On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other
Open accessAbstract
Let $x$ and $y$ be two random variables with continuous cumulative distribution functions $f$ and $g$. A statistic $U$ depending on the relative ranks of the $x$'s and $y$'s is proposed for testing the hypothesis $f = g$. Wilcoxon proposed an equivalent test in the Biometrics Bulletin, December, 1945, but gave only a few points of the distribution of his statistic. Under the hypothesis $f = g$ the probability of obtaining a given $U$ in a sample of $n x's$ and $m y's$ is the solution of a certain recurrence relation involving $n$ and $m$. Using this recurrence relation tables have been computed giving the probability of $U$ for samples up to $n = m = 8$. At this point the distribution is almost normal. From the recurrence relation explicit expressions for the mean, variance, and fourth moment are obtained. The 2rth moment is shown to have a certain form which enabled us to prove that the limit distribution is normal if $m, n$ go to infinity in any arbitrary manner. The test is shown to be consistent with respect to the class of alternatives $f(x) > g(x)$ for every $x$.
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Mann-Whitney U Test was used for inferential statistics because the data being compared are ordinal (Likert scale).
“We use a Mann-Whitney U Test for inferential statistics because the data being compared are ordinal (Likert scale) [93].”
From "It's trained by non-disabled people": Evaluating How Image Quality Affects Product Captioning with Vision-Language Models (2026) · cites this paper as [93]
On p. 1, Mann and Whitney define U using the relative ranks of two samples, supporting the citation’s identification of a rank-based test. The paper does not discuss ordinal or Likert-scale data as a reason to use it; its stated derivation assumes continuous distributions and no ties. (LLM, conf=0.86)
Experimental — accuracy not yet measuredPost-hoc tests reveal significant effects for each pairwise comparison, except E2FGVI vs. ProPainters yield comparable results.
“Post-hoc tests using Mann-Whitney tests [29] with Bonferroni correction reveal significant effects ( p ă 0 . 05 ˚ , | r | ą 0 . 1 ) for each pairwise comparison, except E2FGVI vs. ProPainters yield comparable results.”
From SVG: 3D Stereoscopic Video Generation via Denoising Frame Matrix (2024) · cites this paper as [29]
Post-hoc Mann-Whitney tests with Bonferroni correction revealed significant effects for each pairwise comparison, except E2FGVI vs. ProPainters.
“We further performed post-hoc tests using Mann-Whitney tests [29] with Bonferroni correction, which revealed significant effects ( p ă 0 . 05 , | r | ą 0 . 1 ) for each pairwise comparison, except E2FGVI vs. ProPainters.”
From SVG: 3D Stereoscopic Video Generation via Denoising Frame Matrix (2024) · cites this paper as [29]
Vcp is a housekeeping gene that has been proposed for calibration in quantitative experiments.
“The fold-change (FC) in gene expression was determined by the 2 -DDC T method 100 , and all values were normalized to the endogenous expression of Vcp; a housekeeping gene that has been proposed for calibration in quantitative experiments 101 .”
From Single-cell transcriptomic profiling of the aging mouse brain (2019) · cites this paper as [101]
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Cites
Individual Comparisons by Ranking Methods
Wilcoxon, F. (1945) · Biometrics Bulletin · doi:10.2307/3001968 · Cited by 15,354 · see citing works
On a Test Whether Two Samples are from the Same Population
Wald, A., & Wolfowitz, J. (1940) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177731909 · Cited by 934 · see citing works
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Metagenomic biomarker discovery and explanation
Segata, N., Izard, J., Waldron, L., Gevers, D., Miropolsky, L., Garrett, W. S., & Huttenhower, C. (2011) · Genome Biology · doi:10.1186/gb-2011-12-6-r60 · Cited by 16,192 · see citing works
Use of Ranks in One-Criterion Variance Analysis
Kruskal, W. H., & Wallis, W. A. (1952) · Journal of the American Statistical Association · doi:10.1080/01621459.1952.10483441 · Cited by 13,912 · see citing works
Van der Auwera, G. A., Carneiro, M. O., Hartl, C., Poplin, R., del Angel, G., Levy‐Moonshine, A., Jordan, T., Shakir, K., Roazen, D., Thibault, J., et al. (2013) · Current Protocols in Bioinformatics · doi:10.1002/0471250953.bi1110s43 · Cited by 6,687 · see citing works
A clinically applicable approach to continuous prediction of future acute kidney injury
Tomašev, N., Glorot, X., Rae, J. W., Zielinski, M., Askham, H., Saraiva, A., Mottram, A., Meyer, C., Ravuri, S., Protsyuk, I., et al. (2019) · Nature · doi:10.1038/s41586-019-1390-1 · Cited by 1,086 · see citing works
UCell: robust and scalable single-cell gene signature scoring
Andreatta, M., & Carmona, S. J. (2021) · Computational and Structural Biotechnology Journal · doi:10.1016/j.csbj.2021.06.043 · Cited by 1,104 · see citing works
Wild Mouse Gut Microbiota Promotes Host Fitness and Improves Disease Resistance
Rosshart, S. P., Vassallo, B. G., Angeletti, D., Hutchinson, D. S., Morgan, A. P., Takeda, K., Hickman, H. D., McCulloch, J. A., Badger, J. H., Ajami, N. J., et al. (2017) · Cell · doi:10.1016/j.cell.2017.09.016 · Cited by 862 · see citing works
Schurch, N. J., Schofield, P., Gierliński, M., Cole, C., Sherstnev, A., Singh, V., Wrobel, N., Gharbi, K., Simpson, G. G., Owen-Hughes, T., et al. (2016) · RNA · doi:10.1261/rna.053959.115 · Cited by 966 · see citing works
Systematic classification of unknown metabolites using high-resolution fragmentation mass spectra
Dührkop, K., Nothias, L.-F., Fleischauer, M., Reher, R., Ludwig, M., Hoffmann, M. A., Petras, D., Gerwick, W. H., Rousu, J., Dorrestein, P. C., et al. (2021) · Nature Biotechnology · doi:10.1038/s41587-020-0740-8 · Cited by 860 · see citing works
The simple difference formula: An approach to teaching nonparametric correlation
Kerby, D. S. (2014) · Comprehensive Psychology · doi:10.2466/11.it.3.1 · Cited by 806 · see citing works
Influence of COVID-19 confinement on students’ performance in higher education
Gonzalez, T., de la Rubia, M. A., Hincz, K. P., Comas-Lopez, M., Subirats, L., Fort, S., & Sacha, G. M. (2020) · PLOS ONE · doi:10.1371/journal.pone.0239490 · Cited by 743 · see citing works
“Means were compared by a Kruskal-Wallis test [46] and, when differences were found, by a Mann-Whitney post hoc test [47] to determine which pairs of means were different.”
MethodSingle-cell transcriptomic profiling of the aging mouse brain
Ximerakis, M., Lipnick, S. L., Innes, B. T., Simmons, S. K., Adiconis, X., Dionne, D., Mayweather, B. A., Nguyen, L., Niziolek, Z., Ozek, C., et al. (2019) · Nature Neuroscience · doi:10.1038/s41593-019-0491-3 · Cited by 736 · see citing works
Transposable elements reveal a stem cell-specific class of long noncoding RNAs
Kelley, D., & Rinn, J. (2012) · Genome Biology · doi:10.1186/gb-2012-13-11-r107 · Cited by 531 · see citing works
Nonparametric statistical tests for the continuous data: the basic concept and the practical use
Nahm, F. S. (2016) · Korean Journal of Anesthesiology · doi:10.4097/kjae.2016.69.1.8 · Cited by 389 · see citing works
Debunking in a world of tribes
Zollo, F., Bessi, A., Del Vicario, M., Scala, A., Caldarelli, G., Shekhtman, L., Havlin, S., & Quattrociocchi, W. (2017) · PLOS ONE · doi:10.1371/journal.pone.0181821 · Cited by 345 · see citing works
Li, Y., Ge, X., Peng, F., Li, W., & Li, J. J. (2022) · Genome Biology · doi:10.1186/s13059-022-02648-4 · Cited by 303 · see citing works
Small-sample precision of ROC-related estimates
Hanczar, B., Hua, J., Sima, C., Weinstein, J., Bittner, M., & Dougherty, E. R. (2010) · Bioinformatics · doi:10.1093/bioinformatics/btq037 · Cited by 323 · see citing works
Measuring discrimination in algorithmic decision making
Žliobaitė, I. (2017) · Data Mining and Knowledge Discovery · doi:10.1007/s10618-017-0506-1 · Cited by 272 · see citing works
Lenz, H.-J., Ou, F.-S., Venook, A. P., Hochster, H. S., Niedzwiecki, D., Goldberg, R. M., Mayer, R. J., Bertagnolli, M. M., Blanke, C. D., Zemla, T., et al. (2019) · Journal of Clinical Oncology · doi:10.1200/jco.18.02258 · Cited by 246 · see citing works
Benchmark evaluation of DeepSeek large language models in clinical decision-making
Sandmann, S., Hegselmann, S., Fujarski, M., Bickmann, L., Wild, B., Eils, R., & Varghese, J. (2025) · Nature Medicine · doi:10.1038/s41591-025-03727-2 · Cited by 233 · see citing works
Studying user income through language, behaviour and affect in social media
Preoţiuc-Pietro, D., Volkova, S., Lampos, V., Bachrach, Y., & Aletras, N. (2015) · PLOS ONE · doi:10.1371/journal.pone.0138717 · Cited by 219 · see citing works
Chapman, M. J., Laplaud, P. M., Luc, G., Forgez, P., Bruckert, E., Goulinet, S., & Lagrange, D. (1988) · Journal of Lipid Research · doi:10.1016/s0022-2275(20)38518-7 · Cited by 216 · see citing works
Chronic Obstructive Pulmonary Disease: An Original Model of Cognitive Decline
Incalzi, R. A., Gemma, A., Marra, C., Muzzolon, R., Capparella, O., & Carbonin, P. (1993) · American Review of Respiratory Disease · doi:10.1164/ajrccm/148.2.418 · Cited by 198 · see citing works
Burned forests impact water supplies
Hallema, D. W., Sun, G., Caldwell, P. V., Norman, S. P., Cohen, E. C., Liu, Y., Bladon, K. D., & McNulty, S. G. (2018) · Nature Communications · doi:10.1038/s41467-018-03735-6 · Cited by 193 · see citing works
Guidelines and evaluation of clinical explainable AI in medical image analysis
Jin, W., Li, X., Fatehi, M., & Hamarneh, G. (2023) · Medical Image Analysis · doi:10.1016/j.media.2022.102684 · Cited by 199 · see citing works
CXC chemokines located in the 4q21 region are up-regulated in breast cancer
Bieche, I., Chavey, C., Andrieu, C., Busson, M., Vacher, S., Le Corre, L., Guinebretiere, J.-M., Burlinchon, S., Lidereau, R., & Lazennec, G. (2007) · Endocrine Related Cancer · doi:10.1677/erc.1.01301 · Cited by 183 · see citing works
Molecular hallmarks of heterochronic parabiosis at single-cell resolution
Pálovics, R., Keller, A., Schaum, N., Tan, W., Fehlmann, T., Borja, M., Kern, F., Bonanno, L., Calcuttawala, K., Webber, J., et al. (2022) · Nature · doi:10.1038/s41586-022-04461-2 · Cited by 153 · see citing works
Refining ChatGPT-Generated Code: Characterizing and Mitigating Code Quality Issues
Liu, Y., Le-Cong, T., Widyasari, R., Tantithamthavorn, C., Li, L., Le, X.-B. D., & Lo, D. (2024) · ACM Transactions on Software Engineering and Methodology · doi:10.1145/3643674 · Cited by 149 · see citing works
Bartus, R. T., Dean, R. L., Sherman, K. A., Friedman, E., & Beer, B. (1981) · Neurobiology of Aging · doi:10.1016/0197-4580(81)90007-5 · Cited by 140 · see citing works
AlphaFold2-aware protein–DNA binding site prediction using graph transformer
Yuan, Q., Chen, S., Rao, J., Zheng, S., Zhao, H., & Yang, Y. (2022) · Briefings in Bioinformatics · doi:10.1093/bib/bbab564 · Cited by 137 · see citing works
Evolution and impact of bias in human and machine learning algorithm interaction
Sun, W., Nasraoui, O., & Shafto, P. (2020) · PLOS ONE · doi:10.1371/journal.pone.0235502 · Cited by 116 · see citing works
How can I choose an explainer?: An Application-grounded Evaluation of Post-hoc Explanations
Jesus, S., Belém, C., Balayan, V., Bento, J., Saleiro, P., Bizarro, P., & Gama, J. (2021) · Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency · doi:10.1145/3442188.3445941 · Cited by 112 · see citing works
Determinants of mHealth success: An empirical investigation of the user perspective
Birkmeyer, S., Wirtz, B. W., & Langer, P. F. (2021) · International Journal of Information Management · doi:10.1016/j.ijinfomgt.2021.102351 · Cited by 115 · see citing works
Kuzovkin, I., Vicente, R., Petton, M., Lachaux, J.-P., Baciu, M., Kahane, P., Rheims, S., Vidal, J. R., & Aru, J. (2018) · Communications Biology · doi:10.1038/s42003-018-0110-y · Cited by 104 · see citing works
Luczynski, K. C., & Hanley, G. P. (2013) · Journal of Applied Behavior Analysis · doi:10.1002/jaba.44 · Cited by 102 · see citing works
Heyvaert, M., & Onghena, P. (2014) · Journal of Contextual Behavioral Science · doi:10.1016/j.jcbs.2013.10.002 · Cited by 98 · see citing works
Papini, G. B., Fonseca, P., van Gilst, M. M., Bergmans, J. W. M., Vullings, R., & Overeem, S. (2020) · Scientific Reports · doi:10.1038/s41598-020-69935-7 · Cited by 90 · see citing works
BioReader: a text mining tool for performing classification of biomedical literature
Simon, C., Davidsen, K., Hansen, C., Seymour, E., Barnkob, M. B., & Olsen, L. R. (2019) · BMC Bioinformatics · doi:10.1186/s12859-019-2607-x · Cited by 74 · see citing works
Machine learning based feedback on textual student answers in large courses
Bernius, J. P., Krusche, S., & Bruegge, B. (2022) · Computers and Education: Artificial Intelligence · doi:10.1016/j.caeai.2022.100081 · Cited by 75 · see citing works
Czarnowska, P., Vyas, Y., & Shah, K. (2021) · Transactions of the Association for Computational Linguistics · doi:10.1162/tacl_a_00425 · Cited by 72 · see citing works
VisuoSpatial Foresight for Multi-Step, Multi-Task Fabric Manipulation
Hoque, R., Seita, D., Balakrishna, A., Ganapathi, A., Tanwani, A., Jamali, N., Yamane, K., Iba, S., & Goldberg, K. (2020) · Robotics: Science and Systems XVI · doi:10.15607/rss.2020.xvi.034 · Cited by 74 · see citing works
On-field player workload exposure and knee injury risk monitoring via deep learning
Johnson, W. R., Mian, A., Lloyd, D. G., & Alderson, J. A. (2019) · Journal of Biomechanics · doi:10.1016/j.jbiomech.2019.07.002 · Cited by 69 · see citing works
Iron Regulation in Clostridioides difficile
Berges, M., Michel, A.-M., Lassek, C., Nuss, A. M., Beckstette, M., Dersch, P., Riedel, K., Sievers, S., Becher, D., Otto, A., et al. (2018) · Frontiers in Microbiology · doi:10.3389/fmicb.2018.03183 · Cited by 63 · see citing works
Bloch, L., Friedrich, C. M., & Initiative, F. T. A. D. N. (2021) · Alzheimer's Research & Therapy · doi:10.1186/s13195-021-00879-4 · Cited by 68 · see citing works
Schoeffer, J., Kuehl, N., & Machowski, Y. (2022) · 2022 ACM Conference on Fairness Accountability and Transparency · doi:10.1145/3531146.3533218 · Cited by 67 · see citing works
Wu, X., Kondragunta, V., Kornman, K. S., Wang, H. Y., Duff, G. W., Renner, J. B., & Jordan, J. M. (2013) · Osteoarthritis and Cartilage · doi:10.1016/j.joca.2013.04.003 · Cited by 60 · see citing works
Influence of non-steroidal anti-inflammatory drugs on <i>Drosophila melanogaster</i> longevity
Danilov, A., Shaposhnikov, M., Shevchenko, O., Zemskaya, N., Zhavoronkov, A., & Moskalev, A. (2015) · Oncotarget · doi:10.18632/oncotarget.5118 · Cited by 64 · see citing works
Creagh, A. P., Hamy, V., Yuan, H., Mertes, G., Tomlinson, R., Chen, W.-H., Williams, R., Llop, C., Yee, C., Duh, M. S., et al. (2024) · npj Digital Medicine · doi:10.1038/s41746-024-01013-y · Cited by 64 · see citing works
Deploying nEmesis: Preventing Foodborne Illness by Data Mining Social Media
Sadilek, A., Kautz, H., DiPrete, L., Labus, B., Portman, E., Teitel, J., & Silenzio, V. (2017) · AI Magazine · doi:10.1609/aimag.v38i1.2711 · Cited by 56 · see citing works
Manual refactoring changes with automated refactoring validation
Ge, X., & Murphy-Hill, E. (2014) · Proceedings of the 36th International Conference on Software Engineering · doi:10.1145/2568225.2568280 · Cited by 55 · see citing works
Identifying schizophrenia subgroups using clustering and supervised learning
Talpalaru, A., Bhagwat, N., Devenyi, G. A., Lepage, M., & Chakravarty, M. M. (2019) · Schizophrenia Research · doi:10.1016/j.schres.2019.05.044 · Cited by 53 · see citing works
Poncet, A., Courvoisier, D. S., Combescure, C., & Perneger, T. V. (2016) · Methodology · doi:10.1027/1614-2241/a000110 · Cited by 49 · see citing works
Task Contamination: Language Models May Not Be Few-Shot Anymore
Li, C., & Flanigan, J. (2024) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v38i16.29808 · Cited by 47 · see citing works
Visuospatial foresight for physical sequential fabric manipulation
Hoque, R., Seita, D., Balakrishna, A., Ganapathi, A., Tanwani, A. K., Jamali, N., Yamane, K., Iba, S., & Goldberg, K. (2022) · Autonomous Robots · doi:10.1007/s10514-021-10001-0 · Cited by 45 · see citing works
CREF: An LLM-Based Conversational Software Repair Framework for Programming Tutors
Yang, B., Tian, H., Pian, W., Yu, H., Wang, H., Klein, J., Bissyandé, T. F., & Jin, S. (2024) · Proceedings of the 33rd ACM SIGSOFT International Symposium on Software Testing and Analysis · doi:10.1145/3650212.3680328 · Cited by 41 · see citing works
Passive mobile sensing and psychological traits for large scale mood prediction
Spathis, D., Servia-Rodriguez, S., Farrahi, K., Mascolo, C., & Rentfrow, J. (2019) · Proceedings of the 13th EAI International Conference on Pervasive Computing Technologies for Healthcare · doi:10.1145/3329189.3329213 · Cited by 40 · see citing works
Tewari, K. S., Java, J. J., Gatcliffe, T. A., Bookman, M. A., & Monk, B. J. (2014) · Gynecologic Oncology · doi:10.1016/j.ygyno.2014.03.013 · Cited by 39 · see citing works
Ng, L., Pitt, V., Huckvale, K., Clavisi, O., Turner, T., Gruen, R., & Elliott, J. H. (2014) · Systematic Reviews · doi:10.1186/2046-4053-3-121 · Cited by 38 · see citing works
Sarkar, R. (2014) · Indian Journal of Clinical Biochemistry · doi:10.1007/s12291-013-0339-7 · Cited by 34 · see citing works
Which Contributions Deserve Credit? Perceptions of Attribution in Human-AI Co-Creation
He, J., Houde, S., & Weisz, J. D. (2025) · Proceedings of the 2025 CHI Conference on Human Factors in Computing Systems · doi:10.1145/3706598.3713522 · Cited by 36 · see citing works
Comes, M. C., Fucci, L., Mele, F., Bove, S., Cristofaro, C., De Risi, I., Fanizzi, A., Milella, M., Strippoli, S., Zito, A., et al. (2022) · Scientific Reports · doi:10.1038/s41598-022-24315-1 · Cited by 33 · see citing works
A High-Throughput Screening Model of the Tumor Microenvironment for Ovarian Cancer Cell Growth
Lal-Nag, M., McGee, L., Guha, R., Lengyel, E., Kenny, H. A., & Ferrer, M. (2017) · SLAS Discovery · doi:10.1177/2472555216687082 · Cited by 33 · see citing works
Effects of Water-Soluble Antioxidant from Spinach, NAO, on Doxorubicin-Induced Heart Injury
