On the accuracy of bonferroni significance levels for detecting outliers in linear models

R. Dennis Cook; P. Prescott

doi:10.1080/00401706.1981.10486237

On the accuracy of bonferroni significance levels for detecting outliers in linear models

R. Dennis Cook
, P. Prescott

Statistics (Twin Cities)

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

31 Scopus citations

Abstract

At present, the first-order Bonferroni upper bound is the only practically useful tool for determining approximate critical values or p values for the maximum absolute studentized residual as a criterion for detecting a single outlier in a linear model. Available methods for assessing the accuracy of this bound require numerical integration and are difficult to apply routinely. We present a relatively simple alternative method that can be applied to any linear model and is suitable for routine use. The application to analyses of 2^m factorial experiments and regression models is illustrated with several examples.

Original language	English (US)
Pages (from-to)	59-63
Number of pages	5
Journal	Technometrics
Volume	23
Issue number	1
DOIs	https://doi.org/10.1080/00401706.1981.10486237
State	Published - Feb 1981

Bibliographical note

Funding Information:
This work was undertaken while the first author was a Hartley Visiting Fellow at the University of Southampton and was supported in part by grant l-ROl-GM25587 from the National Institute of General Medical Science, U.S. Department of Health, Education and Welfare. The authors are grateful to the editor, associatee ditor, and the refereesf or many helpful suggestions.

Keywords

Bonferroni bounds
Factorial experiments
Maximum absolute studentized residual
Outliers
P values
Regression

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10.1080/00401706.1981.10486237

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N2 - At present, the first-order Bonferroni upper bound is the only practically useful tool for determining approximate critical values or p values for the maximum absolute studentized residual as a criterion for detecting a single outlier in a linear model. Available methods for assessing the accuracy of this bound require numerical integration and are difficult to apply routinely. We present a relatively simple alternative method that can be applied to any linear model and is suitable for routine use. The application to analyses of 2m factorial experiments and regression models is illustrated with several examples.

AB - At present, the first-order Bonferroni upper bound is the only practically useful tool for determining approximate critical values or p values for the maximum absolute studentized residual as a criterion for detecting a single outlier in a linear model. Available methods for assessing the accuracy of this bound require numerical integration and are difficult to apply routinely. We present a relatively simple alternative method that can be applied to any linear model and is suitable for routine use. The application to analyses of 2m factorial experiments and regression models is illustrated with several examples.

KW - Bonferroni bounds

KW - Factorial experiments

KW - Maximum absolute studentized residual

KW - Outliers

KW - P values

KW - Regression

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On the accuracy of bonferroni significance levels for detecting outliers in linear models

Abstract

Bibliographical note

Keywords

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