Mann–Whitney U test (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Mann–Whitney U test" in English language version.

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Mann, Henry B.; Whitney, Donald R. (1947). "On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other". Annals of Mathematical Statistics. 18 (1): 50–60. doi:10.1214/aoms/1177730491. MR 0022058. Zbl 0041.26103.
Fay, Michael P.; Proschan, Michael A. (2010). "Wilcoxon–Mann–Whitney or t-test? On assumptions for hypothesis tests and multiple interpretations of decision rules". Statistics Surveys. 4: 1–39. doi:10.1214/09-SS051. MR 2595125. PMC 2857732. PMID 20414472.

apa.org

doi.apa.org

Fritz, Catherine O.; Morris, Peter E.; Richler, Jennifer J. (2012). "Effect size estimates: Current use, calculations, and interpretation". Journal of Experimental Psychology: General. 141 (1): 2–18. doi:10.1037/a0024338. ISSN 1939-2222. PMID 21823805.

apache.org

commons.apache.org

"MannWhitneyUTest (Apache Commons Math 3.3 API)". commons.apache.org.

bu.edu

sphweb.bumc.bu.edu

Boston University (SPH), 2017

doi.org

Mann, Henry B.; Whitney, Donald R. (1947). "On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other". Annals of Mathematical Statistics. 18 (1): 50–60. doi:10.1214/aoms/1177730491. MR 0022058. Zbl 0041.26103.
Fay, Michael P.; Proschan, Michael A. (2010). "Wilcoxon–Mann–Whitney or t-test? On assumptions for hypothesis tests and multiple interpretations of decision rules". Statistics Surveys. 4: 1–39. doi:10.1214/09-SS051. MR 2595125. PMC 2857732. PMID 20414472.
Divine, George W.; Norton, H. James; Barón, Anna E.; Juarez-Colunga, Elizabeth (2018). "The Wilcoxon–Mann–Whitney Procedure Fails as a Test of Medians". The American Statistician. 72 (3): 278–286. doi:10.1080/00031305.2017.1305291.
Conroy, Ronán (2012). "What Hypotheses do "Nonparametric" Two-Group Tests Actually Test?". Stata Journal. 12 (2): 182–190. doi:10.1177/1536867X1201200202. S2CID 118445807. Retrieved 24 May 2021.
Hart, Anna (2001). "Mann–Whitney test is not just a test of medians: differences in spread can be important". BMJ. 323 (7309): 391–393. doi:10.1136/bmj.323.7309.391. PMC 1120984. PMID 11509435.
Mason, S. J., Graham, N. E. (2002). "Areas beneath the relative operating characteristics (ROC) and relative operating levels (ROL) curves: Statistical significance and interpretation". Quarterly Journal of the Royal Meteorological Society. 128 (584): 2145–2166. doi:10.1256/003590002320603584. ISSN 1477-870X.
Hand, David J.; Till, Robert J. (2001). "A Simple Generalisation of the Area Under the ROC Curve for Multiple Class Classification Problems". Machine Learning. 45 (2): 171–186. doi:10.1023/A:1010920819831.
Fritz, Catherine O.; Morris, Peter E.; Richler, Jennifer J. (2012). "Effect size estimates: Current use, calculations, and interpretation". Journal of Experimental Psychology: General. 141 (1): 2–18. doi:10.1037/a0024338. ISSN 1939-2222. PMID 21823805.
Wilkinson, Leland (1999). "Statistical methods in psychology journals: Guidelines and explanations". American Psychologist. 54 (8): 594–604. doi:10.1037/0003-066X.54.8.594.
Nakagawa, Shinichi; Cuthill, Innes C (2007). "Effect size, confidence interval and statistical significance: a practical guide for biologists". Biological Reviews of the Cambridge Philosophical Society. 82 (4): 591–605. doi:10.1111/j.1469-185X.2007.00027.x. PMID 17944619. S2CID 615371.
Kerby, D.S. (2014). "The simple difference formula: An approach to teaching nonparametric correlation". Comprehensive Psychology. 3: 11.IT.3.1. doi:10.2466/11.IT.3.1. S2CID 120622013.
McGraw, K.O.; Wong, J.J. (1992). "A common language effect size statistic". Psychological Bulletin. 111 (2): 361–365. doi:10.1037/0033-2909.111.2.361.
Grissom RJ (1994). "Statistical analysis of ordinal categorical status after therapies". Journal of Consulting and Clinical Psychology. 62 (2): 281–284. doi:10.1037/0022-006X.62.2.281. PMID 8201065.
Herrnstein, Richard J.; Loveland, Donald H.; Cable, Cynthia (1976). "Natural Concepts in Pigeons". Journal of Experimental Psychology: Animal Behavior Processes. 2 (4): 285–302. doi:10.1037/0097-7403.2.4.285. PMID 978139.
Cureton, E.E. (1956). "Rank-biserial correlation". Psychometrika. 21 (3): 287–290. doi:10.1007/BF02289138. S2CID 122500836.
Wendt, H.W. (1972). "Dealing with a common problem in social science: A simplified rank-biserial coefficient of correlation based on the U statistic". European Journal of Social Psychology. 2 (4): 463–465. doi:10.1002/ejsp.2420020412.
Zimmerman, Donald W. (1998-01-01). "Invalidation of Parametric and Nonparametric Statistical Tests by Concurrent Violation of Two Assumptions". The Journal of Experimental Education. 67 (1): 55–68. doi:10.1080/00220979809598344. ISSN 0022-0973.
Lumley, Thomas; Diehr, Paula; Emerson, Scott; Chen, Lu (May 2002). "The Importance of the Normality Assumption in Large Public Health Data Sets". Annual Review of Public Health. 23 (1): 151–169. doi:10.1146/annurev.publhealth.23.100901.140546. ISSN 0163-7525. PMID 11910059.
Conover, William J.; Iman, Ronald L. (1981). "Rank Transformations as a Bridge Between Parametric and Nonparametric Statistics". The American Statistician. 35 (3): 124–129. doi:10.2307/2683975. JSTOR 2683975.
Vaart, A. W. van der (1998-10-13). Asymptotic Statistics. Cambridge University Press. doi:10.1017/cbo9780511802256. ISBN 978-0-511-80225-6.
Brunner, Edgar; Bathke, Arne C.; Konietschke, Frank (2018). Rank and pseudo-rank procedures for independent observations in factorial designs: Using R and SAS. Springer Series in Statistics. Cham: Springer International Publishing. doi:10.1007/978-3-030-02914-2. ISBN 978-3-030-02912-8.
Karch, Julian D. (2021). "Psychologists Should Use Brunner–Munzel's Instead of Mann–Whitney's U Test as the Default Nonparametric Procedure". Advances in Methods and Practices in Psychological Science. 4 (2). doi:10.1177/2515245921999602. hdl:1887/3209569. ISSN 2515-2459.
Kasuya, Eiiti (2001). "Mann–Whitney U test when variances are unequal". Animal Behaviour. 61 (6): 1247–1249. doi:10.1006/anbe.2001.1691. S2CID 140209347.
Karch, Julian (2021). "Psychologists Should Use Brunner–Munzel's Instead of Mann–Whitney's U Test as the Default Nonparametric Procedure". Advances in Methods and Practices in Psychological Science. 4 (2). doi:10.1177/2515245921999602. hdl:1887/3209569. S2CID 235521799.
Bergmann, Reinhard; Ludbrook, John; Spooren, Will P.J.M. (2000). "Different Outcomes of the Wilcoxon–Mann–Whitney Test from Different Statistics Packages". The American Statistician. 54 (1): 72–77. doi:10.1080/00031305.2000.10474513. JSTOR 2685616. S2CID 120473946.
Kruskal, William H. (September 1957). "Historical Notes on the Wilcoxon Unpaired Two-Sample Test". Journal of the American Statistical Association. 52 (279): 356–360. doi:10.2307/2280906. JSTOR 2280906.
Wilcoxon, Frank (1945). "Individual comparisons by ranking methods". Biometrics Bulletin. 1 (6): 80–83. doi:10.2307/3001968. hdl:10338.dmlcz/135688. JSTOR 3001968.