Breitbart, E., Lomnitski, L., Nyska, A., Malik, Z., Bergman, M., Sofer, Y., Haseman, J. K., & Grossman, S. (2001) · Human & Experimental Toxicology · doi:10.1191/096032701680350604 · Cited by 31 · see citing works
Asbestos-contaminated drinking water: its impact on household air
Webber, J. S., Syrotynski, S., & King, M. V. (1988) · Environmental Research · doi:10.1016/s0013-9351(88)80029-x · Cited by 29 · see citing works
Basavalingappa, R. H., Arumugam, R., Lasrado, N., Yalaka, B., Massilamany, C., Gangaplara, A., Riethoven, J.-J., Xiang, S.-H., Steffen, D., & Reddy, J. (2020) · Molecular Immunology · doi:10.1016/j.molimm.2020.06.017 · Cited by 29 · see citing works
Persuasive Synthetic Speech: Voice Perception and User Behaviour
Dubiel, M., Halvey, M., Gallegos, P. O., & King, S. (2020) · Proceedings of the 2nd Conference on Conversational User Interfaces · doi:10.1145/3405755.3406120 · Cited by 28 · see citing works
Predictive Comment Updating With Heuristics and AST-Path-Based Neural Learning: A Two-Phase Approach
Lin, B., Wang, S., Liu, Z., Xia, X., & Mao, X. (2023) · IEEE Transactions on Software Engineering · doi:10.1109/tse.2022.3185458 · Cited by 27 · see citing works
Amler, S., Sauerland, M., Deiters, C., Büchner, T., & Schumacher, A. (2015) · Health and Quality of Life Outcomes · doi:10.1186/s12955-015-0222-8 · Cited by 25 · see citing works
Assessing the Scale Dynamics of the Rainfall Retention of Green Roofs in a Subtropical Climate
Persch, C. G., Tassi, R., Minetto, B., Allasia, D. G., & Rippel, E. (2021) · Journal of Environmental Engineering · doi:10.1061/(asce)ee.1943-7870.0001933 · Cited by 16 · see citing works
Chay, J., Tang, R. W. C., Tan, T.-E., Chan, C. M., Mathur, R., Lee, B. J. H., Chan, H. H., Sim, S. S. K. P., Farooqui, S., Teo, K. Y. C., et al. (2023) · Eye · doi:10.1038/s41433-023-02624-7 · Cited by 15 · see citing works
Quinkenstein, A., Pape, D., Freese, D., Schneider, B. U., & Hüttl, R. F. (2012) · International Journal of Forestry Research · doi:10.1155/2012/891798 · Cited by 14 · see citing works
Maillard, J., Ravetta, F., Raut, J.-C., Fochesatto, G. J., & Law, K. S. (2022) · Boundary-Layer Meteorology · doi:10.1007/s10546-022-00737-2 · Cited by 12 · see citing works
Shealy, T., Klotz, L., Weber, E. U., Johnson, E. J., & Bell, R. G. (2019) · Journal of Management in Engineering · doi:10.1061/(asce)me.1943-5479.0000692 · Cited by 11 · see citing works
(2017) · Lecture Notes in Computer Science · doi:10.1007/978-3-319-72038-8 · Cited by 11 · see citing works
Nguyen‐Duc, J., de Riedmatten, I., Spencer, A. P. C., Perot, J., Olszowy, W., & Jelescu, I. (2025) · Human Brain Mapping · doi:10.1002/hbm.70110 · Cited by 11 · see citing works
Automatic enforcement of constraints in real-time collaborative architectural decision making
Gaubatz, P., Lytra, I., & Zdun, U. (2015) · Journal of Systems and Software · doi:10.1016/j.jss.2015.01.056 · Cited by 11 · see citing works
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Saurabh, S. K., & Kumar, D. (2024) · International Journal of System Assurance Engineering and Management · doi:10.1007/s13198-024-02262-6 · Cited by 10 · see citing works
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Takacs, R., & McCulloh, I. (2019) · Proceedings of the 2019 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining · doi:10.1145/3341161.3343852 · Cited by 9 · see citing works
Entropy Guided Spectrum Based Bug Localization Using Statistical Language Model
Chakraborty, S., Li, Y., Irvine, M., Saha, R., & Ray, B. (2018) · arXiv · doi:10.48550/arxiv.1802.06947 · Cited by 7 · see citing works
“These results are also confirmed by Wilcoxon non-parametric test [40, 61].”
