The analysis of transformed data

D. V. Hinkley; G. Runger

doi:10.1080/01621459.1984.10478045

The analysis of transformed data

D. V. Hinkley
, G. Runger

Research output: Contribution to journal › Article › peer-review

137 Scopus citations

Abstract

Recently it was suggested (Bickel and Doksum 1981) that when data are used to select a transformation, the post-transformation analysis of those data may need to be modified considerably from standard form so as to allow for the selection. We argue that common sense and the work of Box and Cox (1964) point to a contrary conclusion. Our argument is based on considerations of parameter interpretation and subsequent Bayesian analysis, within the context of fitting normal-error linear models. Numerical examples are used to illustrate the main points.

Original language	English (US)
Pages (from-to)	302-309
Number of pages	8
Journal	Journal of the American Statistical Association
Volume	79
Issue number	386
DOIs	https://doi.org/10.1080/01621459.1984.10478045
State	Published - Jun 1984
Externally published	Yes

Keywords

Bayesian inference
Box-Cox model
Confidence limits
Contrasts
Power transformation

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1080/01621459.1984.10478045

Cite this

@article{2624e8ea432c48c2a6daef318007a0d9,

title = "The analysis of transformed data",

abstract = "Recently it was suggested (Bickel and Doksum 1981) that when data are used to select a transformation, the post-transformation analysis of those data may need to be modified considerably from standard form so as to allow for the selection. We argue that common sense and the work of Box and Cox (1964) point to a contrary conclusion. Our argument is based on considerations of parameter interpretation and subsequent Bayesian analysis, within the context of fitting normal-error linear models. Numerical examples are used to illustrate the main points.",

keywords = "Bayesian inference, Box-Cox model, Confidence limits, Contrasts, Power transformation",

author = "Hinkley, \{D. V.\} and G. Runger",

note = "Funding Information: * D.V.H inkley is Jane and Roland Blumberg Centennial Professor of Mathematics, and member of the Center for Statistical Sciences, The University of Texas at Austin, Austin, TX 78712. G. Runger is Assistant Professor of Statistics at the University of Iowa, Iowa City, IA 52242. The authors acknowledge helpful advice and comments from George Box, Carl Moms, Stephen Stigler, and an exemplary anonymous referee. Research was supported by NSF Grants MCS-79-04558 and MCS-82-01994 at the University of Minnesota. Since writing the original version of this paper in 1980 the authors have benefited from the implicit support of Box and Cox through publication of their rebuttal (Box and Cox 1982) and from the explicit encouragement of George Box and Stephen Stigler. Box kindly showed the authors a draft of Fung and Box (1982), which also discusses the Bayesian analysis of transformed data. Finally, the authors are grateful to one referee whose extensive and penetrating comments on the original manuscript led to a deeper understanding of some of the relevant issues.",

year = "1984",

month = jun,

doi = "10.1080/01621459.1984.10478045",

language = "English (US)",

volume = "79",

pages = "302--309",

journal = "Journal of the American Statistical Association",

issn = "0162-1459",

publisher = "Taylor and Francis Ltd.",

number = "386",

}

TY - JOUR

T1 - The analysis of transformed data

AU - Hinkley, D. V.

AU - Runger, G.

N1 - Funding Information: * D.V.H inkley is Jane and Roland Blumberg Centennial Professor of Mathematics, and member of the Center for Statistical Sciences, The University of Texas at Austin, Austin, TX 78712. G. Runger is Assistant Professor of Statistics at the University of Iowa, Iowa City, IA 52242. The authors acknowledge helpful advice and comments from George Box, Carl Moms, Stephen Stigler, and an exemplary anonymous referee. Research was supported by NSF Grants MCS-79-04558 and MCS-82-01994 at the University of Minnesota. Since writing the original version of this paper in 1980 the authors have benefited from the implicit support of Box and Cox through publication of their rebuttal (Box and Cox 1982) and from the explicit encouragement of George Box and Stephen Stigler. Box kindly showed the authors a draft of Fung and Box (1982), which also discusses the Bayesian analysis of transformed data. Finally, the authors are grateful to one referee whose extensive and penetrating comments on the original manuscript led to a deeper understanding of some of the relevant issues.

PY - 1984/6

Y1 - 1984/6

N2 - Recently it was suggested (Bickel and Doksum 1981) that when data are used to select a transformation, the post-transformation analysis of those data may need to be modified considerably from standard form so as to allow for the selection. We argue that common sense and the work of Box and Cox (1964) point to a contrary conclusion. Our argument is based on considerations of parameter interpretation and subsequent Bayesian analysis, within the context of fitting normal-error linear models. Numerical examples are used to illustrate the main points.

AB - Recently it was suggested (Bickel and Doksum 1981) that when data are used to select a transformation, the post-transformation analysis of those data may need to be modified considerably from standard form so as to allow for the selection. We argue that common sense and the work of Box and Cox (1964) point to a contrary conclusion. Our argument is based on considerations of parameter interpretation and subsequent Bayesian analysis, within the context of fitting normal-error linear models. Numerical examples are used to illustrate the main points.

KW - Bayesian inference

KW - Box-Cox model

KW - Confidence limits

KW - Contrasts

KW - Power transformation

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UR - https://www.scopus.com/pages/publications/0000811499#tab=citedBy

U2 - 10.1080/01621459.1984.10478045

DO - 10.1080/01621459.1984.10478045

M3 - Article

AN - SCOPUS:0000811499

SN - 0162-1459

VL - 79

SP - 302

EP - 309

JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

IS - 386

ER -

The analysis of transformed data

Abstract

Keywords

ASJC Scopus subject areas

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