dx.doi.org

Vaart, A. W. van der (1998-10-13). Asymptotic Statistics. Cambridge University Press. doi:10.1017/cbo9780511802256. ISBN 978-0-511-80225-6.

fharrell.com

Harrell, Frank (20 September 2020). "Violation of Proportional Odds is Not Fatal". {{cite journal}}: Cite journal requires |journal= (help)

github.com

"JuliaStats/HypothesisTests.jl". GitHub. 30 May 2021.

handle.net

hdl.handle.net

Karch, Julian D. (2021). "Psychologists Should Use Brunner–Munzel's Instead of Mann–Whitney's U Test as the Default Nonparametric Procedure". Advances in Methods and Practices in Psychological Science. 4 (2). doi:10.1177/2515245921999602. hdl:1887/3209569. ISSN 2515-2459.
Karch, Julian (2021). "Psychologists Should Use Brunner–Munzel's Instead of Mann–Whitney's U Test as the Default Nonparametric Procedure". Advances in Methods and Practices in Psychological Science. 4 (2). doi:10.1177/2515245921999602. hdl:1887/3209569. S2CID 235521799.
Wilcoxon, Frank (1945). "Individual comparisons by ranking methods". Biometrics Bulletin. 1 (6): 80–83. doi:10.2307/3001968. hdl:10338.dmlcz/135688. JSTOR 3001968.

