The Interaction Algorithm and Practical Fourier Analysis

This is the authors' abstract. We don't add key points for this paper.

Summary 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.