Accession Number : ADA118666

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

Descriptive Note : Technical rept.,

Corporate Author : PORTLAND STATE UNIV OR DEPT OF PSYCHOLOGY

Personal Author(s) : Paulson,James A

PDF Url : ADA118666

Report Date : 15 Aug 1980

Pagination or Media Count : 27

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)

Descriptors :   *Transformations(Mathematics), *Data processing, *Arrays, Data management, Random variables, Degrees of freedom, Fitting functions(Mathematics), Linearity

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE