Multiple comparisons among means
Abstract
Methods for constructing simultaneous confidence intervals for all possible linear contrasts among several means of normally distributed variables have been given by Scheffé and Tukey. In this paper the possibility is considered of picking in advance a number (say m) of linear contrasts among k means, and then estimating these m linear contrasts by confidence intervals based on a Student t statistic, in such a way that the overall confidence level for the m intervals is greater than or equal to a preassigned value. It is found that for some values of k, and for m not too large, intervals obtained in this way are shorter than those using the F distribution or the Studentized range. When this is so, the experimenter may be willing to select the linear combinations in advance which he wishes to estimate in order to have m shorter intervals instead of an infinite number of longer intervals.
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The Friedman test followed by Dunn's post hoc pairwise test with multiple-comparison correction was conducted to assess temporal discrepancies among onset estimates from documentation-based, narrative-based, and aggregated sources.
“To assess the temporal discrepancies and identify significant differences among the onset estimates from documentation-based, narrative-based, and aggregated sources, we conducted the Friedman test followed by Dunn’s post hoc pairwise test with multiple-comparison correction53,54.”
From TimeX: Phenotype Onset Extraction from Clinical Narratives (2026) · cites this paper as [54]
All relationships presented in this work are at least significant at a Bonferroni-corrected threshold.
“All relationships presented in this work are at least significant at a Bonferroni-corrected [76].”
From Personality, Gender, and Age in the Language of Social Media: The Open-Vocabulary Approach (2013) · cites this paper as [76]
Coefficients are considered significant if they are less than a Bonferroni-corrected two-tailed p of 0.001.
“Since we explore many features at once, we consider coefficients significant if they are less than a Bonferroni-corrected [76] two-tailed of 0.001.”
From Personality, Gender, and Age in the Language of Social Media: The Open-Vocabulary Approach (2013) · cites this paper as [76]
All results in the gender analysis are significant at Bonferroni-corrected p < 0.001.
“All results are significant at Bonferroni-corrected [76] .”
From Personality, Gender, and Age in the Language of Social Media: The Open-Vocabulary Approach (2013) · cites this paper as [76]
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TimeX: Phenotype Onset Extraction from Clinical Narratives
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- Authors
- Dunn, O. J.
- Affiliations
- University of California, Los Angeles (US)
- Corresponding author
- Dunn, Olive Jean
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1961-03
- Volume
- 56
- Issue
- 293
- Pages
- 52-64
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2061554433
- Cited by
- 5,006
- References
- 6
- Citations by year
- 2026: 417 · 2025: 445 · 2024: 360 · 2023: 338 · 2022: 341 · 2021: 337 · 2020: 306 · 2019: 267 · 2018: 254 · 2017: 217 · 2016: 244 · 2015: 184 · 2014: 174 · 2013: 110 · 2012: 95
- FWCI
- 11.21
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the American Statistical Association (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Keywords
- multiple comparisons, linear contrasts, simultaneous confidence intervals, F distribution, Scheffe method, Tukey method, normal distribution, interval length
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