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The Interaction Algorithm and Practical Fourier Analysis

I. J. Good
Journal of the Royal Statistical Society. Series B (Methodological)
Vol. 20, No. 2 (1958), pp. 361-372
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/2983896
Page Count: 12
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The Interaction Algorithm and Practical Fourier Analysis
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Abstract

The interactions in a complete factorial experiment are linear functions of the observations. They can be calculated by means of a stream-lined algorithm, of which the first example was the adding-and-subtracting algorithm of Yates (1937). The relationship between the two methods of calculating the interactions is given a precise and succinct form, which surprisingly does not seem to have been given in the existing literature. The algorithm is logically simplest for the tn experiment. The inverse algorithm is specified and also the method of obtaining the divisors for the analysis of variance. Finally some analogous short cuts in practical Fourier analysis are described.

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