properties of factorial designs. A method of calculating an analysis of a variance suitable for programming as a library subroutine is described. An orthogonal transformation is used to obtain components of variance based on single degrees of freedom. The transformation is done sequentially so that no additional storage for intermediate results is required. The analysis of variance table is obtained by summation of the components according to a simple indexing procedure. An algorithm for the calculation of sums and means over all combinations of factor levels is proposed.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	BAINBRIDGE, J.R. Tabular analysis of factorial experiments and the use of punch cards. J. Arer. Statist. Assoc. 51 (March 1956), 149-158.
	2	CLARINGBOLD, P .J . The automatic design and analysis of biological experiments. Proe. Conf. on Automatic Computation, Weapons Research Establishment, Australia, 1957.
	3	FIsHER, I. A., ANU YTES, F. Stalislical Tables for Biological, Agricultra, and Medical Research. Oliver and Boyd, London, 1963.
	4	HARTLEY, H. O. Analysis of variance. In Mathematical Methods for Digital Computers, A. Ralston and It. S. Wilf (Eds.), Wiley, New York, 1960.
	5	Julius Lieblein, A General Analysis of Variance Scheme Applicable to a Computer With a Very Large Memory, Journal of the ACM (JACM), v.6 n.4, p.469-475, Oct. 1959 [doi>10.1145/320998.321000]
	6	SPAIN, B. Tensor Calculus. Oliver and Boyd, London, 1960.