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A Comparison of Alternative Tests of Significance for the Problem of $m$ Rankings

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Friedman, Milton·1940·The Annals of Mathematical Statistics

DOI 10.1214/aoms/1177731944

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The use of ranks to avoid the assumption of normality implicit in the analysis of variance
Friedman, M. (1937) · Journal of the American Statistical Association · doi:10.1080/01621459.1937.10503522 · Cited by 7,005
Self-citation
Statistical Tables for Biological, Agricultural and Medical Research.
Reed, L. J., Fisher, R. A., & Yates, F. (1944) · Journal of the American Statistical Association · doi:10.2307/2280633 · Cited by 3,012
The Problem of $m$ Rankings
Kendall, M. G., & Smith, B. B. (1939) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177732186 · Cited by 992
The Correlation Ratio for Ranked Data
Wallis, W. A. (1939) · Journal of the American Statistical Association · doi:10.1080/01621459.1939.10503552 · Cited by 58

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“4) Friedman Test: The Friedman test [50] is a nonparametric test for detecting the differences among different algorithms in terms of IGD and GD.”
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“Interestingly, a rank-based analogue of the permutation ANOVA test just described was long ago proposed by economist Milton Friedman (1937, 1939, 1940), who later won a Nobel Prize in Economics for other works.”
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Method
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“, Friedman test [56] and Bonferroni–Dunn test [57], are used to systematically explore the classification performance of different algorithms.”
Method
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“To validate whether MSDS, FSSL, and MLFSL have significant difference, a nonparametric Friedman test [48] is used to compare k algorithms over N multilabel datasets.”
Method
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“We also show the averaged rankings, computed by the Friedman test (Friedman, 1940), obtained by these algorithms (Av.”
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Method
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“In addition, the Friedman test [55] and Bonferoni–Dunn test [56] were used to evaluate the statistical significance of the model performance.”
Method
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“Nonparametric analog of parametric two-way analysis of variance is the Friedman test (Friedman, 1937, 1940).”
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“The Friedman test [137] is a multiple comparison test for ranking the algorithms for each problem separately to distinguish between significantly different algorithms.”
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Authors: Friedman, M.
Corresponding author: Friedman, Milton
Venue: The Annals of Mathematical Statistics
Publisher: Institute of Mathematical Statistics
Published: 1940-03
Volume: 11
Issue: 1
Pages: 86-92
ISSN: 0003-4851 (ISSN-L)
DOI: 10.1214/aoms/1177731944
OpenAlex: W2016944307
Cited by: 2,785
References: 4
Citations by year: 2026: 191 · 2025: 256 · 2024: 244 · 2023: 253 · 2022: 264 · 2021: 231 · 2020: 209 · 2019: 173 · 2018: 133 · 2017: 106 · 2016: 132 · 2015: 93 · 2014: 82 · 2013: 72 · 2012: 67
FWCI: 5.07
Type: journal article
Language: en
Open access: bronze
doi.org
Locations: The Annals of Mathematical Statistics (publishedVersion)
Project Euclid (Cornell University) (submittedVersion)
Topics: Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Game Theory and Voting Systems
Keywords: tests of significance, rank tests, comparison of statistical tests

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A Comparison of Alternative Tests of Significance for the Problem of $m$ Rankings

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