The Interaction Algorithm and Practical Fourier Analysis: An Addendum

SUMMARY In the original paper it was misleadingly stated that the Yates algorithm is effectively self-inverse. This statement is here elucidated, and a numerical example is given. Attention is drawn to a discrete analogue of Poisson's summation formula, which provides many additional relationships between yields and interactions. 1. MODIFICATION OF ALGORITHM MR CUTHBERT DANIEL has pointed out that there is a misleading form of words in Good (1958). I now clarify the matter, and take the opportunity to draw attention to a discrete analogue of Poisson's summation formula, which seems to be of some value in the analysis of confounded factorial experiments. I stated that the Yates adding-and-subtracting algorithm for computing interactions in a 2n factorial experiment, if repeated on the interactions themselves, leads back to multiples of the original yields. The applications intended were (a) to provide a thorough check of the arithmetic, and (b) to enable the original data to be smoothed by equating the higher-order interactions to zero, and then applying the inverse algorithm. I forgot to mention explicitly, though it could be dug out from the formulae, that I had in mind a slight modification of the Yates algorithm. In the modification, consecutive columns of the calculation are obtained by multiplying the preceding column by a matrix, A, whereas the original Yates algorithm uses a matrix, B, where, for the case n = 3,

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