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Round your numbers in rank tests: exact and asymptotic inference and ties

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Abstract

Non-parametric statistical tests are commonly used in the behavioral sciences. Researchers need to be aware that non-parameteric methods involving ranks can perform unreliably as a result of very small amounts of noise added in the storage and manipulation of values by computers, causing spurious reduction in the number of ties. In order to avoid this problem, researchers should round values to an appropriate number of decimal places prior to the ranking procedure to ensure that data points whose values cannot be separated according to the precision of their measurement are recorded as having identical rank. We also recommend exact rather than asymptotic evaluation of p values in non-parametric statistical tests.

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References

  • Berger VW (2001) The p-value interval as an inferential tool. Statistician 50:79–85

    Google Scholar 

  • Berger VW (2007) Reply to Senn (2007). Biometrics 63:298–299

    Article  Google Scholar 

  • Berger VW, Matthews JR, Grosch EN (2008) On improving research methodology in clinical trials. Stat Methods Med Res 17:231–242

    Article  PubMed  Google Scholar 

  • Bergmann R, Ludbrook J, Spooren WPJM (2000) Different outcomes of the Wilcoxon–Mann–Whitney test from different statistics packages. Am Stat 54:72–77

    Article  Google Scholar 

  • Bortz J, Lienert GA (2008) Kurzgefasste Statistik für die Klinische Forschung. Leitfaden für die verteilungsfreie Analyse kleiner Stichproben, 3rd edn. Springer, Heidelberg

    Google Scholar 

  • Brunner E, Munzel U (2000) The nonparametric Behrens-Fisher problem: asymptotic theory and a small sample approximation. Biom J 42:17–25

    Article  Google Scholar 

  • Brunner E, Munzel U (2002) Nichtparametrische Datenanalyse. Springer, Berlin

    Google Scholar 

  • Cliff N (1996) Ordinal methods for behavioral data analysis. Lawrence Erlbaum, Mahwah

    Google Scholar 

  • Coakley CW, Heise MA (1996) Versions of the sign test in the presence of ties. Biometrics 52:1242–1251

    Article  Google Scholar 

  • Dixon WJ, Mood AM (1946) The statistical sign test. J Am Stat Assoc 41:557–566

    Article  CAS  PubMed  Google Scholar 

  • Fong DYT, Kwan CW, Lam KF, Lam KSL (2003) Use of the sign test for the median in the presence of ties. Am Stat 57:237–240

    Article  Google Scholar 

  • Good PI (2000) Permutation Tests, 2nd edn. Springer, New York

    Google Scholar 

  • Good PI (2005) Introduction to statistics through resampling methods and R/S-Plus. Wiley, Hoboken

    Book  Google Scholar 

  • Haffer J (2008) Ornithology, evolution, and philosophy. Springer, Berlin

    Google Scholar 

  • Higgins JJ (2000) Letter to the editor. Am Stat 54:86

    Google Scholar 

  • Hollander M, Wolfe DA (1999) Nonparametric statistical methods, 2nd edn. Wiley, New York

    Google Scholar 

  • Ivanova A, Berger VW (2001) Drawbacks to integer scoring for ordered categorical data. Biometrics 57:567–570

    Article  CAS  PubMed  Google Scholar 

  • Larocque D, Randles RH (2008) Confidence intervals for a discrete population median. Am Stat 62:32–39

    Article  Google Scholar 

  • Lehmacher W (1976) Asymptotische Eigenschaften linearer Zweistichproben-Rangtests bei beliebigen Verteilungen. PhD thesis, Department of Statistics, University of Dortmund

  • Manly BFJ (2007) Randomization, bootstrap and Monte Carlo methods in biology, 3rd edn. Chapman & Hall, Boca Raton

    Google Scholar 

  • Mehta CR, Patel N, Senchaudhuri P (1992) Exact stratified linear rank tests for ordered categorical and binary data. J Comput Graph Stat 1:21–40

    Article  Google Scholar 

  • Mundry R, Fischer J (1998) Use of statistical programs for nonparametric tests of small samples often leads to incorrect P values: examples from Animal Behaviour. Anim Behav 56:256–259

    Article  PubMed  Google Scholar 

  • Neuhäuser M (2005) Efficiency comparisons of rank and permutation tests (letter to the editor). Stat Med 24:1777–1778

    Article  PubMed  Google Scholar 

  • Neuhäuser M (2009) A note on a maximum test for the analysis of ordered categorical data. J Mod Appl Stat Methods (in press)

  • Neuhäuser M, Ruxton GD (2009) Distribution-free two-sample comparisons in the case of heterogeneous variances. Behav Ecol Sociobiol 63:617–623

    Article  Google Scholar 

  • Neuhäuser M, Boes T, Jöckel KH (2007) Pseudo-precision in gene expression values can reduce efficiency. Methods Inf Med 46:538–541

    PubMed  Google Scholar 

  • Putter J (1955) The treatment of ties in some nonparametric tests. Ann Math Stat 26:368–386

    Article  Google Scholar 

  • Randles RH (2001) On neutral responses (zeros) in the sign test and ties in the Wilcoxon–Mann–Whitney test. Am Stat 55:96–101

    Article  Google Scholar 

  • Rayner JCW, Best DJ (1999) Modelling ties in the sign test. Biometrics 55:663–665

    Article  CAS  PubMed  Google Scholar 

  • Senn S (2007) Drawbacks to noninteger scoring for ordered categorical data. Biometrics 63:296–298

    Article  PubMed  Google Scholar 

  • Sokal RR, Rohlf FJ (1995) Biometry, 3rd edn. W.H. Freeman and Company, New York

    Google Scholar 

  • Tilquin P, van Keilegom I, Coppieters W, le Boulenge E, Baret PV (2003) Non-parametric interval mapping in half-sib designs: use of midranks to account for ties. Genet Res 81:221–228

    Article  CAS  PubMed  Google Scholar 

  • Wittkowski KM (1998) Versions of the sign test in the presence of ties. Biometrics 54:789–791

    Article  Google Scholar 

Download references

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Correspondence to Markus Neuhäuser.

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Communicated by LZ Garamszegi

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Neuhäuser, M., Ruxton, G.D. Round your numbers in rank tests: exact and asymptotic inference and ties. Behav Ecol Sociobiol 64, 297–303 (2009). https://doi.org/10.1007/s00265-009-0843-1

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  • DOI: https://doi.org/10.1007/s00265-009-0843-1

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