jstor.org

[1], See Table 2.1 of Pratt (1964) "Robustness of Some Procedures for the Two-Sample Location Problem." Journal of the American Statistical Association. 59 (307): 655–680. If the two distributions are normal with the same mean but different variances, then Pr[X > Y] = Pr[Y < X] but the size of the Mann–Whitney test can be larger than the nominal level. So we cannot define the null hypothesis as Pr[X > Y] = Pr[Y < X] and get a valid test.
Conover, William J.; Iman, Ronald L. (1981). "Rank Transformations as a Bridge Between Parametric and Nonparametric Statistics". The American Statistician. 35 (3): 124–129. doi:10.2307/2683975. JSTOR 2683975.
Bergmann, Reinhard; Ludbrook, John; Spooren, Will P.J.M. (2000). "Different Outcomes of the Wilcoxon–Mann–Whitney Test from Different Statistics Packages". The American Statistician. 54 (1): 72–77. doi:10.1080/00031305.2000.10474513. JSTOR 2685616. S2CID 120473946.
Kruskal, William H. (September 1957). "Historical Notes on the Wilcoxon Unpaired Two-Sample Test". Journal of the American Statistical Association. 52 (279): 356–360. doi:10.2307/2280906. JSTOR 2280906.
Wilcoxon, Frank (1945). "Individual comparisons by ranking methods". Biometrics Bulletin. 1 (6): 80–83. doi:10.2307/3001968. hdl:10338.dmlcz/135688. JSTOR 3001968.

nih.gov

pubmed.ncbi.nlm.nih.gov

Fay, Michael P.; Proschan, Michael A. (2010). "Wilcoxon–Mann–Whitney or t-test? On assumptions for hypothesis tests and multiple interpretations of decision rules". Statistics Surveys. 4: 1–39. doi:10.1214/09-SS051. MR 2595125. PMC 2857732. PMID 20414472.
Hart, Anna (2001). "Mann–Whitney test is not just a test of medians: differences in spread can be important". BMJ. 323 (7309): 391–393. doi:10.1136/bmj.323.7309.391. PMC 1120984. PMID 11509435.
Fritz, Catherine O.; Morris, Peter E.; Richler, Jennifer J. (2012). "Effect size estimates: Current use, calculations, and interpretation". Journal of Experimental Psychology: General. 141 (1): 2–18. doi:10.1037/a0024338. ISSN 1939-2222. PMID 21823805.
Nakagawa, Shinichi; Cuthill, Innes C (2007). "Effect size, confidence interval and statistical significance: a practical guide for biologists". Biological Reviews of the Cambridge Philosophical Society. 82 (4): 591–605. doi:10.1111/j.1469-185X.2007.00027.x. PMID 17944619. S2CID 615371.
Grissom RJ (1994). "Statistical analysis of ordinal categorical status after therapies". Journal of Consulting and Clinical Psychology. 62 (2): 281–284. doi:10.1037/0022-006X.62.2.281. PMID 8201065.
Herrnstein, Richard J.; Loveland, Donald H.; Cable, Cynthia (1976). "Natural Concepts in Pigeons". Journal of Experimental Psychology: Animal Behavior Processes. 2 (4): 285–302. doi:10.1037/0097-7403.2.4.285. PMID 978139.
Lumley, Thomas; Diehr, Paula; Emerson, Scott; Chen, Lu (May 2002). "The Importance of the Normality Assumption in Large Public Health Data Sets". Annual Review of Public Health. 23 (1): 151–169. doi:10.1146/annurev.publhealth.23.100901.140546. ISSN 0163-7525. PMID 11910059.

ncbi.nlm.nih.gov

Fay, Michael P.; Proschan, Michael A. (2010). "Wilcoxon–Mann–Whitney or t-test? On assumptions for hypothesis tests and multiple interpretations of decision rules". Statistics Surveys. 4: 1–39. doi:10.1214/09-SS051. MR 2595125. PMC 2857732. PMID 20414472.
Hart, Anna (2001). "Mann–Whitney test is not just a test of medians: differences in spread can be important". BMJ. 323 (7309): 391–393. doi:10.1136/bmj.323.7309.391. PMC 1120984. PMID 11509435.

researchgate.net

Conroy, Ronán (2012). "What Hypotheses do "Nonparametric" Two-Group Tests Actually Test?". Stata Journal. 12 (2): 182–190. doi:10.1177/1536867X1201200202. S2CID 118445807. Retrieved 24 May 2021.

sagepub.com

journals.sagepub.com

Karch, Julian (2021). "Psychologists Should Use Brunner–Munzel's Instead of Mann–Whitney's U Test as the Default Nonparametric Procedure". Advances in Methods and Practices in Psychological Science. 4 (2). doi:10.1177/2515245921999602. hdl:1887/3209569. S2CID 235521799.

