Abstract
This paper proposes a new and distribution-free test called “Group Contingency” test (GC, for short) for testing two or several independent samples. Compared with traditional nonparametric tests, GC test tends to explore more information based on samples, and it’s location-, scale-, and shapesensitive. The authors conduct some simulation studies comparing GC test with Wilcoxon rank sum test (W), Kolmogorov-Smirnov test (KS) and Wald-Wolfowitz runs test (WW) for two sample case, and with Kruskal-Wallis (KW) for testing several samples. Simulation results reveal that GC test usually outperforms other methods.
Similar content being viewed by others
References
Erich L. Lehmann, Parametric versus nonparametrics: Two alternative methodologies, Journal of Nonparametric Statistics, 2009, 21(4): 397–405.
M. Hollander and D. A. Wolfe, Nonparametric Statistical Methods, 2nd ed., Wiley, New York, 1999.
P. Sprent and N. C. Smeeton, Applied Nonparametric Statistical Methods, 3rd edition, Chapman and Hall/CRC, Boca Raton, Florida, 2001.
A. Wald and J. Wolfowitz, On a test whether two samples are from the same population, Ann. Math. Stat., 1940, 11(2): 147–162.
C. R. Mehta and Nitin R. Patel, A network algorithm for performing fisher’s exact test in ⊙ × ⊙ contingency table test, Journal of the American Statistical Association, 1983, 78(382): 427–434.
G. J. Gan, C. Q. Ma, and J. H. Wu, Data Clustering: Theory, Algorithms, and Applications, SIAM, Society for Industrial and Applied Mathematics, 2007.
J. B. MacQueen, Some methods for classification and analysis of multivariate observations, Proceedings of 5-th Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, University of California Press, 1967.
C. R. Magela and S. H. Wibowo, Comparing the powers of the Wald-Wolfowitz and Kolmogorov-Smirnov tests, Biometrical Journal, 1997, 39(6): 665–675.
J. M. Chambers, Software for Data Analysis: Programming with R (Statistics and Computing), Springer, 2008.
Author information
Authors and Affiliations
Corresponding author
Additional information
This research is supported by the National Natural Science Foundation of China under Grant No. 10731010 and Ph.D. Program Foundation of Ministry of Education of China under Grant No. 20090001110005.
This paper was recommended for publication by Editor Guohua ZOU.
Rights and permissions
About this article
Cite this article
Zhang, H., Fang, X. & Ma, X. Group contingency test for two or several independent samples. J Syst Sci Complex 24, 1183–1192 (2011). https://doi.org/10.1007/s11424-011-9211-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11424-011-9211-0