Advertisement

Behavioral Ecology and Sociobiology

, Volume 64, Issue 2, pp 297–303 | Cite as

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

  • Markus NeuhäuserEmail author
  • Graeme D. Ruxton
Methods

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.

Keywords

Non-parametric Exact tests Analysis of ranks Mann-Whitney U-test Wilcoxon rank-sum test Paired data 

References

  1. Berger VW (2001) The p-value interval as an inferential tool. Statistician 50:79–85Google Scholar
  2. Berger VW (2007) Reply to Senn (2007). Biometrics 63:298–299CrossRefGoogle Scholar
  3. Berger VW, Matthews JR, Grosch EN (2008) On improving research methodology in clinical trials. Stat Methods Med Res 17:231–242CrossRefPubMedGoogle Scholar
  4. Bergmann R, Ludbrook J, Spooren WPJM (2000) Different outcomes of the Wilcoxon–Mann–Whitney test from different statistics packages. Am Stat 54:72–77CrossRefGoogle Scholar
  5. Bortz J, Lienert GA (2008) Kurzgefasste Statistik für die Klinische Forschung. Leitfaden für die verteilungsfreie Analyse kleiner Stichproben, 3rd edn. Springer, HeidelbergGoogle Scholar
  6. Brunner E, Munzel U (2000) The nonparametric Behrens-Fisher problem: asymptotic theory and a small sample approximation. Biom J 42:17–25CrossRefGoogle Scholar
  7. Brunner E, Munzel U (2002) Nichtparametrische Datenanalyse. Springer, BerlinGoogle Scholar
  8. Cliff N (1996) Ordinal methods for behavioral data analysis. Lawrence Erlbaum, MahwahGoogle Scholar
  9. Coakley CW, Heise MA (1996) Versions of the sign test in the presence of ties. Biometrics 52:1242–1251CrossRefGoogle Scholar
  10. Dixon WJ, Mood AM (1946) The statistical sign test. J Am Stat Assoc 41:557–566CrossRefPubMedGoogle Scholar
  11. Fong DYT, Kwan CW, Lam KF, Lam KSL (2003) Use of the sign test for the median in the presence of ties. Am Stat 57:237–240CrossRefGoogle Scholar
  12. Good PI (2000) Permutation Tests, 2nd edn. Springer, New YorkGoogle Scholar
  13. Good PI (2005) Introduction to statistics through resampling methods and R/S-Plus. Wiley, HobokenCrossRefGoogle Scholar
  14. Haffer J (2008) Ornithology, evolution, and philosophy. Springer, BerlinGoogle Scholar
  15. Higgins JJ (2000) Letter to the editor. Am Stat 54:86Google Scholar
  16. Hollander M, Wolfe DA (1999) Nonparametric statistical methods, 2nd edn. Wiley, New YorkGoogle Scholar
  17. Ivanova A, Berger VW (2001) Drawbacks to integer scoring for ordered categorical data. Biometrics 57:567–570CrossRefPubMedGoogle Scholar
  18. Larocque D, Randles RH (2008) Confidence intervals for a discrete population median. Am Stat 62:32–39CrossRefGoogle Scholar
  19. Lehmacher W (1976) Asymptotische Eigenschaften linearer Zweistichproben-Rangtests bei beliebigen Verteilungen. PhD thesis, Department of Statistics, University of DortmundGoogle Scholar
  20. Manly BFJ (2007) Randomization, bootstrap and Monte Carlo methods in biology, 3rd edn. Chapman & Hall, Boca RatonGoogle Scholar
  21. Mehta CR, Patel N, Senchaudhuri P (1992) Exact stratified linear rank tests for ordered categorical and binary data. J Comput Graph Stat 1:21–40CrossRefGoogle Scholar
  22. 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 56:256–259CrossRefPubMedGoogle Scholar
  23. Neuhäuser M (2005) Efficiency comparisons of rank and permutation tests (letter to the editor). Stat Med 24:1777–1778CrossRefPubMedGoogle Scholar
  24. Neuhäuser M (2009) A note on a maximum test for the analysis of ordered categorical data. J Mod Appl Stat Methods (in press)Google Scholar
  25. Neuhäuser M, Ruxton GD (2009) Distribution-free two-sample comparisons in the case of heterogeneous variances. Behav Ecol Sociobiol 63:617–623CrossRefGoogle Scholar
  26. Neuhäuser M, Boes T, Jöckel KH (2007) Pseudo-precision in gene expression values can reduce efficiency. Methods Inf Med 46:538–541PubMedGoogle Scholar
  27. Putter J (1955) The treatment of ties in some nonparametric tests. Ann Math Stat 26:368–386CrossRefGoogle Scholar
  28. Randles RH (2001) On neutral responses (zeros) in the sign test and ties in the Wilcoxon–Mann–Whitney test. Am Stat 55:96–101CrossRefGoogle Scholar
  29. Rayner JCW, Best DJ (1999) Modelling ties in the sign test. Biometrics 55:663–665CrossRefPubMedGoogle Scholar
  30. Senn S (2007) Drawbacks to noninteger scoring for ordered categorical data. Biometrics 63:296–298CrossRefPubMedGoogle Scholar
  31. Sokal RR, Rohlf FJ (1995) Biometry, 3rd edn. W.H. Freeman and Company, New YorkGoogle Scholar
  32. 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 81:221–228CrossRefPubMedGoogle Scholar
  33. Wittkowski KM (1998) Versions of the sign test in the presence of ties. Biometrics 54:789–791CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Mathematics and Technique, RheinAhrCampusKoblenz University of Applied SciencesRemagenGermany
  2. 2.Division of Ecology and Evolutionary Biology, Faculty of Biomedical and Life Sciences, Graham Kerr BuildingUniversity of GlasgowGlasgowUK

Personalised recommendations