Use of Half-Normal Plots in Interpreting Factorial Two-Level Experiments
Abstract
Plotting the empirical cumulative distribution of the usual set of orthogonal contrasts computed from a 2 p experiment on a special grid may aid in its criticism and interpretation. Bad values, heteroscedasticity, dependence of variance on mean, and some types of defective randomization, all leave characteristic stigmata. The halfnormal plot can be used to estimate the error standard deviation and to make judgments about the reality of the observed effects. An accompanying paper by A. Birnbaum gives some operating characteristics of these judgments. Examples are given of the use of half-normal plots in each of these ways.
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In typical settings of analysis of variance, most sources of variation are small but some are large.
“which seems reasonable in the typical settings of analysis of variance, in which most sources of variation are small but some are large (Daniel, 1959, Gelman, 2005).”
From Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper) (2006) · cites this paper as Daniel, 1959
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An analysis of variance test for normality (complete samples)
SHAPIRO, S. S., & WILK, M. B. (1965) · Biometrika · doi:10.1093/biomet/52.3-4.591 · Cited by 23,480 · see citing works
Gelman, A. (2006) · Bayesian Analysis · doi:10.1214/06-ba117a · Cited by 4,050 · see citing works
“The hierarchical half-Cauchy model allows most of the variance parameters to be small but with the occasionally large σα, which seems reasonable in the typical settings of analysis of variance, in which most sources of variation are small but some are large (Daniel, 1959, Gelman, 2005).”
BackgroundGraphs in Statistical Analysis
Anscombe, F. J. (1973) · The American Statistician · doi:10.1080/00031305.1973.10478966 · Cited by 976 · see citing works
- Authors
- Daniel, C.
- Corresponding author
- Daniel, Cuthbert
- Venue
- Technometrics
- Publisher
- Informa UK Limited
- Published
- 1959-11
- Volume
- 1
- Issue
- 4
- Pages
- 311-341
- ISSN
- 0040-1706 (ISSN-L)
- 1537-2723
- OpenAlex
- W1984597404
- Cited by
- 798
- References
- 0
- Citations by year
- 2026: 6 · 2025: 14 · 2024: 13 · 2023: 12 · 2022: 12 · 2021: 16 · 2020: 18 · 2019: 18 · 2018: 17 · 2017: 14 · 2016: 15 · 2015: 24 · 2014: 31 · 2013: 27 · 2012: 18
- FWCI
- 7.65
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Technometrics (publishedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Optimal Experimental Design Methods
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Keywords
- half-normal plots, orthogonal contrasts, empirical cumulative distribution, heteroscedasticity, mean-variance relationship
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