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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“adopted nonparametric methods, namely, the Friedman test [39] and the Iman–Davenport test [40].”
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“To further study whether FQC has a better performance than other uncertainty-based quality control methods with statistical signiﬁcance, Friedman test [44] and Bonferroni-Dunn post hoc test [45] are applied on the ﬁve datasets.”
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“The critical difference and the corresponding critical difference diagram [66] are a Friedman test [67, 68] using 640 the statistic derived by Iman and Davenport [69].”
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“The Friedman test (Friedman two-way analysis of variances by ranks) is a nonparametric analog of the parametric two-way analysis of variance (Friedman 1937, 1940).”
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“non-parametric Friedman test [79,80] is used to evaluate the hypothesis that all datasets perform the same.”
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“The Friedman aligned test Friedman ( 1940) was conducted along with a two-way variance analysis by ranks with associated Holm post hoc procedure as it was recommended in Derrac et al. (2011).”
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“Also, in order to determine, statistically, the model with greater classification performance, we apply the Friedman test (Friedman, 1940) with significance level 𝛼 = 0.05, since it establishes a performance rank for the investigated models.”
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“Moreover, to further explorewhether the observed differences are statistically significant, the Friedman test [37] for multiple”
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“Next, the Friedman test is utilized in this experiments [39].”
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“The performance of models were compared using RMSE and were validated statistically using non-parametric Wilcoxon Signed Rank Test, Friedman Test and post hoc Nemeyi test.”
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“The Friedman test was used as an analog of the two-way analysis of variance [24,25], but in this case, by range variance.”
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“The ﬁrst step involved the application of Friedman’s non-parametric test [59] with a signiﬁcance level of a ¼ 0 : 05 to ascertain the statistical signiﬁcance of the differences in the mean ranks for each measure.”
Least absolute deviation-based robust support vector regression
Chen, C., Li, Y., Yan, C., Guo, J., & Liu, G. (2017) · Knowledge-Based Systems · doi:10.1016/j.knosys.2017.06.009 · Cited by 26
“The Friedman test is a non-parametric statistical test developed by Milton Friedman [38].”
Method
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“Statistical analysis In this study, the ranking of discretization algorithms is obtained from the Friedman test [72, 73].”
Method
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“, 2010), an alternative to the Friedman test (Friedman, 1940) used by Gardner and Brooks (2018) that relies on more information than the latter test by making inter-dataset comparisons and by using information about performance of each algorithm relative the average performance achieved on a dataset by all other algor…”
Method
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Ensembles of extremely randomized predictive clustering trees for predicting structured outputs
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“In particular, we use the Friedman test (Friedman 1940) for statistical significance—it is a non-parametric test for multiple hypotheses testing.”
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Multiple graph kernel learning based on GMDH-type neural network
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“The Friedman test (Friedman two-way analysis of variances by ranks) is a nonparametric analog of the parametric two-way analysis of variance (Friedman 1940; Abramowitz 1974).”
Method
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“For this purpose, the Friedman test was used (Friedman, 1937, 1940).”
Method
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“In particular, the Friedman test is a non-parametric test used to determine whether or not there is a statistically signiﬁcant difference between the accuracy of classiﬁers when the same subjects show up in each classiﬁer [52,53].”
Method
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Otuo-Acheampong, D., Rashed, G. I., Akwasi, A. M., & Haider, H. (2023) · International Transactions on Electrical Energy Systems · doi:10.1155/2023/9930954 · Cited by 28
MC-YOLOv5: A Multi-Class Small Object Detection Algorithm
Chen, H., Liu, H., Sun, T., Lou, H., Duan, X., Bi, L., & Liu, L. (2023) · Biomimetics · doi:10.3390/biomimetics8040342 · Cited by 28
“The performance of the models employed in the ablation experiments was evaluated on three datasets using the Friedman test [25,26].”
An Experimental Study about Simple Decision Trees for Bagging Ensemble on Datasets with Classification Noise
Abellán, J., & Masegosa, A. R. (2009) · Lecture notes in computer science · doi:10.1007/978-3-642-02906-6_39 · Cited by 28
Proximal gradient method for huberized support vector machine
Xu, Y., Akrotirianakis, I., & Chakraborty, A. (2015) · Pattern Analysis and Applications · doi:10.1007/s10044-015-0485-z · Cited by 26
Multi-Label Hierarchical Classification using a Competitive Neural Network for protein function prediction
Borges, H. B., & Nievola, J. C. (2012) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.2012.6252736 · Cited by 28
Effective lazy learning algorithm based on a data gravitation model for multi-label learning
Reyes, Ó., Morell, C., & Ventura, S. (2016) · Information Sciences · doi:10.1016/j.ins.2016.01.006 · Cited by 28
A class of hybrid multilayer perceptrons for software development effort estimation problems
Araújo, R. D. A., Oliveira, A. L. I., & Meira, S. R. L. (2017) · Expert Systems with Applications · doi:10.1016/j.eswa.2017.07.050 · Cited by 28
Rough Noise-Filtered Easy Ensemble for Software Fault Prediction
Riaz, S., Ali, A., & Jiao, L. (2018) · IEEE Access · doi:10.1109/access.2018.2865383 · Cited by 28
Anxiety-like behavior induced by salicylate depends on age and can be prevented by a single dose of 5-MeO-DMT
Winne, J., Ciralli, B., Malfatti, T., Brisa, E., Doerl, J. G., Nogueira, I., Leão, K. E., & Leão, R. N. (2020) · Experimental Neurology · doi:10.1016/j.expneurol.2020.113175 · Cited by 27
“For non-normal distributed data, we used the non-parametrical Friedman's test to calculate statistical significance (Friedman, 1940).”
Method
A Multi-Label Learning Based Kernel Automatic Recommendation Method for Support Vector Machine
Zhang, X., & Song, Q. (2015) · PLoS ONE · doi:10.1371/journal.pone.0120455 · Cited by 28
A Note on the Equivalence of Several Marginal Homogeneity Test Criteria for Categorical Data
White, A. A., Landis, J. R., & Cooper, M. M. (1982) · International Statistical Review · doi:10.2307/1402457 · Cited by 28
Handling Multi-Class Problem by Intuitionistic Fuzzy Twin Support Vector Machines Based on Relative Density Information
Rezvani, S., & Wu, J. (2023) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2023.3310908 · Cited by 27
Attribute reduction for heterogeneous data based on monotonic relative neighborhood granularity
Dai, J., Zhu, Z., Li, M., Zou, X., & Zhang, C. (2024) · International Journal of Approximate Reasoning · doi:10.1016/j.ijar.2024.109210 · Cited by 27
Sparse multi-label feature selection via pseudo-label learning and dynamic graph constraints
Zhang, Y., Tang, J., Cao, Z., & Chen, H. (2025) · Information Fusion · doi:10.1016/j.inffus.2025.102975 · Cited by 27
Predicting long-term population dynamics with bagging and boosting of process-based models
Simidjievski, N., Todorovski, L., & Džeroski, S. (2015) · Expert Systems with Applications · doi:10.1016/j.eswa.2015.07.004 · Cited by 27
Confidence curves: an alternative to null hypothesis significance testing for the comparison of classifiers
Berrar, D. (2016) · Machine Learning · doi:10.1007/s10994-016-5612-6 · Cited by 29
“The Friedman test is a non-parametric omnibus test for analyzing randomized complete block designs (Friedman 1937, 1940).”
Method

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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