Volume 26, Issue 2 p. 211-243
Article

An Analysis of Transformations

G. E. P. Box

G. E. P. Box

University of Wisconsin

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D. R. Cox

D. R. Cox

Birkbeck College, University of London

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First published: July 1964
Citations: 3,276

Summary

In the analysis of data it is often assumed that observations y1, y2, …, yn are independently normally distributed with constant variance and with expectations specified by a model linear in a set of parameters θ. In this paper we make the less restrictive assumption that such a normal, homoscedastic, linear model is appropriate after some suitable transformation has been applied to the y's. Inferences about the transformation and about the parameters of the linear model are made by computing the likelihood function and the relevant posterior distribution. The contributions of normality, homoscedasticity and additivity to the transformation are separated. The relation of the present methods to earlier procedures for finding transformations is discussed. The methods are illustrated with examples.