ResultAutomatic analysis of available source code of top artificial intelligence conference papers
Lin, J., Wang, Y., Yu, Y., Zhou, Y., Chen, Y., & Shi, X. (2022) · International Journal of Software Engineering and Knowledge Engineering · doi:10.1142/s0218194022500358 · Cited by 7 · see citing works
Lesovoy, D., Roshchin, K., Sala, B. M., Sandalova, T., Achour, A., Agback, T., Orekhov, V., & Agback, P. (2025) · doi:10.1101/2025.02.07.637034 · Cited by 6 · see citing works
She, Y., Klimczak, K. S., Levin, M. E., & Liao, S. N. (2024) · Proceedings of the 55th ACM Technical Symposium on Computer Science Education V. 1 · doi:10.1145/3626252.3630805 · Cited by 3 · see citing works
N., K., E., S., J., D., C., G., J., K., N., K., M., Z., & O., Z. (2024) · Environmental Science: Processes & Impacts · doi:10.1039/d4em00415a · Cited by 3 · see citing works
Garg, K., Tang, X., Heo, J., Morgan, D. R., Gergle, D., Sudderth, E. B., & Piper, A. M. (2026) · Proceedings of the 2026 CHI Conference on Human Factors in Computing Systems · doi:10.1145/3772318.3791309 · Cited by 3 · see citing works
“We use a Mann-Whitney U Test for inferential statistics because the data being compared are ordinal (Likert scale) [93].”
Porta, T., & Hudson, C. (2025) · Cogent Education · doi:10.1080/2331186x.2025.2464339 · Cited by 2 · see citing works
Matejić, T., Knežević, S., Milojević, S., Adamović, M., & Milošević, M. (2025) · BizInfo Blace · doi:10.71159/bizinfo250023m · Cited by 2 · see citing works
Perceptions of the Fairness Impacts of Multiplicity in Machine Learning
Meyer, A. P., Kim, Y.-S., D'Antoni, L., & Albarghouthi, A. (2025) · Proceedings of the 2025 CHI Conference on Human Factors in Computing Systems · doi:10.1145/3706598.3713524 · Cited by 1 · see citing works
Self-Admitted GenAI Usage in Open-Source Software
Xiao, T., Fan, Y., Calefato, F., Treude, C., Kula, R. G., Hata, H., & Baltes, S. (2026) · IEEE Transactions on Software Engineering · doi:10.1109/tse.2026.3681886 · Cited by 1 · see citing works
Global vs. segmental acoustic features for dysarthria assessment in motor neuron diseases
Attia, M., Simmatis, L., Sejdic, E., & Yunusova, Y. (2025) · Computers in Biology and Medicine · doi:10.1016/j.compbiomed.2025.111291
Jung, W., Jeon, K., & Babon-Ayeng, P. (2026) · Proceedings of the 2026 ACM Sustainability Week · doi:10.1145/3765611.3815499
SVG: 3D Stereoscopic Video Generation via Denoising Frame Matrix
Dai, P., Tan, F., Xu, Q., Futschik, D., Du, R., Fanello, S., Qi, X., & Zhang, Y. (2024) · arXiv · doi:10.48550/arxiv.2407.00367
When Agents Coordinate: Measuring Coordination in Multi-Agent AI Coding
Destefanis, G., & Aste, T. (2026) · arXiv · doi:10.48550/arxiv.2608.16801
- Authors
- Mann, H. B., & Whitney, D. R.
- Venue
- The Annals of Mathematical Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1947-03
- Volume
- 18
- Issue
- 1
- Pages
- 50-60
- ISSN
- 0003-4851 (ISSN-L)
- OpenAlex
- W1972978214
- Cited by
- 14,320
- References
- 2
- Citations by year
- 2026: 1351 · 2025: 1107 · 2024: 974 · 2023: 929 · 2022: 945 · 2021: 953 · 2020: 825 · 2019: 708 · 2018: 679 · 2017: 486 · 2016: 525 · 2015: 471 · 2014: 502 · 2013: 357 · 2012: 336
- FWCI
- 4.62
- 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
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
- Keywords
- stochastic dominance, Mann-Whitney test, two-sample test, rank statistics, recurrence relations, probability tables, asymptotic normality, consistency of tests, continuous distributions
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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.
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