A Transformation Yielding an Additive Representation of Data in a Two-Way Array.

Abstract

It is common practice when seeking an additive representation of data in a two-way array to try out various transformations using Tukey's single degree of freedom for nonadditivity as an index of the extent of the deviation of the reexpressed data from additivity. It is shown that when data fit Tukey's model and an additive representation exists in the sense defined by Luce and Tukey (1964), the transformation required to obtain the additive representation is f(y)=log (wavelength gamma + 1 - wavelength microns), where wavelength is the weight for the degree of freedom for nonadditivity. The transformation is unique up to a linear transformation. This result is in apparent conflict with power transformations suggested by Anscombe and Tukey (1963). (Author)

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Document Details

Document Type
Technical Report
Publication Date
Aug 15, 1980
Accession Number
ADA118666

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  • James A. Paulson

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