Statistical significance of ranking paradoxes. (English) Zbl 1318.62141
Summary: When nonparametric statistical tests are used to rank-order a list of alternatives, Simpson-like paradoxes arise, in which the individual parts give rise to a common decision, but the aggregate of those parts gives rise to a different decision. D. B. Haunsperger [Soc. Choice Welfare 20, No. 2, 261–272 (2003; Zbl 1073.62531)] and A. E. Bargagliotti [Math. Soc. Sci. 58, No. 3, 354–366 (2009; Zbl 1283.91053)] showed that the Kruskal-Wallis [W. H. Kruskal and W. A. Wallis, J. Am. Stat. Assoc. 47, 583–621 (1952; Zbl 0048.11703)], Mann-Whitney [H. B. Mann and D. R. Whitney, Ann. Math. Stat. 18, 50–60 (1947; Zbl 0041.26103)], and V. P. Bhapkar’s \(V\) [Ann. Math. Stat. 32, 1108–1117 (1961; Zbl 0208.20501)] nonparametric statistical tests are subject to these types of paradoxes. We further investigate these ranking paradoxes by showing that when they occur, the differences in rankings are not statistically significant.
MSC:
| 62G10 | Nonparametric hypothesis testing |
References:
| [1] | Alexander D. A., University of North Carolina School of Public Health, Institute of Statistics Mimeo Series No. 602. (1968) |
| [2] | DOI: 10.1016/j.mathsocsci.2009.07.006 · Zbl 1283.91053 · doi:10.1016/j.mathsocsci.2009.07.006 |
| [3] | Bargagliotti , A. E. , Saari , D. G. ( 2011 ). Symmetry of nonparametric statistical tests on three samples . In press . · Zbl 1219.62073 |
| [4] | DOI: 10.1214/aoms/1177704849 · Zbl 0208.20501 · doi:10.1214/aoms/1177704849 |
| [5] | DOI: 10.2307/2684305 · doi:10.2307/2684305 |
| [6] | DOI: 10.2307/2290463 · Zbl 0769.62034 · doi:10.2307/2290463 |
| [7] | DOI: 10.2307/3315692 · Zbl 0852.62046 · doi:10.2307/3315692 |
| [8] | DOI: 10.1007/s003550200179 · Zbl 1073.62531 · doi:10.1007/s003550200179 |
| [9] | DOI: 10.2307/2280779 · Zbl 0048.11703 · doi:10.2307/2280779 |
| [10] | Lehman E. L., Nonparametrics: Statistical Methods based on Ranks (1975) |
| [11] | DOI: 10.1214/aoms/1177730491 · Zbl 0041.26103 · doi:10.1214/aoms/1177730491 |
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