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Parameters behind “Nonparametric” Statistics: Kendall's tau, Somers’ D and Median Differences
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So-called “nonparametric” statistical methods are often in fact based on population parameters, which can be estimated (with confidence limits) using the corresponding sample statistics. This article reviews the uses of three such parameters, namely Kendall's τ a , Somers’ D and the Hodges–Lehmann median difference. Confidence intervals for these are demonstrated using the somersd package. It is argued that confidence limits for these parameters, and their differences, are more informative than the traditional practice of reporting only p-values. These three parameters are also important in defining other tests and parameters, such as the Wilcoxon test, the area under the receiver operating characteristic (ROC) curve, Harrell's C, and the Theil median slope.
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“For instance, for prediction models with a binary outcome, the c-statistic is a reparameterization of Somer’s D,19 and can also be derived from the distribution of the linear predictor,20 Cohen’s effect size,20 or several correlation indices.21”
From A framework for meta-analysis of prediction model studies with binary and time-to-event outcomes (2019) · cites this paper as [19]
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Metadata
- Authors
- Newson, R.
- Affiliations
- King's College London (GB)
- Corresponding author
- Newson, Roger
- Venue
- The Stata Journal: Promoting communications on statistics and Stata
- Publisher
- SAGE Publications
- Published
- 2002-03
- Volume
- 2
- Issue
- 1
- Pages
- 45-64
- ISSN
- 1536-867X (ISSN-L)
- 1536-8734
- OpenAlex
- W2112690682
- Cited by
- 394
- References
- 32
- Citations by year
- 2026: 12 · 2025: 12 · 2024: 17 · 2023: 36 · 2022: 42 · 2021: 38 · 2020: 25 · 2019: 19 · 2018: 22 · 2017: 21 · 2016: 24 · 2015: 18 · 2014: 16 · 2013: 12 · 2012: 9
- FWCI
- 7.62
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Stata Journal Promoting communications on statistics and Stata (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- AgEcon Search (University of Minnesota, USA) (submittedVersion, cc-by-nc-nd)
- AgEcon Search (University of Minnesota, USA)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Multidisciplinary Science and Engineering Research
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Keywords
- Kendall's tau, nonparametric statistics, confidence intervals, concordant and discordant pairs, Wilcoxon test, area under the ROC curve, rank correlation
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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