scipy.org

docs.scipy.org

"scipy.stats.mannwhitneyu". SciPy v0.16.0 Reference Guide. The Scipy community. 24 July 2015. Retrieved 11 September 2015. scipy.stats.mannwhitneyu(x, y, use_continuity=True): Computes the Mann–Whitney rank test on samples x and y.

semanticscholar.org

api.semanticscholar.org

Conroy, Ronán (2012). "What Hypotheses do "Nonparametric" Two-Group Tests Actually Test?". Stata Journal. 12 (2): 182–190. doi:10.1177/1536867X1201200202. S2CID 118445807. Retrieved 24 May 2021.
Nakagawa, Shinichi; Cuthill, Innes C (2007). "Effect size, confidence interval and statistical significance: a practical guide for biologists". Biological Reviews of the Cambridge Philosophical Society. 82 (4): 591–605. doi:10.1111/j.1469-185X.2007.00027.x. PMID 17944619. S2CID 615371.
Kerby, D.S. (2014). "The simple difference formula: An approach to teaching nonparametric correlation". Comprehensive Psychology. 3: 11.IT.3.1. doi:10.2466/11.IT.3.1. S2CID 120622013.
Cureton, E.E. (1956). "Rank-biserial correlation". Psychometrika. 21 (3): 287–290. doi:10.1007/BF02289138. S2CID 122500836.
Kasuya, Eiiti (2001). "Mann–Whitney U test when variances are unequal". Animal Behaviour. 61 (6): 1247–1249. doi:10.1006/anbe.2001.1691. S2CID 140209347.
Karch, Julian (2021). "Psychologists Should Use Brunner–Munzel's Instead of Mann–Whitney's U Test as the Default Nonparametric Procedure". Advances in Methods and Practices in Psychological Science. 4 (2). doi:10.1177/2515245921999602. hdl:1887/3209569. S2CID 235521799.
Bergmann, Reinhard; Ludbrook, John; Spooren, Will P.J.M. (2000). "Different Outcomes of the Wilcoxon–Mann–Whitney Test from Different Statistics Packages". The American Statistician. 54 (1): 72–77. doi:10.1080/00031305.2000.10474513. JSTOR 2685616. S2CID 120473946.

springer.com

link.springer.com

Brunner, Edgar; Bathke, Arne C.; Konietschke, Frank (2018). Rank and pseudo-rank procedures for independent observations in factorial designs: Using R and SAS. Springer Series in Statistics. Cham: Springer International Publishing. doi:10.1007/978-3-030-02914-2. ISBN 978-3-030-02912-8.

trb.org

onlinepubs.trb.org

Conover, William J.; Practical Nonparametric Statistics, John Wiley & Sons, 1980 (2nd Edition), pp. 225–226

ucdavis.edu

math.ucdavis.edu

Fawcett, Tom (2006); An introduction to ROC analysis, Pattern Recognition Letters, 27, 861–874.

worldcat.org

search.worldcat.org

Mason, S. J., Graham, N. E. (2002). "Areas beneath the relative operating characteristics (ROC) and relative operating levels (ROL) curves: Statistical significance and interpretation". Quarterly Journal of the Royal Meteorological Society. 128 (584): 2145–2166. doi:10.1256/003590002320603584. ISSN 1477-870X.
Fritz, Catherine O.; Morris, Peter E.; Richler, Jennifer J. (2012). "Effect size estimates: Current use, calculations, and interpretation". Journal of Experimental Psychology: General. 141 (1): 2–18. doi:10.1037/a0024338. ISSN 1939-2222. PMID 21823805.
Zimmerman, Donald W. (1998-01-01). "Invalidation of Parametric and Nonparametric Statistical Tests by Concurrent Violation of Two Assumptions". The Journal of Experimental Education. 67 (1): 55–68. doi:10.1080/00220979809598344. ISSN 0022-0973.
Lumley, Thomas; Diehr, Paula; Emerson, Scott; Chen, Lu (May 2002). "The Importance of the Normality Assumption in Large Public Health Data Sets". Annual Review of Public Health. 23 (1): 151–169. doi:10.1146/annurev.publhealth.23.100901.140546. ISSN 0163-7525. PMID 11910059.
Karch, Julian D. (2021). "Psychologists Should Use Brunner–Munzel's Instead of Mann–Whitney's U Test as the Default Nonparametric Procedure". Advances in Methods and Practices in Psychological Science. 4 (2). doi:10.1177/2515245921999602. hdl:1887/3209569. ISSN 2515-2459.

zbmath.org

Mann, Henry B.; Whitney, Donald R. (1947). "On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other". Annals of Mathematical Statistics. 18 (1): 50–60. doi:10.1214/aoms/1177730491. MR 0022058. Zbl 0041.26103.