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An Analysis of Transformations

Box, G. E. P., Cox, D. R.·1964·Journal of the Royal Statistical Society Series B: Statistical Methodology
DOI 10.1111/j.2517-6161.1964.tb00553.x
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Abstract

Summary: In the analysis of data it is often assumed that observations y 1, y 2, …, 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.

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Research works printed but not linked: 13

  1. Anscombe, 1961, Examination of residuals, Proc. Fourth Berkeley Symp. Math. Statist. and Prob., 1, 1
  2. Anscombe, 1963, The examination and analysis of residuals, Technometrics, 5, 141, 10.1080/00401706.1963.10490071 · DOI
  3. Bartlett, 1937, Properties of sufficiency and statistical tests, Proc. Roy. Soc. A, 160, 268
  4. Bartlett, 1947, The use of transformations, Biometrics, 3, 39, 10.2307/3001536 · DOI · Paper page
  5. Box, 1962, Transformation of the independent variables, Technometrics, 4, 531, 10.1080/00401706.1962.10490038 · DOI
  6. Cochran, 1940, The analysis of variance when experimental errors follow the Poisson or binomial laws, Ann. math. Statist., 11, 335, 10.1214/aoms/1177731871 · DOI
  7. Cornish, 1954, The multivariate t distribution associated with a set of normal sample deviates, Austral. J. Physics, 7, 531, 10.1071/PH540531 · DOI
  8. Dunnett, 1954, A bivariate generalization of Student's t distribution, Biometrika, 41, 153, 10.1093/biomet/41.1-2.153 · DOI
  9. Jeffreys, 1961, Theory of Probability
  10. Kleczkowski, 1949, The transformation of local lesion counts for statistical analysis, Ann. appl. Biol., 36, 139, 10.1111/j.1744-7348.1949.tb06404.x · DOI
  11. Tukey, 1949, One degree of freedom for non-additivity, Biometrics, 5, 232, 10.2307/3001938 · DOI · Paper page
  12. Tukey, 1950, Dyadic anova, an analysis of variance for vectors, Human Biology, 21, 65
  13. Tukey, 1954, Answer to query 112, Biometrics, 10, 562, 10.2307/3001625 · DOI

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Metadata

Authors
Box, G. E. P., & Cox, D. R.
Venue
Journal of the Royal Statistical Society Series B: Statistical Methodology
Publisher
Oxford University Press (OUP)
Published
1964-07-01
Volume
26
Issue
2
Pages
211-243
ISSN
  • 1369-7412 (ISSN-L)
  • 1467-9868
DOI
10.1111/j.2517-6161.1964.tb00553.x
OpenAlex
W129305155
Cited by
15,052
References
0
FWCI
16.59
Type
journal article
Language
en
Open access
closed
Licence
academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)

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