Cited by 2,785Probability and Statistical ResearchStatistical Distribution Estimation and ApplicationsGame Theory and Voting Systems

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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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“e critical value [64] can be obtained from Friedman statistics FF with (m − 1) and (m − 1) × (N − 1) degree of freedom.”
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“It can be taken as a gatekeeper that manages the flow of information in the network structure (Friedman 1940; Freeman 1979).”
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“Both ALBERT and”
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Method
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“This paper uses the accuracy obtained by 10-fold cross-validation in The Friedman test, and it ranks the data of each fold together; then there are some values of ranks for each model that can lead to detecting the most effective classifiers among other models (Friedman 1940).”
Method
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Method
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“In particular, first, we applied the Friedman test (Friedman 1940) with a significance level equal to 0.05 to reject the null hypothesis.”
MethodInfluential
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“We ﬁ rst examine whether there are signi ﬁ cant differences among the six algorithms on these datasets, utilizing the Friedman test statistic ( Friedman, 1940 ): where r i represents the average rank of the algorithm, n denotes the number of datasets, and k represents the number of algorithms.”
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“To analyze the results, we applied the Friedman test [30] considering a confidence level of 95%; the null hypothesis assumes all algorithms have equal performance.”
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“For reference, Friedman’s test is a parametric statistical test that was proposed by Milton Friedman [ In the first stage, Friedman’s test requires comparison of the average ranking of different algorithms , where, j i r is the rank of the j -th of k algorithms on the i -th of N datasets.”
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Feature selections based on two-type overlap degrees and three-view granulation measures for k -nearest-neighbor rough sets
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“We used Friedman’s test [9], a two-way non-parametric ANOVA where column effects are tested for significant differences after adjusting for possible row effects.”

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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