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
Berger VW (2007) Reply to Senn (2007). Biometrics 63:298–299
Berger VW, Matthews JR, Grosch EN (2008) On improving research methodology in clinical trials. Stat Methods Med Res 17:231–242
Bergmann R, Ludbrook J, Spooren WPJM (2000) Different outcomes of the Wilcoxon–Mann–Whitney test from different statistics packages. Am Stat 54:72–77
Bortz J, Lienert GA (2008) Kurzgefasste Statistik für die Klinische Forschung. Leitfaden für die verteilungsfreie Analyse kleiner Stichproben, 3rd edn. Springer, Heidelberg
Brunner E, Munzel U (2000) The nonparametric Behrens-Fisher problem: asymptotic theory and a small sample approximation. Biom J 42:17–25
Brunner E, Munzel U (2002) Nichtparametrische Datenanalyse. Springer, Berlin
Cliff N (1996) Ordinal methods for behavioral data analysis. Lawrence Erlbaum, Mahwah
Coakley CW, Heise MA (1996) Versions of the sign test in the presence of ties. Biometrics 52:1242–1251
Dixon WJ, Mood AM (1946) The statistical sign test. J Am Stat Assoc 41:557–566
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
Good PI (2000) Permutation Tests, 2nd edn. Springer, New York
Good PI (2005) Introduction to statistics through resampling methods and R/S-Plus. Wiley, Hoboken
Haffer J (2008) Ornithology, evolution, and philosophy. Springer, Berlin
Higgins JJ (2000) Letter to the editor. Am Stat 54:86
Hollander M, Wolfe DA (1999) Nonparametric statistical methods, 2nd edn. Wiley, New York
Ivanova A, Berger VW (2001) Drawbacks to integer scoring for ordered categorical data. Biometrics 57:567–570
Larocque D, Randles RH (2008) Confidence intervals for a discrete population median. Am Stat 62:32–39
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
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
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
Neuhäuser M (2005) Efficiency comparisons of rank and permutation tests (letter to the editor). Stat Med 24:1777–1778
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
Neuhäuser M, Boes T, Jöckel KH (2007) Pseudo-precision in gene expression values can reduce efficiency. Methods Inf Med 46:538–541
Putter J (1955) The treatment of ties in some nonparametric tests. Ann Math Stat 26:368–386
Randles RH (2001) On neutral responses (zeros) in the sign test and ties in the Wilcoxon–Mann–Whitney test. Am Stat 55:96–101
Rayner JCW, Best DJ (1999) Modelling ties in the sign test. Biometrics 55:663–665
Senn S (2007) Drawbacks to noninteger scoring for ordered categorical data. Biometrics 63:296–298
Sokal RR, Rohlf FJ (1995) Biometry, 3rd edn. W.H. Freeman and Company, New York
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
Wittkowski KM (1998) Versions of the sign test in the presence of ties. Biometrics 54:789–791
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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